id	sid	tid	token	lemma	pos
american_scientific_journal-3703	1	1	110	110	NUM
american_scientific_journal-3703	1	2	american	american	ADJ
american_scientific_journal-3703	1	3	scientific	scientific	ADJ
american_scientific_journal-3703	1	4	research	research	NOUN
american_scientific_journal-3703	1	5	journal	journal	NOUN
american_scientific_journal-3703	1	6	for	for	ADP
american_scientific_journal-3703	1	7	engineering	engineering	NOUN
american_scientific_journal-3703	1	8	,	,	PUNCT
american_scientific_journal-3703	1	9	technology	technology	NOUN
american_scientific_journal-3703	1	10	,	,	PUNCT
american_scientific_journal-3703	1	11	and	and	CCONJ
american_scientific_journal-3703	1	12	sciences	science	NOUN
american_scientific_journal-3703	1	13	(	(	PUNCT
american_scientific_journal-3703	1	14	asrjets	asrjet	NOUN
american_scientific_journal-3703	1	15	)	)	PUNCT
american_scientific_journal-3703	1	16	issn	issn	PROPN
american_scientific_journal-3703	1	17	(	(	PUNCT
american_scientific_journal-3703	1	18	print	print	NOUN
american_scientific_journal-3703	1	19	)	)	PUNCT
american_scientific_journal-3703	1	20	2313	2313	NUM
american_scientific_journal-3703	1	21	-	-	SYM
american_scientific_journal-3703	1	22	4410	4410	NUM
american_scientific_journal-3703	1	23	,	,	PUNCT
american_scientific_journal-3703	1	24	issn	issn	PROPN
american_scientific_journal-3703	1	25	(	(	PUNCT
american_scientific_journal-3703	1	26	online	online	ADJ
american_scientific_journal-3703	1	27	)	)	PUNCT
american_scientific_journal-3703	1	28	2313	2313	NUM
american_scientific_journal-3703	1	29	-	-	SYM
american_scientific_journal-3703	1	30	4402	4402	NUM
american_scientific_journal-3703	1	31	©	©	PROPN
american_scientific_journal-3703	1	32	global	global	ADJ
american_scientific_journal-3703	1	33	society	society	NOUN
american_scientific_journal-3703	1	34	of	of	ADP
american_scientific_journal-3703	1	35	scientific	scientific	ADJ
american_scientific_journal-3703	1	36	research	research	NOUN
american_scientific_journal-3703	1	37	and	and	CCONJ
american_scientific_journal-3703	1	38	researchers	researcher	NOUN
american_scientific_journal-3703	1	39	http://asrjetsjournal.org/	http://asrjetsjournal.org/	VERB
american_scientific_journal-3703	1	40	several	several	ADJ
american_scientific_journal-3703	1	41	chaotic	chaotic	ADJ
american_scientific_journal-3703	1	42	approaches	approach	NOUN
american_scientific_journal-3703	1	43	of	of	ADP
american_scientific_journal-3703	1	44	one	one	NUM
american_scientific_journal-3703	1	45	dimensional	dimensional	ADJ
american_scientific_journal-3703	1	46	doubling	doubling	NOUN
american_scientific_journal-3703	1	47	map	map	NOUN
american_scientific_journal-3703	1	48	md	md	PROPN
american_scientific_journal-3703	1	49	.	.	PUNCT
american_scientific_journal-3703	2	1	zakir	zakir	PROPN
american_scientific_journal-3703	2	2	hosena	hosena	PROPN
american_scientific_journal-3703	2	3	*	*	PROPN
american_scientific_journal-3703	2	4	,	,	PUNCT
american_scientific_journal-3703	2	5	md	md	PROPN
american_scientific_journal-3703	2	6	.	.	PUNCT
american_scientific_journal-3703	2	7	mohiuddin	mohiuddin	NOUN
american_scientific_journal-3703	2	8	zillub	zillub	NOUN
american_scientific_journal-3703	2	9	,	,	PUNCT
american_scientific_journal-3703	2	10	payer	payer	NOUN
american_scientific_journal-3703	2	11	ahmedc	ahmedc	PROPN
american_scientific_journal-3703	2	12	alecturer	alecturer	PROPN
american_scientific_journal-3703	2	13	,	,	PUNCT
american_scientific_journal-3703	2	14	department	department	NOUN
american_scientific_journal-3703	2	15	of	of	ADP
american_scientific_journal-3703	2	16	mathematics	mathematics	PROPN
american_scientific_journal-3703	2	17	,	,	PUNCT
american_scientific_journal-3703	2	18	jagannath	jagannath	PROPN
american_scientific_journal-3703	2	19	university	university	PROPN
american_scientific_journal-3703	2	20	,	,	PUNCT
american_scientific_journal-3703	2	21	dhaka-1100	dhaka-1100	VERB
american_scientific_journal-3703	2	22	,	,	PUNCT
american_scientific_journal-3703	2	23	bangladesh	bangladesh	NOUN
american_scientific_journal-3703	2	24	blecturer	blecturer	NOUN
american_scientific_journal-3703	2	25	,	,	PUNCT
american_scientific_journal-3703	2	26	department	department	NOUN
american_scientific_journal-3703	2	27	of	of	ADP
american_scientific_journal-3703	2	28	mathematics	mathematics	PROPN
american_scientific_journal-3703	2	29	,	,	PUNCT
american_scientific_journal-3703	2	30	european	european	PROPN
american_scientific_journal-3703	2	31	university	university	PROPN
american_scientific_journal-3703	2	32	of	of	ADP
american_scientific_journal-3703	2	33	bangladesh	bangladesh	PROPN
american_scientific_journal-3703	2	34	,	,	PUNCT
american_scientific_journal-3703	2	35	dhaka1216	dhaka1216	PROPN
american_scientific_journal-3703	2	36	,	,	PUNCT
american_scientific_journal-3703	2	37	bangladesh	bangladesh	NOUN
american_scientific_journal-3703	2	38	cprofessor	cprofessor	NOUN
american_scientific_journal-3703	2	39	,	,	PUNCT
american_scientific_journal-3703	2	40	department	department	NOUN
american_scientific_journal-3703	2	41	of	of	ADP
american_scientific_journal-3703	2	42	mathematics	mathematics	PROPN
american_scientific_journal-3703	2	43	,	,	PUNCT
american_scientific_journal-3703	2	44	jagannath	jagannath	PROPN
american_scientific_journal-3703	2	45	university	university	PROPN
american_scientific_journal-3703	2	46	,	,	PUNCT
american_scientific_journal-3703	2	47	dhaka-1100	dhaka-1100	VERB
american_scientific_journal-3703	2	48	,	,	PUNCT
american_scientific_journal-3703	3	1	bangladesh	bangladesh	NOUN
american_scientific_journal-3703	3	2	aemail	aemail	NOUN
american_scientific_journal-3703	3	3	:	:	PUNCT
american_scientific_journal-3703	3	4	zakirhosen2008@gmail.com	zakirhosen2008@gmail.com	X
american_scientific_journal-3703	3	5	bemail	bemail	NOUN
american_scientific_journal-3703	3	6	:	:	PUNCT
american_scientific_journal-3703	3	7	zillujnu123@gmail.com	zillujnu123@gmail.com	X
american_scientific_journal-3703	3	8	cemail	cemail	NOUN
american_scientific_journal-3703	3	9	:	:	PUNCT
american_scientific_journal-3703	4	1	dr.payerahmed@yahoo.com	dr.payerahmed@yahoo.com	X
american_scientific_journal-3703	4	2	abstract	abstract	NOUN
american_scientific_journal-3703	4	3	in	in	ADP
american_scientific_journal-3703	4	4	this	this	DET
american_scientific_journal-3703	4	5	paper	paper	NOUN
american_scientific_journal-3703	4	6	,	,	PUNCT
american_scientific_journal-3703	4	7	we	we	PRON
american_scientific_journal-3703	4	8	study	study	VERB
american_scientific_journal-3703	4	9	basic	basic	ADJ
american_scientific_journal-3703	4	10	dynamical	dynamical	ADJ
american_scientific_journal-3703	4	11	behavior	behavior	NOUN
american_scientific_journal-3703	4	12	of	of	ADP
american_scientific_journal-3703	4	13	one	one	NUM
american_scientific_journal-3703	4	14	-	-	PUNCT
american_scientific_journal-3703	4	15	dimensional	dimensional	ADJ
american_scientific_journal-3703	4	16	doubling	doubling	NOUN
american_scientific_journal-3703	4	17	map	map	NOUN
american_scientific_journal-3703	4	18	.	.	PUNCT
american_scientific_journal-3703	5	1	especially	especially	ADV
american_scientific_journal-3703	5	2	emphasis	emphasis	NOUN
american_scientific_journal-3703	5	3	is	be	AUX
american_scientific_journal-3703	5	4	given	give	VERB
american_scientific_journal-3703	5	5	on	on	ADP
american_scientific_journal-3703	5	6	the	the	DET
american_scientific_journal-3703	5	7	chaotic	chaotic	ADJ
american_scientific_journal-3703	5	8	behaviors	behavior	NOUN
american_scientific_journal-3703	5	9	of	of	ADP
american_scientific_journal-3703	5	10	the	the	DET
american_scientific_journal-3703	5	11	said	say	VERB
american_scientific_journal-3703	5	12	map	map	NOUN
american_scientific_journal-3703	5	13	.	.	PUNCT
american_scientific_journal-3703	6	1	several	several	ADJ
american_scientific_journal-3703	6	2	approaches	approach	NOUN
american_scientific_journal-3703	6	3	of	of	ADP
american_scientific_journal-3703	6	4	chaotic	chaotic	ADJ
american_scientific_journal-3703	6	5	behaviors	behavior	NOUN
american_scientific_journal-3703	6	6	by	by	ADP
american_scientific_journal-3703	6	7	some	some	DET
american_scientific_journal-3703	6	8	pioneers	pioneer	NOUN
american_scientific_journal-3703	6	9	it	it	PRON
american_scientific_journal-3703	6	10	is	be	AUX
american_scientific_journal-3703	6	11	found	find	VERB
american_scientific_journal-3703	6	12	that	that	SCONJ
american_scientific_journal-3703	6	13	the	the	DET
american_scientific_journal-3703	6	14	doubling	double	VERB
american_scientific_journal-3703	6	15	map	map	NOUN
american_scientific_journal-3703	6	16	is	be	AUX
american_scientific_journal-3703	6	17	chaotic	chaotic	ADJ
american_scientific_journal-3703	6	18	in	in	ADP
american_scientific_journal-3703	6	19	different	different	ADJ
american_scientific_journal-3703	6	20	senses	sense	NOUN
american_scientific_journal-3703	6	21	.	.	PUNCT
american_scientific_journal-3703	7	1	we	we	PRON
american_scientific_journal-3703	7	2	mainly	mainly	ADV
american_scientific_journal-3703	7	3	focused	focus	VERB
american_scientific_journal-3703	7	4	on	on	ADP
american_scientific_journal-3703	7	5	orbit	orbit	NOUN
american_scientific_journal-3703	7	6	analysis	analysis	NOUN
american_scientific_journal-3703	7	7	,	,	PUNCT
american_scientific_journal-3703	7	8	sensitivity	sensitivity	NOUN
american_scientific_journal-3703	7	9	to	to	ADP
american_scientific_journal-3703	7	10	initial	initial	ADJ
american_scientific_journal-3703	7	11	conditions	condition	NOUN
american_scientific_journal-3703	7	12	,	,	PUNCT
american_scientific_journal-3703	7	13	sensitivity	sensitivity	NOUN
american_scientific_journal-3703	7	14	to	to	ADP
american_scientific_journal-3703	7	15	numerical	numerical	ADJ
american_scientific_journal-3703	7	16	inaccuracies	inaccuracy	NOUN
american_scientific_journal-3703	7	17	,	,	PUNCT
american_scientific_journal-3703	7	18	trajectories	trajectory	NOUN
american_scientific_journal-3703	7	19	and	and	CCONJ
american_scientific_journal-3703	7	20	staircase	staircase	NOUN
american_scientific_journal-3703	7	21	diagram	diagram	NOUN
american_scientific_journal-3703	7	22	of	of	ADP
american_scientific_journal-3703	7	23	the	the	DET
american_scientific_journal-3703	7	24	doubling	double	VERB
american_scientific_journal-3703	7	25	map	map	NOUN
american_scientific_journal-3703	7	26	.	.	PUNCT
american_scientific_journal-3703	8	1	the	the	DET
american_scientific_journal-3703	8	2	graphical	graphical	ADJ
american_scientific_journal-3703	8	3	representations	representation	NOUN
american_scientific_journal-3703	8	4	show	show	VERB
american_scientific_journal-3703	8	5	that	that	SCONJ
american_scientific_journal-3703	8	6	this	this	DET
american_scientific_journal-3703	8	7	map	map	NOUN
american_scientific_journal-3703	8	8	is	be	AUX
american_scientific_journal-3703	8	9	chaotic	chaotic	ADJ
american_scientific_journal-3703	8	10	in	in	ADP
american_scientific_journal-3703	8	11	different	different	ADJ
american_scientific_journal-3703	8	12	senses	sense	NOUN
american_scientific_journal-3703	8	13	.	.	PUNCT
american_scientific_journal-3703	9	1	the	the	DET
american_scientific_journal-3703	9	2	behavior	behavior	NOUN
american_scientific_journal-3703	9	3	of	of	ADP
american_scientific_journal-3703	9	4	the	the	DET
american_scientific_journal-3703	9	5	said	say	VERB
american_scientific_journal-3703	9	6	map	map	NOUN
american_scientific_journal-3703	9	7	is	be	AUX
american_scientific_journal-3703	9	8	found	find	VERB
american_scientific_journal-3703	9	9	irregular	irregular	ADJ
american_scientific_journal-3703	9	10	,	,	PUNCT
american_scientific_journal-3703	9	11	that	that	ADV
american_scientific_journal-3703	9	12	is	is	ADV
american_scientific_journal-3703	9	13	,	,	PUNCT
american_scientific_journal-3703	9	14	chaotic	chaotic	ADJ
american_scientific_journal-3703	9	15	.	.	PUNCT
american_scientific_journal-3703	10	1	keywords	keyword	NOUN
american_scientific_journal-3703	10	2	:	:	PUNCT
american_scientific_journal-3703	10	3	approaches	approach	NOUN
american_scientific_journal-3703	10	4	;	;	PUNCT
american_scientific_journal-3703	10	5	orbit	orbit	NOUN
american_scientific_journal-3703	10	6	;	;	PUNCT
american_scientific_journal-3703	10	7	sensitivity	sensitivity	NOUN
american_scientific_journal-3703	10	8	;	;	PUNCT
american_scientific_journal-3703	10	9	staircase	staircase	NOUN
american_scientific_journal-3703	10	10	diagram	diagram	NOUN
american_scientific_journal-3703	10	11	;	;	PUNCT
american_scientific_journal-3703	10	12	trajectories	trajectory	NOUN
american_scientific_journal-3703	10	13	;	;	PUNCT
american_scientific_journal-3703	10	14	transitivity	transitivity	NOUN
american_scientific_journal-3703	10	15	.	.	PUNCT
american_scientific_journal-3703	11	1	1	1	X
american_scientific_journal-3703	11	2	.	.	X
american_scientific_journal-3703	11	3	introduction	introduction	NOUN
american_scientific_journal-3703	11	4	dynamical	dynamical	ADJ
american_scientific_journal-3703	11	5	systems	system	NOUN
american_scientific_journal-3703	11	6	is	be	AUX
american_scientific_journal-3703	11	7	a	a	DET
american_scientific_journal-3703	11	8	branch	branch	NOUN
american_scientific_journal-3703	11	9	of	of	ADP
american_scientific_journal-3703	11	10	mathematics	mathematic	NOUN
american_scientific_journal-3703	11	11	that	that	PRON
american_scientific_journal-3703	11	12	attempts	attempt	VERB
american_scientific_journal-3703	11	13	to	to	PART
american_scientific_journal-3703	11	14	understand	understand	VERB
american_scientific_journal-3703	11	15	processes	process	NOUN
american_scientific_journal-3703	11	16	in	in	ADP
american_scientific_journal-3703	11	17	motion	motion	NOUN
american_scientific_journal-3703	11	18	.	.	PUNCT
american_scientific_journal-3703	12	1	there	there	PRON
american_scientific_journal-3703	12	2	are	be	VERB
american_scientific_journal-3703	12	3	many	many	ADJ
american_scientific_journal-3703	12	4	branches	branch	NOUN
american_scientific_journal-3703	12	5	of	of	ADP
american_scientific_journal-3703	12	6	dynamical	dynamical	ADJ
american_scientific_journal-3703	12	7	systems	system	NOUN
american_scientific_journal-3703	12	8	but	but	CCONJ
american_scientific_journal-3703	12	9	chaos	chaos	NOUN
american_scientific_journal-3703	12	10	is	be	AUX
american_scientific_journal-3703	12	11	one	one	NUM
american_scientific_journal-3703	12	12	of	of	ADP
american_scientific_journal-3703	12	13	them	they	PRON
american_scientific_journal-3703	12	14	and	and	CCONJ
american_scientific_journal-3703	12	15	it	it	PRON
american_scientific_journal-3703	12	16	explains	explain	VERB
american_scientific_journal-3703	12	17	how	how	SCONJ
american_scientific_journal-3703	12	18	very	very	ADV
american_scientific_journal-3703	12	19	small	small	ADJ
american_scientific_journal-3703	12	20	changes	change	NOUN
american_scientific_journal-3703	12	21	in	in	ADP
american_scientific_journal-3703	12	22	the	the	DET
american_scientific_journal-3703	12	23	initial	initial	ADJ
american_scientific_journal-3703	12	24	configuration	configuration	NOUN
american_scientific_journal-3703	12	25	of	of	ADP
american_scientific_journal-3703	12	26	a	a	DET
american_scientific_journal-3703	12	27	system	system	NOUN
american_scientific_journal-3703	12	28	model	model	NOUN
american_scientific_journal-3703	12	29	may	may	AUX
american_scientific_journal-3703	12	30	lead	lead	VERB
american_scientific_journal-3703	12	31	great	great	ADJ
american_scientific_journal-3703	12	32	discrepancies	discrepancy	NOUN
american_scientific_journal-3703	12	33	over	over	ADP
american_scientific_journal-3703	12	34	time	time	NOUN
american_scientific_journal-3703	12	35	.	.	PUNCT
american_scientific_journal-3703	13	1	called	call	VERB
american_scientific_journal-3703	13	2	‘	'	PUNCT
american_scientific_journal-3703	13	3	butterfly	butterfly	NOUN
american_scientific_journal-3703	13	4	effect	effect	NOUN
american_scientific_journal-3703	13	5	’	'	PUNCT
american_scientific_journal-3703	13	6	,	,	PUNCT
american_scientific_journal-3703	13	7	this	this	DET
american_scientific_journal-3703	13	8	phenomena	phenomena	NOUN
american_scientific_journal-3703	13	9	accounts	account	VERB
american_scientific_journal-3703	13	10	our	our	PRON
american_scientific_journal-3703	13	11	accurate	accurate	ADJ
american_scientific_journal-3703	13	12	prediction	prediction	NOUN
american_scientific_journal-3703	13	13	for	for	ADP
american_scientific_journal-3703	13	14	a	a	DET
american_scientific_journal-3703	13	15	long	long	ADJ
american_scientific_journal-3703	13	16	period	period	NOUN
american_scientific_journal-3703	13	17	of	of	ADP
american_scientific_journal-3703	13	18	time	time	NOUN
american_scientific_journal-3703	13	19	.	.	PUNCT
american_scientific_journal-3703	14	1	a	a	DET
american_scientific_journal-3703	14	2	dictionary	dictionary	ADJ
american_scientific_journal-3703	14	3	definition	definition	NOUN
american_scientific_journal-3703	14	4	of	of	ADP
american_scientific_journal-3703	14	5	chaos	chaos	NOUN
american_scientific_journal-3703	14	6	is	be	AUX
american_scientific_journal-3703	14	7	a	a	DET
american_scientific_journal-3703	14	8	‘	'	PUNCT
american_scientific_journal-3703	14	9	disordered	disordered	ADJ
american_scientific_journal-3703	14	10	state	state	NOUN
american_scientific_journal-3703	14	11	of	of	ADP
american_scientific_journal-3703	14	12	collection	collection	NOUN
american_scientific_journal-3703	14	13	;	;	PUNCT
american_scientific_journal-3703	14	14	a	a	DET
american_scientific_journal-3703	14	15	confused	confused	ADJ
american_scientific_journal-3703	14	16	mixture	mixture	NOUN
american_scientific_journal-3703	14	17	.	.	PUNCT
american_scientific_journal-3703	14	18	’	'	PUNCT
american_scientific_journal-3703	15	1	with	with	ADP
american_scientific_journal-3703	15	2	the	the	DET
american_scientific_journal-3703	15	3	advancement	advancement	NOUN
american_scientific_journal-3703	15	4	of	of	ADP
american_scientific_journal-3703	15	5	chaos	chaos	NOUN
american_scientific_journal-3703	15	6	research	research	NOUN
american_scientific_journal-3703	15	7	,	,	PUNCT
american_scientific_journal-3703	15	8	more	more	ADJ
american_scientific_journal-3703	15	9	and	and	CCONJ
american_scientific_journal-3703	15	10	more	more	ADJ
american_scientific_journal-3703	15	11	chaos	chaos	NOUN
american_scientific_journal-3703	15	12	phenomena	phenomenon	NOUN
american_scientific_journal-3703	15	13	have	have	AUX
american_scientific_journal-3703	15	14	been	be	AUX
american_scientific_journal-3703	15	15	discovered	discover	VERB
american_scientific_journal-3703	15	16	in	in	ADP
american_scientific_journal-3703	15	17	the	the	DET
american_scientific_journal-3703	15	18	mathematics	mathematic	NOUN
american_scientific_journal-3703	15	19	,	,	PUNCT
american_scientific_journal-3703	15	20	engineering	engineering	NOUN
american_scientific_journal-3703	15	21	and	and	CCONJ
american_scientific_journal-3703	15	22	other	other	ADJ
american_scientific_journal-3703	15	23	fields	field	NOUN
american_scientific_journal-3703	15	24	.	.	PUNCT
american_scientific_journal-3703	16	1	many	many	ADJ
american_scientific_journal-3703	16	2	researchers	researcher	NOUN
american_scientific_journal-3703	16	3	have	have	AUX
american_scientific_journal-3703	16	4	focused	focus	VERB
american_scientific_journal-3703	16	5	on	on	ADP
american_scientific_journal-3703	16	6	the	the	DET
american_scientific_journal-3703	16	7	demonstration	demonstration	NOUN
american_scientific_journal-3703	16	8	of	of	ADP
american_scientific_journal-3703	16	9	chaos	chaos	NOUN
american_scientific_journal-3703	16	10	phenomena	phenomenon	NOUN
american_scientific_journal-3703	16	11	using	use	VERB
american_scientific_journal-3703	16	12	simulation	simulation	NOUN
american_scientific_journal-3703	16	13	.	.	PUNCT
american_scientific_journal-3703	17	1	-----------------------------------------------------------------------	-----------------------------------------------------------------------	PUNCT
american_scientific_journal-3703	18	1	*	*	PUNCT
american_scientific_journal-3703	18	2	corresponding	correspond	VERB
american_scientific_journal-3703	18	3	author	author	NOUN
american_scientific_journal-3703	18	4	.	.	PUNCT
american_scientific_journal-3703	19	1	http://asrjetsjournal.org/	http://asrjetsjournal.org/	PROPN
american_scientific_journal-3703	19	2	american	american	PROPN
american_scientific_journal-3703	19	3	scientific	scientific	PROPN
american_scientific_journal-3703	19	4	research	research	NOUN
american_scientific_journal-3703	19	5	journal	journal	NOUN
american_scientific_journal-3703	19	6	for	for	ADP
american_scientific_journal-3703	19	7	engineering	engineering	NOUN
american_scientific_journal-3703	19	8	,	,	PUNCT
american_scientific_journal-3703	19	9	technology	technology	NOUN
american_scientific_journal-3703	19	10	,	,	PUNCT
american_scientific_journal-3703	19	11	and	and	CCONJ
american_scientific_journal-3703	19	12	sciences	science	NOUN
american_scientific_journal-3703	19	13	(	(	PUNCT
american_scientific_journal-3703	19	14	asrjets	asrjet	NOUN
american_scientific_journal-3703	19	15	)	)	PUNCT
american_scientific_journal-3703	19	16	(	(	PUNCT
american_scientific_journal-3703	19	17	2018	2018	NUM
american_scientific_journal-3703	19	18	)	)	PUNCT
american_scientific_journal-3703	19	19	volume	volume	NOUN
american_scientific_journal-3703	19	20	43	43	NUM
american_scientific_journal-3703	19	21	,	,	PUNCT
american_scientific_journal-3703	19	22	no	no	DET
american_scientific_journal-3703	19	23	1	1	NUM
american_scientific_journal-3703	19	24	,	,	PUNCT
american_scientific_journal-3703	19	25	pp	pp	ADV
american_scientific_journal-3703	19	26	110	110	NUM
american_scientific_journal-3703	19	27	-	-	SYM
american_scientific_journal-3703	19	28	133	133	NUM
american_scientific_journal-3703	19	29	111	111	NUM
american_scientific_journal-3703	19	30	the	the	DET
american_scientific_journal-3703	19	31	graphical	graphical	ADJ
american_scientific_journal-3703	19	32	analysis	analysis	NOUN
american_scientific_journal-3703	19	33	of	of	ADP
american_scientific_journal-3703	19	34	the	the	DET
american_scientific_journal-3703	19	35	doubling	double	VERB
american_scientific_journal-3703	19	36	map	map	NOUN
american_scientific_journal-3703	19	37	significantly	significantly	ADV
american_scientific_journal-3703	19	38	has	have	AUX
american_scientific_journal-3703	19	39	contributed	contribute	VERB
american_scientific_journal-3703	19	40	to	to	ADP
american_scientific_journal-3703	19	41	our	our	PRON
american_scientific_journal-3703	19	42	understanding	understanding	NOUN
american_scientific_journal-3703	19	43	of	of	ADP
american_scientific_journal-3703	19	44	the	the	DET
american_scientific_journal-3703	19	45	essence	essence	NOUN
american_scientific_journal-3703	19	46	of	of	ADP
american_scientific_journal-3703	19	47	chaos	chaos	NOUN
american_scientific_journal-3703	19	48	.	.	PUNCT
american_scientific_journal-3703	20	1	the	the	DET
american_scientific_journal-3703	20	2	use	use	NOUN
american_scientific_journal-3703	20	3	of	of	ADP
american_scientific_journal-3703	20	4	the	the	DET
american_scientific_journal-3703	20	5	term	term	NOUN
american_scientific_journal-3703	20	6	“	"	PUNCT
american_scientific_journal-3703	20	7	chaos	chaos	NOUN
american_scientific_journal-3703	20	8	”	"	PUNCT
american_scientific_journal-3703	20	9	was	be	AUX
american_scientific_journal-3703	20	10	first	first	ADV
american_scientific_journal-3703	20	11	introduced	introduce	VERB
american_scientific_journal-3703	20	12	into	into	ADP
american_scientific_journal-3703	20	13	dynamical	dynamical	ADJ
american_scientific_journal-3703	20	14	systems	system	NOUN
american_scientific_journal-3703	20	15	by	by	ADP
american_scientific_journal-3703	20	16	li	li	PROPN
american_scientific_journal-3703	20	17	and	and	CCONJ
american_scientific_journal-3703	20	18	yorke	yorke	PROPN
american_scientific_journal-3703	21	1	[	[	X
american_scientific_journal-3703	21	2	7	7	NUM
american_scientific_journal-3703	21	3	]	]	PUNCT
american_scientific_journal-3703	21	4	for	for	ADP
american_scientific_journal-3703	21	5	a	a	DET
american_scientific_journal-3703	21	6	map	map	NOUN
american_scientific_journal-3703	21	7	on	on	ADP
american_scientific_journal-3703	21	8	a	a	DET
american_scientific_journal-3703	21	9	compact	compact	ADJ
american_scientific_journal-3703	21	10	interval	interval	NOUN
american_scientific_journal-3703	21	11	.	.	PUNCT
american_scientific_journal-3703	22	1	another	another	DET
american_scientific_journal-3703	22	2	explicit	explicit	ADJ
american_scientific_journal-3703	22	3	definition	definition	NOUN
american_scientific_journal-3703	22	4	of	of	ADP
american_scientific_journal-3703	22	5	chaos	chaos	NOUN
american_scientific_journal-3703	22	6	belongs	belong	VERB
american_scientific_journal-3703	22	7	to	to	ADP
american_scientific_journal-3703	22	8	devaney	devaney	PROPN
american_scientific_journal-3703	22	9	[	[	X
american_scientific_journal-3703	22	10	11	11	NUM
american_scientific_journal-3703	22	11	]	]	PUNCT
american_scientific_journal-3703	22	12	.	.	PUNCT
american_scientific_journal-3703	23	1	then	then	ADV
american_scientific_journal-3703	23	2	robinson	robinson	PROPN
american_scientific_journal-3703	23	3	gave	give	VERB
american_scientific_journal-3703	23	4	a	a	DET
american_scientific_journal-3703	23	5	refined	refined	ADJ
american_scientific_journal-3703	23	6	definition	definition	NOUN
american_scientific_journal-3703	23	7	[	[	X
american_scientific_journal-3703	23	8	1	1	NUM
american_scientific_journal-3703	23	9	]	]	PUNCT
american_scientific_journal-3703	23	10	.	.	PUNCT
american_scientific_journal-3703	24	1	the	the	DET
american_scientific_journal-3703	24	2	remarkable	remarkable	ADJ
american_scientific_journal-3703	24	3	feature	feature	NOUN
american_scientific_journal-3703	24	4	of	of	ADP
american_scientific_journal-3703	24	5	the	the	DET
american_scientific_journal-3703	24	6	doubling	double	VERB
american_scientific_journal-3703	24	7	map	map	NOUN
american_scientific_journal-3703	24	8	is	be	AUX
american_scientific_journal-3703	24	9	in	in	ADP
american_scientific_journal-3703	24	10	the	the	DET
american_scientific_journal-3703	24	11	simplicity	simplicity	NOUN
american_scientific_journal-3703	24	12	of	of	ADP
american_scientific_journal-3703	24	13	its	its	PRON
american_scientific_journal-3703	24	14	form	form	NOUN
american_scientific_journal-3703	24	15	and	and	CCONJ
american_scientific_journal-3703	24	16	the	the	DET
american_scientific_journal-3703	24	17	complexity	complexity	NOUN
american_scientific_journal-3703	24	18	of	of	ADP
american_scientific_journal-3703	24	19	its	its	PRON
american_scientific_journal-3703	24	20	dynamics	dynamic	NOUN
american_scientific_journal-3703	24	21	.	.	PUNCT
american_scientific_journal-3703	25	1	it	it	PRON
american_scientific_journal-3703	25	2	is	be	AUX
american_scientific_journal-3703	25	3	the	the	DET
american_scientific_journal-3703	25	4	simplest	simple	ADJ
american_scientific_journal-3703	25	5	model	model	NOUN
american_scientific_journal-3703	25	6	that	that	PRON
american_scientific_journal-3703	25	7	shows	show	VERB
american_scientific_journal-3703	25	8	chaos	chaos	NOUN
american_scientific_journal-3703	25	9	.	.	PUNCT
american_scientific_journal-3703	26	1	the	the	DET
american_scientific_journal-3703	26	2	doubling	double	VERB
american_scientific_journal-3703	26	3	map	map	NOUN
american_scientific_journal-3703	26	4	(	(	PUNCT
american_scientific_journal-3703	26	5	)	)	PUNCT
american_scientific_journal-3703	26	6	2	2	NUM
american_scientific_journal-3703	26	7	if	if	SCONJ
american_scientific_journal-3703	26	8	0	0	NUM
american_scientific_journal-3703	26	9	<	<	X
american_scientific_journal-3703	26	10	0.5	0.5	NUM
american_scientific_journal-3703	26	11	2	2	NUM
american_scientific_journal-3703	26	12	1	1	NUM
american_scientific_journal-3703	26	13	if	if	SCONJ
american_scientific_journal-3703	26	14	0.5	0.5	NUM
american_scientific_journal-3703	26	15	<	<	X
american_scientific_journal-3703	26	16	1	1	NUM
american_scientific_journal-3703	26	17	.	.	PUNCT
american_scientific_journal-3703	26	18	x	x	SYM
american_scientific_journal-3703	27	1	x	x	PUNCT
american_scientific_journal-3703	27	2	d	d	NOUN
american_scientific_journal-3703	27	3	x	x	X
american_scientific_journal-3703	27	4	x	x	PUNCT
american_scientific_journal-3703	27	5	x	x	NOUN
american_scientific_journal-3703	27	6	≤	≤	NOUN
american_scientific_journal-3703	27	7	=	=	PUNCT
american_scientific_journal-3703	27	8			PRON
american_scientific_journal-3703	27	9	−	−	NOUN
american_scientific_journal-3703	27	10	≤	≤	NOUN
american_scientific_journal-3703	27	11	is	be	AUX
american_scientific_journal-3703	27	12	very	very	ADV
american_scientific_journal-3703	27	13	interesting	interesting	ADJ
american_scientific_journal-3703	27	14	and	and	CCONJ
american_scientific_journal-3703	27	15	representative	representative	ADJ
american_scientific_journal-3703	27	16	model	model	NOUN
american_scientific_journal-3703	27	17	of	of	ADP
american_scientific_journal-3703	27	18	dynamical	dynamical	ADJ
american_scientific_journal-3703	27	19	systems	system	NOUN
american_scientific_journal-3703	27	20	.	.	PUNCT
american_scientific_journal-3703	28	1	the	the	DET
american_scientific_journal-3703	28	2	dynamical	dynamical	ADJ
american_scientific_journal-3703	28	3	behavior	behavior	NOUN
american_scientific_journal-3703	28	4	of	of	ADP
american_scientific_journal-3703	28	5	the	the	DET
american_scientific_journal-3703	28	6	doubling	double	VERB
american_scientific_journal-3703	28	7	map	map	NOUN
american_scientific_journal-3703	28	8	is	be	AUX
american_scientific_journal-3703	28	9	very	very	ADV
american_scientific_journal-3703	28	10	complicated	complicated	ADJ
american_scientific_journal-3703	28	11	.	.	PUNCT
american_scientific_journal-3703	29	1	we	we	PRON
american_scientific_journal-3703	29	2	have	have	AUX
american_scientific_journal-3703	29	3	shown	show	VERB
american_scientific_journal-3703	29	4	that	that	SCONJ
american_scientific_journal-3703	29	5	doubling	double	VERB
american_scientific_journal-3703	29	6	map	map	NOUN
american_scientific_journal-3703	29	7	is	be	AUX
american_scientific_journal-3703	29	8	chaotic	chaotic	ADJ
american_scientific_journal-3703	29	9	in	in	ADP
american_scientific_journal-3703	29	10	the	the	DET
american_scientific_journal-3703	29	11	sense	sense	NOUN
american_scientific_journal-3703	29	12	of	of	ADP
american_scientific_journal-3703	29	13	devaney	devaney	PROPN
american_scientific_journal-3703	29	14	,	,	PUNCT
american_scientific_journal-3703	29	15	li	li	PROPN
american_scientific_journal-3703	29	16	-	-	PROPN
american_scientific_journal-3703	29	17	yorke	yorke	PROPN
american_scientific_journal-3703	29	18	,	,	PUNCT
american_scientific_journal-3703	29	19	lyapunov	lyapunov	NOUN
american_scientific_journal-3703	29	20	and	and	CCONJ
american_scientific_journal-3703	29	21	wiggin	wiggin	PROPN
american_scientific_journal-3703	29	22	.	.	PUNCT
american_scientific_journal-3703	30	1	in	in	ADP
american_scientific_journal-3703	30	2	this	this	DET
american_scientific_journal-3703	30	3	paper	paper	NOUN
american_scientific_journal-3703	30	4	,	,	PUNCT
american_scientific_journal-3703	30	5	we	we	PRON
american_scientific_journal-3703	30	6	discussed	discuss	VERB
american_scientific_journal-3703	30	7	chaotic	chaotic	ADJ
american_scientific_journal-3703	30	8	dynamical	dynamical	ADJ
american_scientific_journal-3703	30	9	behavior	behavior	NOUN
american_scientific_journal-3703	30	10	of	of	ADP
american_scientific_journal-3703	30	11	one	one	NUM
american_scientific_journal-3703	30	12	dimensional	dimensional	ADJ
american_scientific_journal-3703	30	13	doubling	doubling	NOUN
american_scientific_journal-3703	30	14	map	map	NOUN
american_scientific_journal-3703	30	15	.	.	PUNCT
american_scientific_journal-3703	31	1	the	the	DET
american_scientific_journal-3703	31	2	doubling	double	VERB
american_scientific_journal-3703	31	3	map	map	NOUN
american_scientific_journal-3703	31	4	is	be	AUX
american_scientific_journal-3703	31	5	topologically	topologically	ADV
american_scientific_journal-3703	31	6	conjugate	conjugate	ADJ
american_scientific_journal-3703	31	7	to	to	ADP
american_scientific_journal-3703	31	8	the	the	DET
american_scientific_journal-3703	31	9	logistic	logistic	ADJ
american_scientific_journal-3703	31	10	map	map	NOUN
american_scientific_journal-3703	31	11	shift	shift	NOUN
american_scientific_journal-3703	31	12	map	map	NOUN
american_scientific_journal-3703	31	13	and	and	CCONJ
american_scientific_journal-3703	31	14	also	also	ADV
american_scientific_journal-3703	31	15	semi	semi	ADJ
american_scientific_journal-3703	31	16	-	-	ADJ
american_scientific_journal-3703	31	17	conjugacy	conjugacy	ADJ
american_scientific_journal-3703	31	18	to	to	ADP
american_scientific_journal-3703	31	19	tent	tent	NOUN
american_scientific_journal-3703	31	20	map	map	NOUN
american_scientific_journal-3703	31	21	.	.	PUNCT
american_scientific_journal-3703	32	1	we	we	PRON
american_scientific_journal-3703	32	2	also	also	ADV
american_scientific_journal-3703	32	3	have	have	AUX
american_scientific_journal-3703	32	4	shown	show	VERB
american_scientific_journal-3703	32	5	that	that	SCONJ
american_scientific_journal-3703	32	6	the	the	DET
american_scientific_journal-3703	32	7	dynamical	dynamical	ADJ
american_scientific_journal-3703	32	8	behavior	behavior	NOUN
american_scientific_journal-3703	32	9	of	of	ADP
american_scientific_journal-3703	32	10	doubling	double	VERB
american_scientific_journal-3703	32	11	map	map	NOUN
american_scientific_journal-3703	32	12	is	be	AUX
american_scientific_journal-3703	32	13	chaotic	chaotic	ADJ
american_scientific_journal-3703	32	14	considering	consider	VERB
american_scientific_journal-3703	32	15	the	the	DET
american_scientific_journal-3703	32	16	initial	initial	ADJ
american_scientific_journal-3703	32	17	seeds	seed	NOUN
american_scientific_journal-3703	32	18	,	,	PUNCT
american_scientific_journal-3703	32	19	orbit	orbit	NOUN
american_scientific_journal-3703	32	20	analysis	analysis	NOUN
american_scientific_journal-3703	32	21	,	,	PUNCT
american_scientific_journal-3703	32	22	sensitivity	sensitivity	NOUN
american_scientific_journal-3703	32	23	to	to	ADP
american_scientific_journal-3703	32	24	initial	initial	ADJ
american_scientific_journal-3703	32	25	conditions	condition	NOUN
american_scientific_journal-3703	32	26	,	,	PUNCT
american_scientific_journal-3703	32	27	sensitivity	sensitivity	NOUN
american_scientific_journal-3703	32	28	to	to	ADP
american_scientific_journal-3703	32	29	numerical	numerical	ADJ
american_scientific_journal-3703	32	30	inaccuracies	inaccuracy	NOUN
american_scientific_journal-3703	32	31	,	,	PUNCT
american_scientific_journal-3703	32	32	trajectories	trajectory	NOUN
american_scientific_journal-3703	32	33	and	and	CCONJ
american_scientific_journal-3703	32	34	staircase	staircase	NOUN
american_scientific_journal-3703	32	35	diagram	diagram	NOUN
american_scientific_journal-3703	32	36	.	.	PUNCT
american_scientific_journal-3703	33	1	these	these	PRON
american_scientific_journal-3703	33	2	are	be	AUX
american_scientific_journal-3703	33	3	the	the	DET
american_scientific_journal-3703	33	4	main	main	ADJ
american_scientific_journal-3703	33	5	results	result	NOUN
american_scientific_journal-3703	33	6	of	of	ADP
american_scientific_journal-3703	33	7	this	this	DET
american_scientific_journal-3703	33	8	article	article	NOUN
american_scientific_journal-3703	33	9	.	.	PUNCT
american_scientific_journal-3703	34	1	2	2	X
american_scientific_journal-3703	34	2	.	.	X
american_scientific_journal-3703	34	3	methodology	methodology	NOUN
american_scientific_journal-3703	34	4	there	there	PRON
american_scientific_journal-3703	34	5	are	be	VERB
american_scientific_journal-3703	34	6	some	some	PRON
american_scientific_journal-3703	34	7	of	of	ADP
american_scientific_journal-3703	34	8	senses	sense	NOUN
american_scientific_journal-3703	34	9	to	to	PART
american_scientific_journal-3703	34	10	analyze	analyze	VERB
american_scientific_journal-3703	34	11	the	the	DET
american_scientific_journal-3703	34	12	chaos	chaos	NOUN
american_scientific_journal-3703	34	13	like	like	ADP
american_scientific_journal-3703	34	14	henri	henri	PROPN
american_scientific_journal-3703	34	15	poincare′	poincare′	PROPN
american_scientific_journal-3703	34	16	,	,	PUNCT
american_scientific_journal-3703	34	17	r.	r.	PROPN
american_scientific_journal-3703	34	18	l.	l.	PROPN
american_scientific_journal-3703	34	19	devaney	devaney	PROPN
american_scientific_journal-3703	34	20	,	,	PUNCT
american_scientific_journal-3703	34	21	li	li	PROPN
american_scientific_journal-3703	34	22	and	and	CCONJ
american_scientific_journal-3703	34	23	yorke	yorke	PROPN
american_scientific_journal-3703	34	24	,	,	PUNCT
american_scientific_journal-3703	34	25	lyapunov	lyapunov	PROPN
american_scientific_journal-3703	34	26	exponent	exponent	NOUN
american_scientific_journal-3703	34	27	,	,	PUNCT
american_scientific_journal-3703	34	28	wiggins	wiggins	PROPN
american_scientific_journal-3703	34	29	etc	etc	X
american_scientific_journal-3703	34	30	.	.	X
american_scientific_journal-3703	35	1	in	in	ADP
american_scientific_journal-3703	35	2	our	our	PRON
american_scientific_journal-3703	35	3	research	research	NOUN
american_scientific_journal-3703	35	4	we	we	PRON
american_scientific_journal-3703	35	5	tried	try	VERB
american_scientific_journal-3703	35	6	to	to	PART
american_scientific_journal-3703	35	7	present	present	VERB
american_scientific_journal-3703	35	8	one	one	NUM
american_scientific_journal-3703	35	9	dimensional	dimensional	ADJ
american_scientific_journal-3703	35	10	doubling	doubling	NOUN
american_scientific_journal-3703	35	11	map	map	NOUN
american_scientific_journal-3703	35	12	in	in	ADP
american_scientific_journal-3703	35	13	the	the	DET
american_scientific_journal-3703	35	14	sense	sense	NOUN
american_scientific_journal-3703	35	15	of	of	ADP
american_scientific_journal-3703	35	16	r.	r.	PROPN
american_scientific_journal-3703	35	17	l.	l.	PROPN
american_scientific_journal-3703	35	18	devaney	devaney	PROPN
american_scientific_journal-3703	35	19	,	,	PUNCT
american_scientific_journal-3703	35	20	li	li	PROPN
american_scientific_journal-3703	35	21	and	and	CCONJ
american_scientific_journal-3703	35	22	yorke	yorke	PROPN
american_scientific_journal-3703	35	23	,	,	PUNCT
american_scientific_journal-3703	35	24	lyapunov	lyapunov	PROPN
american_scientific_journal-3703	35	25	exponent	exponent	NOUN
american_scientific_journal-3703	35	26	,	,	PUNCT
american_scientific_journal-3703	35	27	wiggins	wiggins	PROPN
american_scientific_journal-3703	35	28	etc	etc	X
american_scientific_journal-3703	35	29	.	.	X
american_scientific_journal-3703	36	1	we	we	PRON
american_scientific_journal-3703	36	2	use	use	VERB
american_scientific_journal-3703	36	3	mathematical	mathematical	ADJ
american_scientific_journal-3703	36	4	software	software	NOUN
american_scientific_journal-3703	36	5	’s	’s	PART
american_scientific_journal-3703	36	6	like	like	ADP
american_scientific_journal-3703	36	7	mathematica	mathematica	PROPN
american_scientific_journal-3703	36	8	,	,	PUNCT
american_scientific_journal-3703	36	9	matlab	matlab	PROPN
american_scientific_journal-3703	36	10	to	to	PART
american_scientific_journal-3703	36	11	analyse	analyse	VERB
american_scientific_journal-3703	36	12	the	the	DET
american_scientific_journal-3703	36	13	numerical	numerical	ADJ
american_scientific_journal-3703	36	14	results	result	NOUN
american_scientific_journal-3703	36	15	to	to	PART
american_scientific_journal-3703	36	16	be	be	AUX
american_scientific_journal-3703	36	17	found	find	VERB
american_scientific_journal-3703	36	18	in	in	ADP
american_scientific_journal-3703	36	19	the	the	DET
american_scientific_journal-3703	36	20	future	future	NOUN
american_scientific_journal-3703	36	21	so	so	SCONJ
american_scientific_journal-3703	36	22	that	that	SCONJ
american_scientific_journal-3703	36	23	we	we	PRON
american_scientific_journal-3703	36	24	can	can	AUX
american_scientific_journal-3703	36	25	describe	describe	VERB
american_scientific_journal-3703	36	26	the	the	DET
american_scientific_journal-3703	36	27	graphical	graphical	ADJ
american_scientific_journal-3703	36	28	representation	representation	NOUN
american_scientific_journal-3703	36	29	of	of	ADP
american_scientific_journal-3703	36	30	our	our	PRON
american_scientific_journal-3703	36	31	mathematical	mathematical	ADJ
american_scientific_journal-3703	36	32	research	research	NOUN
american_scientific_journal-3703	36	33	.	.	PUNCT
american_scientific_journal-3703	37	1	3	3	X
american_scientific_journal-3703	37	2	.	.	X
american_scientific_journal-3703	37	3	mathematical	mathematical	ADJ
american_scientific_journal-3703	37	4	preliminaries	preliminary	NOUN
american_scientific_journal-3703	37	5	we	we	PRON
american_scientific_journal-3703	37	6	need	need	VERB
american_scientific_journal-3703	37	7	some	some	DET
american_scientific_journal-3703	37	8	basic	basic	ADJ
american_scientific_journal-3703	37	9	definitions	definition	NOUN
american_scientific_journal-3703	37	10	to	to	PART
american_scientific_journal-3703	37	11	be	be	AUX
american_scientific_journal-3703	37	12	used	use	VERB
american_scientific_journal-3703	37	13	elsewhere	elsewhere	ADV
american_scientific_journal-3703	37	14	of	of	ADP
american_scientific_journal-3703	37	15	this	this	DET
american_scientific_journal-3703	37	16	article	article	NOUN
american_scientific_journal-3703	37	17	.	.	PUNCT
american_scientific_journal-3703	38	1	we	we	PRON
american_scientific_journal-3703	38	2	mention	mention	VERB
american_scientific_journal-3703	38	3	these	these	DET
american_scientific_journal-3703	38	4	definitions	definition	NOUN
american_scientific_journal-3703	38	5	as	as	SCONJ
american_scientific_journal-3703	38	6	follows	follow	VERB
american_scientific_journal-3703	38	7	.	.	PUNCT
american_scientific_journal-3703	39	1	3.1	3.1	NUM
american_scientific_journal-3703	39	2	basic	basic	ADJ
american_scientific_journal-3703	39	3	definitions	definition	NOUN
american_scientific_journal-3703	39	4	3.1.1	3.1.1	NUM
american_scientific_journal-3703	39	5	orbit	orbit	NOUN
american_scientific_journal-3703	39	6	given	give	VERB
american_scientific_journal-3703	39	7	0x	0x	PROPN
american_scientific_journal-3703	39	8	r∈	r∈	PROPN
american_scientific_journal-3703	40	1	(	(	PUNCT
american_scientific_journal-3703	40	2	0x	0x	NOUN
american_scientific_journal-3703	40	3	is	be	AUX
american_scientific_journal-3703	40	4	called	call	VERB
american_scientific_journal-3703	40	5	the	the	DET
american_scientific_journal-3703	40	6	seed	seed	NOUN
american_scientific_journal-3703	40	7	or	or	CCONJ
american_scientific_journal-3703	40	8	initial	initial	ADJ
american_scientific_journal-3703	40	9	value	value	NOUN
american_scientific_journal-3703	40	10	of	of	ADP
american_scientific_journal-3703	40	11	the	the	DET
american_scientific_journal-3703	40	12	orbit	orbit	NOUN
american_scientific_journal-3703	40	13	)	)	PUNCT
american_scientific_journal-3703	40	14	,	,	PUNCT
american_scientific_journal-3703	40	15	we	we	PRON
american_scientific_journal-3703	40	16	define	define	VERB
american_scientific_journal-3703	40	17	the	the	DET
american_scientific_journal-3703	40	18	orbit	orbit	NOUN
american_scientific_journal-3703	40	19	of	of	ADP
american_scientific_journal-3703	40	20	0x	0x	PROPN
american_scientific_journal-3703	40	21	under	under	ADP
american_scientific_journal-3703	40	22	f	f	PROPN
american_scientific_journal-3703	40	23	to	to	PART
american_scientific_journal-3703	40	24	be	be	AUX
american_scientific_journal-3703	40	25	the	the	DET
american_scientific_journal-3703	40	26	sequence	sequence	NOUN
american_scientific_journal-3703	40	27	{	{	PUNCT
american_scientific_journal-3703	40	28	}	}	PUNCT
american_scientific_journal-3703	40	29	2	2	NUM
american_scientific_journal-3703	40	30	0	0	NUM
american_scientific_journal-3703	40	31	1	1	NUM
american_scientific_journal-3703	40	32	0	0	NUM
american_scientific_journal-3703	40	33	2	2	NUM
american_scientific_journal-3703	40	34	0	0	NUM
american_scientific_journal-3703	40	35	0	0	NUM
american_scientific_journal-3703	40	36	,	,	PUNCT
american_scientific_journal-3703	40	37	(	(	PUNCT
american_scientific_journal-3703	40	38	)	)	PUNCT
american_scientific_journal-3703	40	39	,	,	PUNCT
american_scientific_journal-3703	40	40	(	(	PUNCT
american_scientific_journal-3703	40	41	)	)	PUNCT
american_scientific_journal-3703	40	42	,	,	PUNCT
american_scientific_journal-3703	40	43	,	,	PUNCT
american_scientific_journal-3703	40	44	(	(	PUNCT
american_scientific_journal-3703	40	45	)	)	PUNCT
american_scientific_journal-3703	40	46	,	,	PUNCT
american_scientific_journal-3703	40	47	n	n	PRON
american_scientific_journal-3703	40	48	nx	nx	NOUN
american_scientific_journal-3703	41	1	x	x	SYM
american_scientific_journal-3703	41	2	f	f	NOUN
american_scientific_journal-3703	41	3	x	x	X
american_scientific_journal-3703	41	4	x	x	X
american_scientific_journal-3703	41	5	f	f	NOUN
american_scientific_journal-3703	41	6	x	x	X
american_scientific_journal-3703	41	7	x	x	X
american_scientific_journal-3703	41	8	f	f	NOUN
american_scientific_journal-3703	41	9	x=	x=	PUNCT
american_scientific_journal-3703	41	10	=	=	PUNCT
american_scientific_journal-3703	42	1	=	=	NOUN
american_scientific_journal-3703	42	2	l	l	NOUN
american_scientific_journal-3703	42	3	l	l	NOUN
american_scientific_journal-3703	42	4	.	.	PUNCT
american_scientific_journal-3703	43	1	for	for	ADP
american_scientific_journal-3703	43	2	example	example	NOUN
american_scientific_journal-3703	43	3	,	,	PUNCT
american_scientific_journal-3703	43	4	let	let	VERB
american_scientific_journal-3703	43	5	(	(	PUNCT
american_scientific_journal-3703	43	6	)	)	PUNCT
american_scientific_journal-3703	43	7	f	f	PROPN
american_scientific_journal-3703	43	8	x	x	PUNCT
american_scientific_journal-3703	43	9	x=	x=	PROPN
american_scientific_journal-3703	43	10	and	and	CCONJ
american_scientific_journal-3703	43	11	0	0	NUM
american_scientific_journal-3703	43	12	16,x	16,x	NUM
american_scientific_journal-3703	44	1	=	=	PRON
american_scientific_journal-3703	44	2	then	then	ADV
american_scientific_journal-3703	44	3	the	the	DET
american_scientific_journal-3703	44	4	orbit	orbit	NOUN
american_scientific_journal-3703	44	5	of	of	ADP
american_scientific_journal-3703	44	6	0x	0x	PROPN
american_scientific_journal-3703	44	7	under	under	ADP
american_scientific_journal-3703	44	8	f	f	PROPN
american_scientific_journal-3703	44	9	to	to	PART
american_scientific_journal-3703	44	10	be	be	AUX
american_scientific_journal-3703	44	11	the	the	DET
american_scientific_journal-3703	44	12	sequence	sequence	NOUN
american_scientific_journal-3703	44	13	{	{	PUNCT
american_scientific_journal-3703	44	14	16,4,2,1.414	16,4,2,1.414	NUM
american_scientific_journal-3703	44	15	,	,	PUNCT
american_scientific_journal-3703	44	16	}	}	PUNCT
american_scientific_journal-3703	44	17	.l	.l	PROPN
american_scientific_journal-3703	44	18	american	american	PROPN
american_scientific_journal-3703	44	19	scientific	scientific	PROPN
american_scientific_journal-3703	44	20	research	research	PROPN
american_scientific_journal-3703	44	21	journal	journal	NOUN
american_scientific_journal-3703	44	22	for	for	ADP
american_scientific_journal-3703	44	23	engineering	engineering	NOUN
american_scientific_journal-3703	44	24	,	,	PUNCT
american_scientific_journal-3703	44	25	technology	technology	NOUN
american_scientific_journal-3703	44	26	,	,	PUNCT
american_scientific_journal-3703	44	27	and	and	CCONJ
american_scientific_journal-3703	44	28	sciences	science	NOUN
american_scientific_journal-3703	44	29	(	(	PUNCT
american_scientific_journal-3703	44	30	asrjets	asrjet	NOUN
american_scientific_journal-3703	44	31	)	)	PUNCT
american_scientific_journal-3703	44	32	(	(	PUNCT
american_scientific_journal-3703	44	33	2018	2018	NUM
american_scientific_journal-3703	44	34	)	)	PUNCT
american_scientific_journal-3703	44	35	volume	volume	NOUN
american_scientific_journal-3703	44	36	43	43	NUM
american_scientific_journal-3703	44	37	,	,	PUNCT
american_scientific_journal-3703	44	38	no	no	DET
american_scientific_journal-3703	44	39	1	1	NUM
american_scientific_journal-3703	44	40	,	,	PUNCT
american_scientific_journal-3703	44	41	pp	pp	ADV
american_scientific_journal-3703	44	42	110	110	NUM
american_scientific_journal-3703	44	43	-	-	SYM
american_scientific_journal-3703	44	44	133	133	NUM
american_scientific_journal-3703	44	45	112	112	NUM
american_scientific_journal-3703	44	46	we	we	PRON
american_scientific_journal-3703	44	47	see	see	VERB
american_scientific_journal-3703	44	48	that	that	SCONJ
american_scientific_journal-3703	44	49	the	the	DET
american_scientific_journal-3703	44	50	point	point	NOUN
american_scientific_journal-3703	44	51	on	on	ADP
american_scientific_journal-3703	44	52	this	this	DET
american_scientific_journal-3703	44	53	orbit	orbit	NOUN
american_scientific_journal-3703	44	54	tend	tend	VERB
american_scientific_journal-3703	44	55	to	to	ADP
american_scientific_journal-3703	44	56	1	1	NUM
american_scientific_journal-3703	44	57	.	.	X
american_scientific_journal-3703	44	58	3.1.2	3.1.2	NUM
american_scientific_journal-3703	44	59	periodic	periodic	ADJ
american_scientific_journal-3703	44	60	orbit	orbit	NOUN
american_scientific_journal-3703	44	61	or	or	CCONJ
american_scientific_journal-3703	44	62	cycle	cycle	NOUN
american_scientific_journal-3703	44	63	the	the	DET
american_scientific_journal-3703	44	64	point	point	NOUN
american_scientific_journal-3703	44	65	0x	0x	NOUN
american_scientific_journal-3703	44	66	is	be	AUX
american_scientific_journal-3703	44	67	called	call	VERB
american_scientific_journal-3703	44	68	periodic	periodic	ADJ
american_scientific_journal-3703	44	69	if	if	SCONJ
american_scientific_journal-3703	44	70	0	0	NUM
american_scientific_journal-3703	44	71	0	0	NUM
american_scientific_journal-3703	44	72	(	(	PUNCT
american_scientific_journal-3703	44	73	)	)	PUNCT
american_scientific_journal-3703	44	74	nf	nf	PROPN
american_scientific_journal-3703	44	75	x	x	X
american_scientific_journal-3703	44	76	x=	x=	NOUN
american_scientific_journal-3703	44	77	for	for	ADP
american_scientific_journal-3703	44	78	some	some	DET
american_scientific_journal-3703	44	79	0	0	NUM
american_scientific_journal-3703	44	80	>	>	SYM
american_scientific_journal-3703	44	81	n	n	NOUN
american_scientific_journal-3703	44	82	,	,	PUNCT
american_scientific_journal-3703	44	83	where	where	SCONJ
american_scientific_journal-3703	44	84	n	n	PRON
american_scientific_journal-3703	44	85	is	be	AUX
american_scientific_journal-3703	44	86	called	call	VERB
american_scientific_journal-3703	44	87	the	the	DET
american_scientific_journal-3703	44	88	prime	prime	ADJ
american_scientific_journal-3703	44	89	period	period	NOUN
american_scientific_journal-3703	44	90	of	of	ADP
american_scientific_journal-3703	44	91	the	the	DET
american_scientific_journal-3703	44	92	orbit	orbit	NOUN
american_scientific_journal-3703	44	93	.	.	PUNCT
american_scientific_journal-3703	45	1	3.1.3	3.1.3	NUM
american_scientific_journal-3703	45	2	periodic	periodic	ADJ
american_scientific_journal-3703	45	3	orbit	orbit	NOUN
american_scientific_journal-3703	45	4	with	with	ADP
american_scientific_journal-3703	45	5	prime	prime	ADJ
american_scientific_journal-3703	45	6	period	period	NOUN
american_scientific_journal-3703	45	7	n	n	CCONJ
american_scientific_journal-3703	45	8	if	if	SCONJ
american_scientific_journal-3703	45	9	the	the	DET
american_scientific_journal-3703	45	10	point	point	NOUN
american_scientific_journal-3703	45	11	0x	0x	NOUN
american_scientific_journal-3703	45	12	is	be	AUX
american_scientific_journal-3703	45	13	periodic	periodic	ADJ
american_scientific_journal-3703	45	14	with	with	ADP
american_scientific_journal-3703	45	15	prime	prime	ADJ
american_scientific_journal-3703	45	16	period	period	NOUN
american_scientific_journal-3703	45	17	,	,	PUNCT
american_scientific_journal-3703	45	18	n	n	CCONJ
american_scientific_journal-3703	45	19	then	then	ADV
american_scientific_journal-3703	45	20	the	the	DET
american_scientific_journal-3703	45	21	periodic	periodic	ADJ
american_scientific_journal-3703	45	22	orbit	orbit	NOUN
american_scientific_journal-3703	45	23	with	with	ADP
american_scientific_journal-3703	45	24	prime	prime	ADJ
american_scientific_journal-3703	45	25	period	period	NOUN
american_scientific_journal-3703	45	26	n	n	PART
american_scientific_journal-3703	45	27	to	to	PART
american_scientific_journal-3703	45	28	be	be	AUX
american_scientific_journal-3703	45	29	the	the	DET
american_scientific_journal-3703	45	30	sequence	sequence	NOUN
american_scientific_journal-3703	45	31	{	{	PUNCT
american_scientific_journal-3703	45	32	0x	0x	NOUN
american_scientific_journal-3703	45	33	,	,	PUNCT
american_scientific_journal-3703	45	34	,	,	PUNCT
american_scientific_journal-3703	45	35	)	)	PUNCT
american_scientific_journal-3703	45	36	,	,	PUNCT
american_scientific_journal-3703	45	37	(	(	PUNCT
american_scientific_journal-3703	45	38	0	0	NUM
american_scientific_journal-3703	45	39	lxf	lxf	NOUN
american_scientific_journal-3703	45	40	)	)	PUNCT
american_scientific_journal-3703	45	41	,	,	PUNCT
american_scientific_journal-3703	45	42	(	(	PUNCT
american_scientific_journal-3703	45	43	0	0	NUM
american_scientific_journal-3703	45	44	1	1	NUM
american_scientific_journal-3703	45	45	xf	xf	NOUN
american_scientific_journal-3703	45	46	n−	n−	PROPN
american_scientific_journal-3703	45	47	0x	0x	NOUN
american_scientific_journal-3703	45	48	,	,	PUNCT
american_scientific_journal-3703	45	49	,	,	PUNCT
american_scientific_journal-3703	45	50	)	)	PUNCT
american_scientific_journal-3703	45	51	,	,	PUNCT
american_scientific_journal-3703	45	52	(	(	PUNCT
american_scientific_journal-3703	45	53	0	0	NUM
american_scientific_journal-3703	45	54	lxf	lxf	PROPN
american_scientific_journal-3703	45	55	l	l	NOUN
american_scientific_journal-3703	45	56	)	)	PUNCT
american_scientific_journal-3703	45	57	,	,	PUNCT
american_scientific_journal-3703	45	58	(	(	PUNCT
american_scientific_journal-3703	45	59	0	0	NUM
american_scientific_journal-3703	45	60	1	1	NUM
american_scientific_journal-3703	45	61	xf	xf	NOUN
american_scientific_journal-3703	45	62	n−	n−	PROPN
american_scientific_journal-3703	45	63	}	}	PUNCT
american_scientific_journal-3703	45	64	.	.	PUNCT
american_scientific_journal-3703	46	1	for	for	ADP
american_scientific_journal-3703	46	2	example	example	NOUN
american_scientific_journal-3703	46	3	,	,	PUNCT
american_scientific_journal-3703	46	4	let	let	VERB
american_scientific_journal-3703	46	5	3	3	NUM
american_scientific_journal-3703	46	6	)	)	PUNCT
american_scientific_journal-3703	46	7	(	(	PUNCT
american_scientific_journal-3703	46	8	xxf	xxf	PROPN
american_scientific_journal-3703	46	9	−=	−=	NOUN
american_scientific_journal-3703	46	10	and	and	CCONJ
american_scientific_journal-3703	46	11	10	10	NUM
american_scientific_journal-3703	46	12	=	=	NOUN
american_scientific_journal-3703	46	13	x	x	NOUN
american_scientific_journal-3703	46	14	,	,	PUNCT
american_scientific_journal-3703	46	15	then	then	ADV
american_scientific_journal-3703	46	16	1)1	1)1	NUM
american_scientific_journal-3703	46	17	(	(	PUNCT
american_scientific_journal-3703	46	18	−=f	−=f	NOUN
american_scientific_journal-3703	46	19	,	,	PUNCT
american_scientific_journal-3703	46	20	1))1(()1(2	1))1(()1(2	NUM
american_scientific_journal-3703	47	1	=	=	SYM
american_scientific_journal-3703	47	2	=	=	SYM
american_scientific_journal-3703	47	3	fff	fff	PROPN
american_scientific_journal-3703	47	4	.	.	PUNCT
american_scientific_journal-3703	48	1	thus	thus	ADV
american_scientific_journal-3703	48	2	1	1	NUM
american_scientific_journal-3703	48	3	is	be	AUX
american_scientific_journal-3703	48	4	periodic	periodic	ADJ
american_scientific_journal-3703	48	5	point	point	NOUN
american_scientific_journal-3703	48	6	with	with	ADP
american_scientific_journal-3703	48	7	prime	prime	ADJ
american_scientific_journal-3703	48	8	period	period	NOUN
american_scientific_journal-3703	48	9	2	2	NUM
american_scientific_journal-3703	48	10	.	.	PUNCT
american_scientific_journal-3703	48	11	similarly	similarly	ADV
american_scientific_journal-3703	48	12	,	,	PUNCT
american_scientific_journal-3703	48	13	-1	-1	ADP
american_scientific_journal-3703	48	14	is	be	AUX
american_scientific_journal-3703	48	15	periodic	periodic	ADJ
american_scientific_journal-3703	48	16	point	point	NOUN
american_scientific_journal-3703	48	17	with	with	ADP
american_scientific_journal-3703	48	18	prime	prime	ADJ
american_scientific_journal-3703	48	19	period	period	NOUN
american_scientific_journal-3703	48	20	2	2	NUM
american_scientific_journal-3703	48	21	and	and	CCONJ
american_scientific_journal-3703	48	22	these	these	DET
american_scientific_journal-3703	48	23	orbits	orbit	NOUN
american_scientific_journal-3703	48	24	are	be	AUX
american_scientific_journal-3703	48	25	:	:	PUNCT
american_scientific_journal-3703	48	26	{	{	PUNCT
american_scientific_journal-3703	48	27	1	1	NUM
american_scientific_journal-3703	48	28	,	,	PUNCT
american_scientific_journal-3703	48	29	1	1	NUM
american_scientific_journal-3703	48	30	,	,	PUNCT
american_scientific_journal-3703	48	31	1	1	NUM
american_scientific_journal-3703	48	32	,	,	PUNCT
american_scientific_journal-3703	48	33	1	1	NUM
american_scientific_journal-3703	48	34	,	,	PUNCT
american_scientific_journal-3703	48	35	}	}	PUNCT
american_scientific_journal-3703	48	36	−	−	NOUN
american_scientific_journal-3703	48	37	−	−	PROPN
american_scientific_journal-3703	48	38	l	l	NOUN
american_scientific_journal-3703	48	39	and	and	CCONJ
american_scientific_journal-3703	48	40	}	}	PUNCT
american_scientific_journal-3703	48	41	,	,	PUNCT
american_scientific_journal-3703	48	42	1,1,1,1	1,1,1,1	NUM
american_scientific_journal-3703	48	43	{	{	PUNCT
american_scientific_journal-3703	48	44	l−−	l−−	NOUN
american_scientific_journal-3703	48	45	.	.	PUNCT
american_scientific_journal-3703	49	1	3.1.4	3.1.4	NUM
american_scientific_journal-3703	49	2	transitivity	transitivity	NOUN
american_scientific_journal-3703	49	3	a	a	DET
american_scientific_journal-3703	49	4	dynamical	dynamical	ADJ
american_scientific_journal-3703	49	5	system	system	NOUN
american_scientific_journal-3703	49	6	is	be	AUX
american_scientific_journal-3703	49	7	transitive	transitive	ADJ
american_scientific_journal-3703	49	8	if	if	SCONJ
american_scientific_journal-3703	49	9	for	for	ADP
american_scientific_journal-3703	49	10	any	any	DET
american_scientific_journal-3703	49	11	pair	pair	NOUN
american_scientific_journal-3703	49	12	of	of	ADP
american_scientific_journal-3703	49	13	points	point	NOUN
american_scientific_journal-3703	49	14	x	x	PUNCT
american_scientific_journal-3703	49	15	and	and	CCONJ
american_scientific_journal-3703	49	16	y	y	PROPN
american_scientific_journal-3703	49	17	and	and	CCONJ
american_scientific_journal-3703	49	18	any	any	DET
american_scientific_journal-3703	49	19	0	0	NUM
american_scientific_journal-3703	49	20	>	>	X
american_scientific_journal-3703	49	21	ε	ε	PROPN
american_scientific_journal-3703	49	22	there	there	PRON
american_scientific_journal-3703	49	23	is	be	VERB
american_scientific_journal-3703	49	24	a	a	DET
american_scientific_journal-3703	49	25	third	third	ADJ
american_scientific_journal-3703	49	26	point	point	NOUN
american_scientific_journal-3703	49	27	z	z	NOUN
american_scientific_journal-3703	49	28	within	within	ADP
american_scientific_journal-3703	49	29	ε	ε	PROPN
american_scientific_journal-3703	49	30	of	of	ADP
american_scientific_journal-3703	49	31	x	x	X
american_scientific_journal-3703	49	32	whose	whose	DET
american_scientific_journal-3703	49	33	orbit	orbit	NOUN
american_scientific_journal-3703	49	34	comes	come	VERB
american_scientific_journal-3703	49	35	within	within	ADP
american_scientific_journal-3703	49	36	ε	ε	PROPN
american_scientific_journal-3703	49	37	of	of	ADP
american_scientific_journal-3703	49	38	y.	y.	PROPN
american_scientific_journal-3703	49	39	in	in	ADP
american_scientific_journal-3703	49	40	other	other	ADJ
american_scientific_journal-3703	49	41	words	word	NOUN
american_scientific_journal-3703	49	42	,	,	PUNCT
american_scientific_journal-3703	49	43	a	a	DET
american_scientific_journal-3703	49	44	transitive	transitive	ADJ
american_scientific_journal-3703	49	45	dynamical	dynamical	ADJ
american_scientific_journal-3703	49	46	system	system	NOUN
american_scientific_journal-3703	49	47	has	have	VERB
american_scientific_journal-3703	49	48	the	the	DET
american_scientific_journal-3703	49	49	property	property	NOUN
american_scientific_journal-3703	49	50	that	that	PRON
american_scientific_journal-3703	49	51	,	,	PUNCT
american_scientific_journal-3703	49	52	given	give	VERB
american_scientific_journal-3703	49	53	any	any	DET
american_scientific_journal-3703	49	54	two	two	NUM
american_scientific_journal-3703	49	55	points	point	NOUN
american_scientific_journal-3703	49	56	,	,	PUNCT
american_scientific_journal-3703	49	57	we	we	PRON
american_scientific_journal-3703	49	58	can	can	AUX
american_scientific_journal-3703	49	59	find	find	VERB
american_scientific_journal-3703	49	60	an	an	DET
american_scientific_journal-3703	49	61	orbit	orbit	NOUN
american_scientific_journal-3703	49	62	that	that	PRON
american_scientific_journal-3703	49	63	comes	come	VERB
american_scientific_journal-3703	49	64	arbitrarily	arbitrarily	ADV
american_scientific_journal-3703	49	65	close	close	ADJ
american_scientific_journal-3703	49	66	to	to	ADP
american_scientific_journal-3703	49	67	both	both	PRON
american_scientific_journal-3703	49	68	.	.	PUNCT
american_scientific_journal-3703	50	1	3.1.5	3.1.5	NUM
american_scientific_journal-3703	50	2	sensitivity	sensitivity	NOUN
american_scientific_journal-3703	50	3	to	to	ADP
american_scientific_journal-3703	50	4	initial	initial	ADJ
american_scientific_journal-3703	50	5	conditions	condition	NOUN
american_scientific_journal-3703	50	6	a	a	DET
american_scientific_journal-3703	50	7	dynamical	dynamical	ADJ
american_scientific_journal-3703	50	8	system	system	NOUN
american_scientific_journal-3703	50	9	f	f	PROPN
american_scientific_journal-3703	50	10	depends	depend	VERB
american_scientific_journal-3703	50	11	sensitively	sensitively	ADV
american_scientific_journal-3703	50	12	on	on	ADP
american_scientific_journal-3703	50	13	initial	initial	ADJ
american_scientific_journal-3703	50	14	conditions	condition	NOUN
american_scientific_journal-3703	50	15	if	if	SCONJ
american_scientific_journal-3703	50	16	there	there	PRON
american_scientific_journal-3703	50	17	is	be	VERB
american_scientific_journal-3703	50	18	a	a	DET
american_scientific_journal-3703	50	19	0β	0β	NOUN
american_scientific_journal-3703	50	20	>	>	PUNCT
american_scientific_journal-3703	50	21	such	such	ADJ
american_scientific_journal-3703	50	22	that	that	PRON
american_scientific_journal-3703	50	23	for	for	ADP
american_scientific_journal-3703	50	24	any	any	DET
american_scientific_journal-3703	50	25	x	x	NOUN
american_scientific_journal-3703	50	26	and	and	CCONJ
american_scientific_journal-3703	50	27	any	any	DET
american_scientific_journal-3703	50	28	0	0	NUM
american_scientific_journal-3703	50	29	>	>	X
american_scientific_journal-3703	50	30	ε	ε	PROPN
american_scientific_journal-3703	50	31	there	there	PRON
american_scientific_journal-3703	50	32	is	be	VERB
american_scientific_journal-3703	50	33	a	a	DET
american_scientific_journal-3703	50	34	y	y	NOUN
american_scientific_journal-3703	50	35	within	within	ADP
american_scientific_journal-3703	50	36	ε	ε	PROPN
american_scientific_journal-3703	50	37	of	of	ADP
american_scientific_journal-3703	50	38	x	x	PROPN
american_scientific_journal-3703	50	39	and	and	CCONJ
american_scientific_journal-3703	50	40	a	a	DET
american_scientific_journal-3703	50	41	k	k	NOUN
american_scientific_journal-3703	50	42	such	such	ADJ
american_scientific_journal-3703	50	43	that	that	SCONJ
american_scientific_journal-3703	50	44	the	the	DET
american_scientific_journal-3703	50	45	distance	distance	NOUN
american_scientific_journal-3703	50	46	between	between	ADP
american_scientific_journal-3703	50	47	)	)	PUNCT
american_scientific_journal-3703	50	48	(	(	PUNCT
american_scientific_journal-3703	50	49	xf	xf	PROPN
american_scientific_journal-3703	50	50	k	k	PROPN
american_scientific_journal-3703	50	51	and	and	CCONJ
american_scientific_journal-3703	50	52	)	)	PUNCT
american_scientific_journal-3703	50	53	(	(	PUNCT
american_scientific_journal-3703	50	54	yf	yf	X
american_scientific_journal-3703	50	55	k	k	PROPN
american_scientific_journal-3703	50	56	is	be	AUX
american_scientific_journal-3703	50	57	at	at	ADV
american_scientific_journal-3703	50	58	least	least	ADJ
american_scientific_journal-3703	50	59	.β	.β	VERB
american_scientific_journal-3703	50	60	in	in	ADP
american_scientific_journal-3703	50	61	this	this	DET
american_scientific_journal-3703	50	62	definition	definition	NOUN
american_scientific_journal-3703	50	63	it	it	PRON
american_scientific_journal-3703	50	64	is	be	AUX
american_scientific_journal-3703	50	65	important	important	ADJ
american_scientific_journal-3703	50	66	to	to	PART
american_scientific_journal-3703	50	67	understand	understand	VERB
american_scientific_journal-3703	50	68	the	the	DET
american_scientific_journal-3703	50	69	order	order	NOUN
american_scientific_journal-3703	50	70	of	of	ADP
american_scientific_journal-3703	50	71	the	the	DET
american_scientific_journal-3703	50	72	quantifiers	quantifier	NOUN
american_scientific_journal-3703	50	73	.	.	PUNCT
american_scientific_journal-3703	51	1	the	the	DET
american_scientific_journal-3703	51	2	definition	definition	NOUN
american_scientific_journal-3703	51	3	says	say	VERB
american_scientific_journal-3703	51	4	that	that	SCONJ
american_scientific_journal-3703	51	5	,	,	PUNCT
american_scientific_journal-3703	51	6	no	no	ADV
american_scientific_journal-3703	51	7	matter	matter	ADV
american_scientific_journal-3703	51	8	which	which	PRON
american_scientific_journal-3703	51	9	x	x	PUNCT
american_scientific_journal-3703	51	10	we	we	PRON
american_scientific_journal-3703	51	11	begin	begin	VERB
american_scientific_journal-3703	51	12	with	with	ADP
american_scientific_journal-3703	51	13	and	and	CCONJ
american_scientific_journal-3703	51	14	no	no	ADV
american_scientific_journal-3703	51	15	matter	matter	ADV
american_scientific_journal-3703	51	16	how	how	SCONJ
american_scientific_journal-3703	51	17	small	small	ADJ
american_scientific_journal-3703	51	18	a	a	DET
american_scientific_journal-3703	51	19	region	region	NOUN
american_scientific_journal-3703	51	20	we	we	PRON
american_scientific_journal-3703	51	21	choose	choose	VERB
american_scientific_journal-3703	51	22	about	about	ADP
american_scientific_journal-3703	51	23	x.	x.	NOUN
american_scientific_journal-3703	51	24	we	we	PRON
american_scientific_journal-3703	51	25	can	can	AUX
american_scientific_journal-3703	51	26	always	always	ADV
american_scientific_journal-3703	51	27	find	find	VERB
american_scientific_journal-3703	51	28	a	a	DET
american_scientific_journal-3703	51	29	y	y	NOUN
american_scientific_journal-3703	51	30	in	in	ADP
american_scientific_journal-3703	51	31	this	this	DET
american_scientific_journal-3703	51	32	region	region	NOUN
american_scientific_journal-3703	51	33	whose	whose	DET
american_scientific_journal-3703	51	34	orbit	orbit	NOUN
american_scientific_journal-3703	51	35	eventually	eventually	ADV
american_scientific_journal-3703	51	36	separates	separate	VERB
american_scientific_journal-3703	51	37	form	form	NOUN
american_scientific_journal-3703	51	38	that	that	PRON
american_scientific_journal-3703	51	39	of	of	ADP
american_scientific_journal-3703	51	40	x	x	PUNCT
american_scientific_journal-3703	51	41	by	by	ADP
american_scientific_journal-3703	51	42	at	at	ADV
american_scientific_journal-3703	51	43	least	least	ADJ
american_scientific_journal-3703	51	44	.β	.β	PUNCT
american_scientific_journal-3703	52	1	the	the	DET
american_scientific_journal-3703	52	2	distance	distance	NOUN
american_scientific_journal-3703	52	3	β	β	NOUN
american_scientific_journal-3703	52	4	is	be	AUX
american_scientific_journal-3703	52	5	independent	independent	ADJ
american_scientific_journal-3703	52	6	of	of	ADP
american_scientific_journal-3703	52	7	x.	x.	NOUN
american_scientific_journal-3703	52	8	as	as	ADP
american_scientific_journal-3703	52	9	a	a	DET
american_scientific_journal-3703	52	10	consequence	consequence	NOUN
american_scientific_journal-3703	52	11	,	,	PUNCT
american_scientific_journal-3703	52	12	for	for	ADP
american_scientific_journal-3703	52	13	each	each	DET
american_scientific_journal-3703	52	14	x	x	NOUN
american_scientific_journal-3703	52	15	,	,	PUNCT
american_scientific_journal-3703	52	16	there	there	PRON
american_scientific_journal-3703	52	17	are	be	VERB
american_scientific_journal-3703	52	18	points	point	NOUN
american_scientific_journal-3703	52	19	arbitrarily	arbitrarily	ADV
american_scientific_journal-3703	52	20	nearby	nearby	ADV
american_scientific_journal-3703	52	21	whose	whose	DET
american_scientific_journal-3703	52	22	orbits	orbit	NOUN
american_scientific_journal-3703	52	23	are	be	AUX
american_scientific_journal-3703	52	24	eventually	eventually	ADV
american_scientific_journal-3703	52	25	“	"	PUNCT
american_scientific_journal-3703	52	26	far	far	ADV
american_scientific_journal-3703	52	27	”	"	PUNCT
american_scientific_journal-3703	52	28	that	that	PRON
american_scientific_journal-3703	52	29	of	of	ADP
american_scientific_journal-3703	52	30	x.	x.	NOUN
american_scientific_journal-3703	52	31	the	the	DET
american_scientific_journal-3703	52	32	idea	idea	NOUN
american_scientific_journal-3703	52	33	of	of	ADP
american_scientific_journal-3703	52	34	sensitive	sensitive	ADJ
american_scientific_journal-3703	52	35	dependence	dependence	NOUN
american_scientific_journal-3703	52	36	on	on	ADP
american_scientific_journal-3703	52	37	initial	initial	ADJ
american_scientific_journal-3703	52	38	conditions	condition	NOUN
american_scientific_journal-3703	52	39	is	be	AUX
american_scientific_journal-3703	52	40	very	very	ADV
american_scientific_journal-3703	52	41	important	important	ADJ
american_scientific_journal-3703	52	42	topics	topic	NOUN
american_scientific_journal-3703	52	43	in	in	ADP
american_scientific_journal-3703	52	44	the	the	DET
american_scientific_journal-3703	52	45	study	study	NOUN
american_scientific_journal-3703	52	46	of	of	ADP
american_scientific_journal-3703	52	47	dynamical	dynamical	ADJ
american_scientific_journal-3703	52	48	system	system	NOUN
american_scientific_journal-3703	52	49	.	.	PUNCT
american_scientific_journal-3703	53	1	if	if	SCONJ
american_scientific_journal-3703	53	2	a	a	DET
american_scientific_journal-3703	53	3	particular	particular	ADJ
american_scientific_journal-3703	53	4	system	system	NOUN
american_scientific_journal-3703	53	5	possesses	possess	VERB
american_scientific_journal-3703	53	6	sensitive	sensitive	ADJ
american_scientific_journal-3703	53	7	dependence	dependence	NOUN
american_scientific_journal-3703	53	8	,	,	PUNCT
american_scientific_journal-3703	53	9	then	then	ADV
american_scientific_journal-3703	53	10	for	for	ADP
american_scientific_journal-3703	53	11	all	all	DET
american_scientific_journal-3703	53	12	practical	practical	ADJ
american_scientific_journal-3703	53	13	purpose	purpose	NOUN
american_scientific_journal-3703	53	14	,	,	PUNCT
american_scientific_journal-3703	53	15	the	the	DET
american_scientific_journal-3703	53	16	dynamics	dynamic	NOUN
american_scientific_journal-3703	53	17	of	of	ADP
american_scientific_journal-3703	53	18	this	this	DET
american_scientific_journal-3703	53	19	system	system	NOUN
american_scientific_journal-3703	53	20	defy	defy	VERB
american_scientific_journal-3703	53	21	numerical	numerical	ADJ
american_scientific_journal-3703	53	22	computation	computation	NOUN
american_scientific_journal-3703	53	23	.	.	PUNCT
american_scientific_journal-3703	54	1	american	american	ADJ
american_scientific_journal-3703	54	2	scientific	scientific	ADJ
american_scientific_journal-3703	54	3	research	research	PROPN
american_scientific_journal-3703	54	4	journal	journal	NOUN
american_scientific_journal-3703	54	5	for	for	ADP
american_scientific_journal-3703	54	6	engineering	engineering	NOUN
american_scientific_journal-3703	54	7	,	,	PUNCT
american_scientific_journal-3703	54	8	technology	technology	NOUN
american_scientific_journal-3703	54	9	,	,	PUNCT
american_scientific_journal-3703	54	10	and	and	CCONJ
american_scientific_journal-3703	54	11	sciences	science	NOUN
american_scientific_journal-3703	54	12	(	(	PUNCT
american_scientific_journal-3703	54	13	asrjets	asrjet	NOUN
american_scientific_journal-3703	54	14	)	)	PUNCT
american_scientific_journal-3703	54	15	(	(	PUNCT
american_scientific_journal-3703	54	16	2018	2018	NUM
american_scientific_journal-3703	54	17	)	)	PUNCT
american_scientific_journal-3703	54	18	volume	volume	NOUN
american_scientific_journal-3703	54	19	43	43	NUM
american_scientific_journal-3703	54	20	,	,	PUNCT
american_scientific_journal-3703	54	21	no	no	DET
american_scientific_journal-3703	54	22	1	1	NUM
american_scientific_journal-3703	54	23	,	,	PUNCT
american_scientific_journal-3703	54	24	pp	pp	ADV
american_scientific_journal-3703	54	25	110	110	NUM
american_scientific_journal-3703	54	26	-	-	SYM
american_scientific_journal-3703	54	27	133	133	NUM
american_scientific_journal-3703	54	28	113	113	NUM
american_scientific_journal-3703	54	29	mathematically	mathematically	ADV
american_scientific_journal-3703	54	30	,	,	PUNCT
american_scientific_journal-3703	54	31	a	a	DET
american_scientific_journal-3703	54	32	continuous	continuous	ADJ
american_scientific_journal-3703	54	33	map	map	NOUN
american_scientific_journal-3703	54	34	:	:	PUNCT
american_scientific_journal-3703	54	35	f	f	X
american_scientific_journal-3703	54	36	x	x	PUNCT
american_scientific_journal-3703	54	37	x→	x→	PROPN
american_scientific_journal-3703	54	38	has	have	AUX
american_scientific_journal-3703	54	39	sensitive	sensitive	ADJ
american_scientific_journal-3703	54	40	dependence	dependence	NOUN
american_scientific_journal-3703	54	41	on	on	ADP
american_scientific_journal-3703	54	42	initial	initial	ADJ
american_scientific_journal-3703	54	43	conditions	condition	NOUN
american_scientific_journal-3703	54	44	if	if	SCONJ
american_scientific_journal-3703	54	45	there	there	PRON
american_scientific_journal-3703	54	46	exists	exist	VERB
american_scientific_journal-3703	54	47	0δ	0δ	PRON
american_scientific_journal-3703	54	48	>	>	PUNCT
american_scientific_journal-3703	54	49	such	such	ADJ
american_scientific_journal-3703	54	50	that	that	SCONJ
american_scientific_journal-3703	54	51	,	,	PUNCT
american_scientific_journal-3703	54	52	for	for	ADP
american_scientific_journal-3703	54	53	any	any	DET
american_scientific_journal-3703	54	54	x	x	SYM
american_scientific_journal-3703	54	55	x∈	x∈	NOUN
american_scientific_journal-3703	54	56	and	and	CCONJ
american_scientific_journal-3703	54	57	any	any	DET
american_scientific_journal-3703	54	58	neighborhood	neighborhood	NOUN
american_scientific_journal-3703	54	59	(	(	PUNCT
american_scientific_journal-3703	54	60	)	)	PUNCT
american_scientific_journal-3703	54	61	of	of	ADP
american_scientific_journal-3703	54	62	n	n	NOUN
american_scientific_journal-3703	54	63	x	x	X
american_scientific_journal-3703	54	64	x	x	X
american_scientific_journal-3703	54	65	,	,	PUNCT
american_scientific_journal-3703	54	66	there	there	PRON
american_scientific_journal-3703	54	67	exist	exist	VERB
american_scientific_journal-3703	54	68	(	(	PUNCT
american_scientific_journal-3703	54	69	)	)	PUNCT
american_scientific_journal-3703	54	70	y	y	PROPN
american_scientific_journal-3703	54	71	n	n	PROPN
american_scientific_journal-3703	54	72	x∈	x∈	PROPN
american_scientific_journal-3703	54	73	,	,	PUNCT
american_scientific_journal-3703	54	74	0n	0n	X
american_scientific_journal-3703	54	75	≥	≥	PRON
american_scientific_journal-3703	54	76	such	such	ADJ
american_scientific_journal-3703	54	77	that	that	PRON
american_scientific_journal-3703	54	78	(	(	PUNCT
american_scientific_journal-3703	54	79	)	)	PUNCT
american_scientific_journal-3703	54	80	(	(	PUNCT
american_scientific_journal-3703	54	81	)	)	PUNCT
american_scientific_journal-3703	54	82	(	(	PUNCT
american_scientific_journal-3703	54	83	)	)	PUNCT
american_scientific_journal-3703	54	84	,	,	PUNCT
american_scientific_journal-3703	54	85	,	,	PUNCT
american_scientific_journal-3703	54	86	n	n	PROPN
american_scientific_journal-3703	54	87	nd	nd	NOUN
american_scientific_journal-3703	54	88	f	f	NOUN
american_scientific_journal-3703	54	89	x	x	X
american_scientific_journal-3703	54	90	f	f	PROPN
american_scientific_journal-3703	54	91	y	y	PROPN
american_scientific_journal-3703	54	92	δ	δ	PROPN
american_scientific_journal-3703	54	93	>	>	X
american_scientific_journal-3703	54	94	(	(	PUNCT
american_scientific_journal-3703	54	95	)	)	PUNCT
american_scientific_journal-3703	54	96	where	where	SCONJ
american_scientific_journal-3703	54	97	,	,	PUNCT
american_scientific_journal-3703	54	98	x	x	PUNCT
american_scientific_journal-3703	54	99	d	d	NOUN
american_scientific_journal-3703	54	100	is	be	AUX
american_scientific_journal-3703	54	101	a	a	DET
american_scientific_journal-3703	54	102	compact	compact	ADJ
american_scientific_journal-3703	54	103	metric	metric	ADJ
american_scientific_journal-3703	54	104	space	space	NOUN
american_scientific_journal-3703	54	105	.	.	PUNCT
american_scientific_journal-3703	55	1	3.1.6	3.1.6	NUM
american_scientific_journal-3703	55	2	topologically	topologically	ADV
american_scientific_journal-3703	55	3	transitivity	transitivity	NOUN
american_scientific_journal-3703	55	4	consider	consider	VERB
american_scientific_journal-3703	55	5	the	the	DET
american_scientific_journal-3703	55	6	metric	metric	ADJ
american_scientific_journal-3703	55	7	space	space	NOUN
american_scientific_journal-3703	55	8	𝑋𝑋	𝑋𝑋	PROPN
american_scientific_journal-3703	55	9	and	and	CCONJ
american_scientific_journal-3703	55	10	the	the	DET
american_scientific_journal-3703	55	11	continuous	continuous	ADJ
american_scientific_journal-3703	55	12	map	map	NOUN
american_scientific_journal-3703	55	13	:	:	PUNCT
american_scientific_journal-3703	55	14	f	f	X
american_scientific_journal-3703	55	15	x	x	SYM
american_scientific_journal-3703	55	16	x→	x→	PUNCT
american_scientific_journal-3703	55	17	.we	.we	PUNCT
american_scientific_journal-3703	56	1	say	say	VERB
american_scientific_journal-3703	56	2	that	that	SCONJ
american_scientific_journal-3703	56	3	f	f	PROPN
american_scientific_journal-3703	56	4	is	be	AUX
american_scientific_journal-3703	56	5	topological	topological	ADJ
american_scientific_journal-3703	56	6	transitive	transitive	ADJ
american_scientific_journal-3703	56	7	if	if	SCONJ
american_scientific_journal-3703	56	8	for	for	ADP
american_scientific_journal-3703	56	9	every	every	DET
american_scientific_journal-3703	56	10	pair	pair	NOUN
american_scientific_journal-3703	56	11	of	of	ADP
american_scientific_journal-3703	56	12	non	non	ADJ
american_scientific_journal-3703	56	13	-	-	ADJ
american_scientific_journal-3703	56	14	empty	empty	ADJ
american_scientific_journal-3703	56	15	open	open	ADJ
american_scientific_journal-3703	56	16	sets	set	NOUN
american_scientific_journal-3703	56	17	u	u	NOUN
american_scientific_journal-3703	56	18	and	and	CCONJ
american_scientific_journal-3703	56	19	v	v	NOUN
american_scientific_journal-3703	56	20	in	in	ADP
american_scientific_journal-3703	56	21	x	x	PUNCT
american_scientific_journal-3703	56	22	there	there	PRON
american_scientific_journal-3703	56	23	exists	exist	VERB
american_scientific_journal-3703	56	24	a	a	DET
american_scientific_journal-3703	56	25	positive	positive	ADJ
american_scientific_journal-3703	56	26	integer	integer	NOUN
american_scientific_journal-3703	56	27	k	k	PROPN
american_scientific_journal-3703	56	28	such	such	ADJ
american_scientific_journal-3703	56	29	that	that	PRON
american_scientific_journal-3703	56	30	(	(	PUNCT
american_scientific_journal-3703	56	31	)	)	PUNCT
american_scientific_journal-3703	56	32	kf	kf	PROPN
american_scientific_journal-3703	56	33	u	u	PROPN
american_scientific_journal-3703	56	34	v	v	ADP
american_scientific_journal-3703	56	35	f∩	f∩	PROPN
american_scientific_journal-3703	56	36	≠	≠	PROPN
american_scientific_journal-3703	56	37	.	.	PUNCT
american_scientific_journal-3703	57	1	3.1.7	3.1.7	NUM
american_scientific_journal-3703	57	2	topological	topological	ADJ
american_scientific_journal-3703	57	3	conjugacy	conjugacy	NOUN
american_scientific_journal-3703	57	4	let	let	VERB
american_scientific_journal-3703	57	5	:	:	PUNCT
american_scientific_journal-3703	57	6	f	f	PROPN
american_scientific_journal-3703	57	7	a	a	DET
american_scientific_journal-3703	57	8	a→	a→	PROPN
american_scientific_journal-3703	57	9	and	and	CCONJ
american_scientific_journal-3703	57	10	:	:	PUNCT
american_scientific_journal-3703	57	11	g	g	PROPN
american_scientific_journal-3703	57	12	b	b	PROPN
american_scientific_journal-3703	57	13	b→	b→	PROPN
american_scientific_journal-3703	57	14	be	be	AUX
american_scientific_journal-3703	57	15	two	two	NUM
american_scientific_journal-3703	57	16	continuous	continuous	ADJ
american_scientific_journal-3703	57	17	mappings	mapping	NOUN
american_scientific_journal-3703	57	18	.	.	PUNCT
american_scientific_journal-3703	58	1	then	then	ADV
american_scientific_journal-3703	58	2	and	and	CCONJ
american_scientific_journal-3703	58	3	f	f	PROPN
american_scientific_journal-3703	58	4	g	g	PROPN
american_scientific_journal-3703	58	5	are	be	AUX
american_scientific_journal-3703	58	6	said	say	VERB
american_scientific_journal-3703	58	7	to	to	PART
american_scientific_journal-3703	58	8	be	be	AUX
american_scientific_journal-3703	58	9	topologically	topologically	ADV
american_scientific_journal-3703	58	10	conjugate	conjugate	ADJ
american_scientific_journal-3703	58	11	if	if	SCONJ
american_scientific_journal-3703	58	12	there	there	PRON
american_scientific_journal-3703	58	13	exists	exist	VERB
american_scientific_journal-3703	58	14	a	a	DET
american_scientific_journal-3703	58	15	homeomorphism	homeomorphism	NOUN
american_scientific_journal-3703	58	16	:	:	PUNCT
american_scientific_journal-3703	58	17	h	h	PRON
american_scientific_journal-3703	58	18	a	a	PRON
american_scientific_journal-3703	58	19	b→	b→	PROPN
american_scientific_journal-3703	59	1	such	such	ADJ
american_scientific_journal-3703	59	2	that	that	SCONJ
american_scientific_journal-3703	59	3	h	h	NOUN
american_scientific_journal-3703	59	4	f	f	NOUN
american_scientific_journal-3703	59	5	g	g	NOUN
american_scientific_journal-3703	59	6	h	h	PROPN
american_scientific_journal-3703	60	1	=	=	NOUN
american_scientific_journal-3703	60	2	o	o	X
american_scientific_journal-3703	60	3	o	o	X
american_scientific_journal-3703	60	4	.	.	PUNCT
american_scientific_journal-3703	61	1	the	the	DET
american_scientific_journal-3703	61	2	homeomorphism	homeomorphism	PROPN
american_scientific_journal-3703	61	3	h	h	PROPN
american_scientific_journal-3703	61	4	is	be	AUX
american_scientific_journal-3703	61	5	called	call	VERB
american_scientific_journal-3703	61	6	a	a	DET
american_scientific_journal-3703	61	7	topological	topological	ADJ
american_scientific_journal-3703	61	8	conjugacy	conjugacy	NOUN
american_scientific_journal-3703	61	9	between	between	ADP
american_scientific_journal-3703	61	10	and	and	CCONJ
american_scientific_journal-3703	61	11	f	f	PROPN
american_scientific_journal-3703	61	12	g	g	PROPN
american_scientific_journal-3703	61	13	.	.	PUNCT
american_scientific_journal-3703	62	1	3.1.9	3.1.9	NUM
american_scientific_journal-3703	62	2	compact	compact	ADJ
american_scientific_journal-3703	62	3	space	space	NOUN
american_scientific_journal-3703	62	4	:	:	PUNCT
american_scientific_journal-3703	62	5	let	let	VERB
american_scientific_journal-3703	62	6	𝑋𝑋	𝑋𝑋	PROPN
american_scientific_journal-3703	62	7	and	and	CCONJ
american_scientific_journal-3703	62	8	𝑌𝑌	𝑌𝑌	PROPN
american_scientific_journal-3703	62	9	be	be	VERB
american_scientific_journal-3703	62	10	metric	metric	ADJ
american_scientific_journal-3703	62	11	spaces	space	NOUN
american_scientific_journal-3703	62	12	.	.	PUNCT
american_scientific_journal-3703	63	1	we	we	PRON
american_scientific_journal-3703	63	2	say	say	VERB
american_scientific_journal-3703	63	3	that	that	SCONJ
american_scientific_journal-3703	63	4	the	the	DET
american_scientific_journal-3703	63	5	metric	metric	ADJ
american_scientific_journal-3703	63	6	space	space	NOUN
american_scientific_journal-3703	63	7	𝑋𝑋	𝑋𝑋	PROPN
american_scientific_journal-3703	63	8	is	be	AUX
american_scientific_journal-3703	63	9	compact	compact	ADJ
american_scientific_journal-3703	63	10	if	if	SCONJ
american_scientific_journal-3703	63	11	every	every	DET
american_scientific_journal-3703	63	12	open	open	ADJ
american_scientific_journal-3703	63	13	cover	cover	NOUN
american_scientific_journal-3703	63	14	of	of	ADP
american_scientific_journal-3703	63	15	𝑋𝑋	𝑋𝑋	PROPN
american_scientific_journal-3703	63	16	has	have	VERB
american_scientific_journal-3703	63	17	a	a	DET
american_scientific_journal-3703	63	18	finite	finite	ADJ
american_scientific_journal-3703	63	19	sub	sub	NOUN
american_scientific_journal-3703	63	20	cover	cover	NOUN
american_scientific_journal-3703	63	21	,	,	PUNCT
american_scientific_journal-3703	63	22	i.e.	i.e.	X
american_scientific_journal-3703	63	23	if	if	SCONJ
american_scientific_journal-3703	63	24	{	{	PUNCT
american_scientific_journal-3703	63	25	𝐼𝐼𝑖𝑖}𝑖𝑖∈𝐼𝐼	𝐼𝐼𝑖𝑖}𝑖𝑖∈𝐼𝐼	NOUN
american_scientific_journal-3703	63	26	is	be	AUX
american_scientific_journal-3703	63	27	a	a	DET
american_scientific_journal-3703	63	28	collection	collection	NOUN
american_scientific_journal-3703	63	29	of	of	ADP
american_scientific_journal-3703	63	30	open	open	ADJ
american_scientific_journal-3703	63	31	sets	set	NOUN
american_scientific_journal-3703	63	32	of	of	ADP
american_scientific_journal-3703	63	33	𝑋𝑋	𝑋𝑋	PROPN
american_scientific_journal-3703	63	34	such	such	ADJ
american_scientific_journal-3703	63	35	that	that	SCONJ
american_scientific_journal-3703	63	36	𝑋𝑋	𝑋𝑋	PROPN
american_scientific_journal-3703	63	37	⊂	⊂	PROPN
american_scientific_journal-3703	64	1	i	i	PRON
american_scientific_journal-3703	65	1	i	i	VERB
american_scientific_journal-3703	65	2	ii	ii	VERB
american_scientific_journal-3703	65	3	∈	∈	NOUN
american_scientific_journal-3703	65	4	u	u	NOUN
american_scientific_journal-3703	65	5	then	then	ADV
american_scientific_journal-3703	65	6	we	we	PRON
american_scientific_journal-3703	65	7	have	have	VERB
american_scientific_journal-3703	65	8	that	that	PRON
american_scientific_journal-3703	65	9	1	1	NUM
american_scientific_journal-3703	65	10	n	n	NOUN
american_scientific_journal-3703	66	1	i	i	PRON
american_scientific_journal-3703	67	1	i	i	INTJ
american_scientific_journal-3703	67	2	x	x	VERB
american_scientific_journal-3703	68	1	i	i	VERB
american_scientific_journal-3703	68	2	=	=	PUNCT
american_scientific_journal-3703	68	3	⊂u	⊂u	NOUN
american_scientific_journal-3703	68	4	.also	.also	PUNCT
american_scientific_journal-3703	68	5	compact	compact	ADJ
american_scientific_journal-3703	68	6	spaces	space	NOUN
american_scientific_journal-3703	68	7	on	on	ADP
american_scientific_journal-3703	68	8	the	the	DET
american_scientific_journal-3703	68	9	real	real	ADJ
american_scientific_journal-3703	68	10	line	line	NOUN
american_scientific_journal-3703	68	11	can	can	AUX
american_scientific_journal-3703	68	12	be	be	AUX
american_scientific_journal-3703	68	13	thought	think	VERB
american_scientific_journal-3703	68	14	as	as	ADP
american_scientific_journal-3703	68	15	closed	closed	ADJ
american_scientific_journal-3703	68	16	and	and	CCONJ
american_scientific_journal-3703	68	17	bounded	bounded	ADJ
american_scientific_journal-3703	68	18	intervals	interval	NOUN
american_scientific_journal-3703	68	19	.	.	PUNCT
american_scientific_journal-3703	69	1	3.1.10	3.1.10	NUM
american_scientific_journal-3703	69	2	lyapunov	lyapunov	ADJ
american_scientific_journal-3703	69	3	exponent	exponent	NOUN
american_scientific_journal-3703	69	4	let	let	VERB
american_scientific_journal-3703	69	5	:	:	PUNCT
american_scientific_journal-3703	69	6	f	f	PROPN
american_scientific_journal-3703	69	7	→	→	SYM
american_scientific_journal-3703	69	8	¡	¡	PROPN
american_scientific_journal-3703	69	9	¡	¡	PROPN
american_scientific_journal-3703	69	10	be	be	AUX
american_scientific_journal-3703	69	11	a	a	DET
american_scientific_journal-3703	69	12	continuous	continuous	ADJ
american_scientific_journal-3703	69	13	and	and	CCONJ
american_scientific_journal-3703	69	14	differentiable	differentiable	ADJ
american_scientific_journal-3703	69	15	map	map	NOUN
american_scientific_journal-3703	69	16	.	.	PUNCT
american_scientific_journal-3703	70	1	then	then	ADV
american_scientific_journal-3703	70	2	x∀	x∀	PROPN
american_scientific_journal-3703	70	3	∈	∈	PROPN
american_scientific_journal-3703	70	4	¡	¡	NOUN
american_scientific_journal-3703	70	5	we	we	PRON
american_scientific_journal-3703	70	6	define	define	VERB
american_scientific_journal-3703	70	7	the	the	DET
american_scientific_journal-3703	70	8	(	(	PUNCT
american_scientific_journal-3703	70	9	local	local	ADJ
american_scientific_journal-3703	70	10	)	)	PUNCT
american_scientific_journal-3703	70	11	lyapunov	lyapunov	NOUN
american_scientific_journal-3703	70	12	exponent	exponent	NOUN
american_scientific_journal-3703	70	13	of	of	ADP
american_scientific_journal-3703	70	14	x	x	PART
american_scientific_journal-3703	70	15	say	say	VERB
american_scientific_journal-3703	70	16	(	(	PUNCT
american_scientific_journal-3703	70	17	)	)	PUNCT
american_scientific_journal-3703	70	18	xλ	xλ	NOUN
american_scientific_journal-3703	70	19	as	as	ADP
american_scientific_journal-3703	70	20	(	(	PUNCT
american_scientific_journal-3703	70	21	)	)	PUNCT
american_scientific_journal-3703	70	22	(	(	PUNCT
american_scientific_journal-3703	70	23	)	)	PUNCT
american_scientific_journal-3703	70	24	1	1	NUM
american_scientific_journal-3703	70	25	'	'	NOUN
american_scientific_journal-3703	70	26	0	0	NUM
american_scientific_journal-3703	71	1	1lim	1lim	NUM
american_scientific_journal-3703	71	2	log	log	NOUN
american_scientific_journal-3703	71	3	n	n	INTJ
american_scientific_journal-3703	71	4	i	i	PRON
american_scientific_journal-3703	71	5	in	in	ADP
american_scientific_journal-3703	71	6	i	i	PROPN
american_scientific_journal-3703	71	7	x	x	PROPN
american_scientific_journal-3703	71	8	f	f	NOUN
american_scientific_journal-3703	71	9	x	x	SYM
american_scientific_journal-3703	71	10	x	x	SYM
american_scientific_journal-3703	71	11	n	n	ADP
american_scientific_journal-3703	71	12	λ	λ	X
american_scientific_journal-3703	71	13	−	−	NOUN
american_scientific_journal-3703	71	14	→∞	→∞	X
american_scientific_journal-3703	71	15	=	=	SYM
american_scientific_journal-3703	71	16	=	=	SYM
american_scientific_journal-3703	71	17	∀	∀	NOUN
american_scientific_journal-3703	71	18	∈∑	∈∑	PROPN
american_scientific_journal-3703	71	19	¡	¡	PROPN
american_scientific_journal-3703	71	20	.	.	PUNCT
american_scientific_journal-3703	72	1	3.1.11	3.1.11	NUM
american_scientific_journal-3703	72	2	scrambled	scramble	VERB
american_scientific_journal-3703	72	3	set	set	NOUN
american_scientific_journal-3703	72	4	consider	consider	VERB
american_scientific_journal-3703	72	5	an	an	DET
american_scientific_journal-3703	72	6	interval	interval	NOUN
american_scientific_journal-3703	72	7	i	i	PRON
american_scientific_journal-3703	72	8	and	and	CCONJ
american_scientific_journal-3703	72	9	the	the	DET
american_scientific_journal-3703	72	10	continuous	continuous	ADJ
american_scientific_journal-3703	72	11	map	map	NOUN
american_scientific_journal-3703	72	12	:	:	PUNCT
american_scientific_journal-3703	72	13	f	f	X
american_scientific_journal-3703	72	14	i	i	PRON
american_scientific_journal-3703	72	15	i→	i→	VERB
american_scientific_journal-3703	72	16	.then	.then	VERB
american_scientific_journal-3703	72	17	an	an	DET
american_scientific_journal-3703	72	18	uncountable	uncountable	ADJ
american_scientific_journal-3703	72	19	subset	subset	NOUN
american_scientific_journal-3703	72	20	𝑆𝑆	𝑆𝑆	PROPN
american_scientific_journal-3703	72	21	of	of	ADP
american_scientific_journal-3703	72	22	i	i	PRON
american_scientific_journal-3703	72	23	containing	contain	VERB
american_scientific_journal-3703	72	24	no	no	DET
american_scientific_journal-3703	72	25	periodic	periodic	ADJ
american_scientific_journal-3703	72	26	points	point	NOUN
american_scientific_journal-3703	72	27	of	of	ADP
american_scientific_journal-3703	72	28	f	f	PROPN
american_scientific_journal-3703	72	29	is	be	AUX
american_scientific_journal-3703	72	30	said	say	VERB
american_scientific_journal-3703	72	31	to	to	PART
american_scientific_journal-3703	72	32	be	be	AUX
american_scientific_journal-3703	72	33	scrambled	scramble	VERB
american_scientific_journal-3703	72	34	if	if	SCONJ
american_scientific_journal-3703	72	35	:	:	PUNCT
american_scientific_journal-3703	73	1	1	1	X
american_scientific_journal-3703	73	2	.	.	X
american_scientific_journal-3703	73	3	any	any	DET
american_scientific_journal-3703	73	4	periodic	periodic	ADJ
american_scientific_journal-3703	73	5	point	point	NOUN
american_scientific_journal-3703	73	6	𝑝𝑝	𝑝𝑝	NOUN
american_scientific_journal-3703	73	7	of	of	ADP
american_scientific_journal-3703	73	8	f	f	PROPN
american_scientific_journal-3703	73	9	and	and	CCONJ
american_scientific_journal-3703	73	10	any	any	DET
american_scientific_journal-3703	73	11	point	point	NOUN
american_scientific_journal-3703	73	12	x	x	PUNCT
american_scientific_journal-3703	73	13	i∈	i∈	ADP
american_scientific_journal-3703	73	14	satisfies	satisfie	NOUN
american_scientific_journal-3703	73	15	(	(	PUNCT
american_scientific_journal-3703	73	16	)	)	PUNCT
american_scientific_journal-3703	73	17	(	(	PUNCT
american_scientific_journal-3703	73	18	)	)	PUNCT
american_scientific_journal-3703	73	19	lim	lim	PROPN
american_scientific_journal-3703	73	20	sup	sup	PROPN
american_scientific_journal-3703	73	21	0n	0n	PROPN
american_scientific_journal-3703	73	22	n	n	CCONJ
american_scientific_journal-3703	73	23	n	n	NOUN
american_scientific_journal-3703	74	1	f	f	NOUN
american_scientific_journal-3703	74	2	x	x	SYM
american_scientific_journal-3703	74	3	f	f	PROPN
american_scientific_journal-3703	74	4	p	p	X
american_scientific_journal-3703	74	5	→∞	→∞	PROPN
american_scientific_journal-3703	74	6	−	−	X
american_scientific_journal-3703	74	7	>	>	X
american_scientific_journal-3703	74	8	.	.	PUNCT
american_scientific_journal-3703	75	1	2	2	X
american_scientific_journal-3703	75	2	.	.	PUNCT
american_scientific_journal-3703	75	3	(	(	PUNCT
american_scientific_journal-3703	75	4	)	)	PUNCT
american_scientific_journal-3703	75	5	(	(	PUNCT
american_scientific_journal-3703	75	6	)	)	PUNCT
american_scientific_journal-3703	75	7	(	(	PUNCT
american_scientific_journal-3703	75	8	)	)	PUNCT
american_scientific_journal-3703	75	9	(	(	PUNCT
american_scientific_journal-3703	75	10	)	)	PUNCT
american_scientific_journal-3703	75	11	x	x	X
american_scientific_journal-3703	75	12	,	,	PUNCT
american_scientific_journal-3703	75	13	y	y	PROPN
american_scientific_journal-3703	75	14	,	,	PUNCT
american_scientific_journal-3703	75	15	lim	lim	PROPN
american_scientific_journal-3703	75	16	sup	sup	PROPN
american_scientific_journal-3703	75	17	0	0	NUM
american_scientific_journal-3703	75	18	and	and	CCONJ
american_scientific_journal-3703	75	19	lim	lim	PROPN
american_scientific_journal-3703	75	20	inf	inf	PROPN
american_scientific_journal-3703	75	21	0.n	0.n	NUM
american_scientific_journal-3703	75	22	n	n	CCONJ
american_scientific_journal-3703	75	23	n	n	CCONJ
american_scientific_journal-3703	75	24	n	n	CCONJ
american_scientific_journal-3703	75	25	n	n	CCONJ
american_scientific_journal-3703	75	26	n	n	NOUN
american_scientific_journal-3703	76	1	x	x	SYM
american_scientific_journal-3703	76	2	f	f	NOUN
american_scientific_journal-3703	76	3	x	x	X
american_scientific_journal-3703	76	4	f	f	PROPN
american_scientific_journal-3703	76	5	y	y	NOUN
american_scientific_journal-3703	76	6	f	f	PROPN
american_scientific_journal-3703	76	7	x	x	X
american_scientific_journal-3703	76	8	f	f	PROPN
american_scientific_journal-3703	76	9	y	y	PROPN
american_scientific_journal-3703	76	10	→∞	→∞	PROPN
american_scientific_journal-3703	76	11	→∞	→∞	PROPN
american_scientific_journal-3703	76	12	∀	∀	NOUN
american_scientific_journal-3703	76	13	∈	∈	NOUN
american_scientific_journal-3703	76	14	−	−	PROPN
american_scientific_journal-3703	76	15	>	>	PUNCT
american_scientific_journal-3703	76	16	−	−	PROPN
american_scientific_journal-3703	77	1	=	=	NOUN
american_scientific_journal-3703	77	2	3.2	3.2	NUM
american_scientific_journal-3703	77	3	several	several	ADJ
american_scientific_journal-3703	77	4	definitions	definition	NOUN
american_scientific_journal-3703	77	5	of	of	ADP
american_scientific_journal-3703	77	6	chaos	chaos	NOUN
american_scientific_journal-3703	77	7	american	american	ADJ
american_scientific_journal-3703	77	8	scientific	scientific	PROPN
american_scientific_journal-3703	77	9	research	research	PROPN
american_scientific_journal-3703	77	10	journal	journal	NOUN
american_scientific_journal-3703	77	11	for	for	ADP
american_scientific_journal-3703	77	12	engineering	engineering	NOUN
american_scientific_journal-3703	77	13	,	,	PUNCT
american_scientific_journal-3703	77	14	technology	technology	NOUN
american_scientific_journal-3703	77	15	,	,	PUNCT
american_scientific_journal-3703	77	16	and	and	CCONJ
american_scientific_journal-3703	77	17	sciences	science	NOUN
american_scientific_journal-3703	77	18	(	(	PUNCT
american_scientific_journal-3703	77	19	asrjets	asrjet	NOUN
american_scientific_journal-3703	77	20	)	)	PUNCT
american_scientific_journal-3703	77	21	(	(	PUNCT
american_scientific_journal-3703	77	22	2018	2018	NUM
american_scientific_journal-3703	77	23	)	)	PUNCT
american_scientific_journal-3703	77	24	volume	volume	NOUN
american_scientific_journal-3703	77	25	43	43	NUM
american_scientific_journal-3703	77	26	,	,	PUNCT
american_scientific_journal-3703	77	27	no	no	DET
american_scientific_journal-3703	77	28	1	1	NUM
american_scientific_journal-3703	77	29	,	,	PUNCT
american_scientific_journal-3703	77	30	pp	pp	ADV
american_scientific_journal-3703	77	31	110	110	NUM
american_scientific_journal-3703	77	32	-	-	SYM
american_scientific_journal-3703	77	33	133	133	NUM
american_scientific_journal-3703	77	34	114	114	NUM
american_scientific_journal-3703	77	35	in	in	ADP
american_scientific_journal-3703	77	36	the	the	DET
american_scientific_journal-3703	77	37	following	following	NOUN
american_scientific_journal-3703	77	38	we	we	PRON
american_scientific_journal-3703	77	39	give	give	VERB
american_scientific_journal-3703	77	40	some	some	DET
american_scientific_journal-3703	77	41	important	important	ADJ
american_scientific_journal-3703	77	42	mathematical	mathematical	ADJ
american_scientific_journal-3703	77	43	definitions	definition	NOUN
american_scientific_journal-3703	77	44	of	of	ADP
american_scientific_journal-3703	77	45	chaos	chaos	NOUN
american_scientific_journal-3703	77	46	by	by	ADP
american_scientific_journal-3703	77	47	some	some	DET
american_scientific_journal-3703	77	48	pioneers	pioneer	NOUN
american_scientific_journal-3703	77	49	.	.	PUNCT
american_scientific_journal-3703	78	1	3.2.1	3.2.1	NUM
american_scientific_journal-3703	78	2	devaney	devaney	PROPN
american_scientific_journal-3703	78	3	’s	’s	PART
american_scientific_journal-3703	78	4	definition	definition	NOUN
american_scientific_journal-3703	78	5	[	[	X
american_scientific_journal-3703	78	6	9	9	NUM
american_scientific_journal-3703	78	7	]	]	PUNCT
american_scientific_journal-3703	78	8	(	(	PUNCT
american_scientific_journal-3703	78	9	r.	r.	PROPN
american_scientific_journal-3703	78	10	l.	l.	PROPN
american_scientific_journal-3703	78	11	devaney	devaney	PROPN
american_scientific_journal-3703	78	12	1989	1989	NUM
american_scientific_journal-3703	78	13	)	)	PUNCT
american_scientific_journal-3703	78	14	let	let	VERB
american_scientific_journal-3703	78	15	x	x	PRON
american_scientific_journal-3703	78	16	be	be	AUX
american_scientific_journal-3703	78	17	a	a	DET
american_scientific_journal-3703	78	18	metric	metric	ADJ
american_scientific_journal-3703	78	19	space	space	NOUN
american_scientific_journal-3703	78	20	.	.	PUNCT
american_scientific_journal-3703	79	1	a	a	DET
american_scientific_journal-3703	79	2	continuous	continuous	ADJ
american_scientific_journal-3703	79	3	function	function	NOUN
american_scientific_journal-3703	79	4	:	:	PUNCT
american_scientific_journal-3703	79	5	f	f	X
american_scientific_journal-3703	79	6	x	x	PUNCT
american_scientific_journal-3703	79	7	x→	x→	PROPN
american_scientific_journal-3703	79	8	is	be	AUX
american_scientific_journal-3703	79	9	said	say	VERB
american_scientific_journal-3703	79	10	to	to	PART
american_scientific_journal-3703	79	11	be	be	AUX
american_scientific_journal-3703	79	12	chaotic	chaotic	ADJ
american_scientific_journal-3703	79	13	on	on	ADP
american_scientific_journal-3703	79	14	x	x	SYM
american_scientific_journal-3703	79	15	if	if	SCONJ
american_scientific_journal-3703	79	16	f	f	PROPN
american_scientific_journal-3703	79	17	has	have	VERB
american_scientific_journal-3703	79	18	the	the	DET
american_scientific_journal-3703	79	19	following	follow	VERB
american_scientific_journal-3703	79	20	three	three	NUM
american_scientific_journal-3703	79	21	properties	property	NOUN
american_scientific_journal-3703	79	22	:	:	PUNCT
american_scientific_journal-3703	79	23	(	(	PUNCT
american_scientific_journal-3703	79	24	c-1	c-1	NOUN
american_scientific_journal-3703	79	25	)	)	PUNCT
american_scientific_journal-3703	79	26	periodic	periodic	ADJ
american_scientific_journal-3703	79	27	points	point	NOUN
american_scientific_journal-3703	79	28	are	be	AUX
american_scientific_journal-3703	79	29	dense	dense	ADJ
american_scientific_journal-3703	79	30	in	in	ADP
american_scientific_journal-3703	79	31	the	the	DET
american_scientific_journal-3703	79	32	space	space	NOUN
american_scientific_journal-3703	79	33	x	x	X
american_scientific_journal-3703	79	34	(	(	PUNCT
american_scientific_journal-3703	79	35	c-2	c-2	NOUN
american_scientific_journal-3703	79	36	)	)	PUNCT
american_scientific_journal-3703	79	37	f	f	PROPN
american_scientific_journal-3703	79	38	is	be	AUX
american_scientific_journal-3703	79	39	topologically	topologically	ADV
american_scientific_journal-3703	79	40	transitive	transitive	ADJ
american_scientific_journal-3703	79	41	(	(	PUNCT
american_scientific_journal-3703	79	42	c-3	c-3	PROPN
american_scientific_journal-3703	79	43	)	)	PUNCT
american_scientific_journal-3703	80	1	f	f	PROPN
american_scientific_journal-3703	80	2	has	have	VERB
american_scientific_journal-3703	80	3	sensitive	sensitive	ADJ
american_scientific_journal-3703	80	4	dependence	dependence	NOUN
american_scientific_journal-3703	80	5	on	on	ADP
american_scientific_journal-3703	80	6	initial	initial	ADJ
american_scientific_journal-3703	80	7	conditions	condition	NOUN
american_scientific_journal-3703	80	8	mathematically	mathematically	ADV
american_scientific_journal-3703	80	9	,	,	PUNCT
american_scientific_journal-3703	80	10	(	(	PUNCT
american_scientific_journal-3703	80	11	c-1	c-1	NOUN
american_scientific_journal-3703	80	12	)	)	PUNCT
american_scientific_journal-3703	80	13	(	(	PUNCT
american_scientific_journal-3703	80	14	)	)	PUNCT
american_scientific_journal-3703	81	1	kp	kp	PROPN
american_scientific_journal-3703	81	2	f	f	PROPN
american_scientific_journal-3703	82	1	=	=	PRON
american_scientific_journal-3703	82	2	{	{	PUNCT
american_scientific_journal-3703	82	3	:	:	PUNCT
american_scientific_journal-3703	82	4	(	(	PUNCT
american_scientific_journal-3703	82	5	)	)	PUNCT
american_scientific_journal-3703	82	6	(	(	PUNCT
american_scientific_journal-3703	82	7	)	)	PUNCT
american_scientific_journal-3703	82	8	}	}	PUNCT
american_scientific_journal-3703	82	9	kx	kx	NOUN
american_scientific_journal-3703	82	10	x	x	X
american_scientific_journal-3703	83	1	f	f	X
american_scientific_journal-3703	83	2	x	x	PUNCT
american_scientific_journal-3703	83	3	x	x	X
american_scientific_journal-3703	83	4	k∈	k∈	PROPN
american_scientific_journal-3703	83	5	=	=	PUNCT
american_scientific_journal-3703	83	6	∃	∃	PROPN
american_scientific_journal-3703	83	7	∈n	∈n	NOUN
american_scientific_journal-3703	83	8	is	be	AUX
american_scientific_journal-3703	83	9	dense	dense	ADJ
american_scientific_journal-3703	83	10	in	in	ADP
american_scientific_journal-3703	83	11	.x	.x	PROPN
american_scientific_journal-3703	83	12	(	(	PUNCT
american_scientific_journal-3703	83	13	c-2	c-2	NOUN
american_scientific_journal-3703	83	14	)	)	PUNCT
american_scientific_journal-3703	83	15	for	for	ADP
american_scientific_journal-3703	83	16	,	,	PUNCT
american_scientific_journal-3703	83	17	:	:	PUNCT
american_scientific_journal-3703	83	18	u	u	NOUN
american_scientific_journal-3703	83	19	v	v	VERB
american_scientific_journal-3703	83	20	non	non	X
american_scientific_journal-3703	83	21	empty	empty	ADJ
american_scientific_journal-3703	83	22	open	open	ADJ
american_scientific_journal-3703	83	23	sets∀	sets∀	PROPN
american_scientific_journal-3703	83	24	−	−	PROPN
american_scientific_journal-3703	83	25	of	of	ADP
american_scientific_journal-3703	83	26	x	x	PROPN
american_scientific_journal-3703	83	27	,	,	PUNCT
american_scientific_journal-3703	83	28	k∃	k∃	VERB
american_scientific_journal-3703	83	29	∈n	∈n	VERB
american_scientific_journal-3703	83	30	such	such	ADJ
american_scientific_journal-3703	83	31	that	that	PRON
american_scientific_journal-3703	83	32	.	.	PUNCT
american_scientific_journal-3703	83	33	)	)	PUNCT
american_scientific_journal-3703	84	1	(	(	PUNCT
american_scientific_journal-3703	84	2	f≠∩vuf	f≠∩vuf	NOUN
american_scientific_journal-3703	84	3	k	k	PROPN
american_scientific_journal-3703	84	4	(	(	PUNCT
american_scientific_journal-3703	84	5	c-3	c-3	NOUN
american_scientific_journal-3703	84	6	)	)	PUNCT
american_scientific_journal-3703	85	1	0>∃δ	0>∃δ	PROPN
american_scientific_journal-3703	85	2	(	(	PUNCT
american_scientific_journal-3703	85	3	sensitive	sensitive	ADJ
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american_scientific_journal-3703	85	5	)	)	PUNCT
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american_scientific_journal-3703	85	7	satisfies	satisfy	VERB
american_scientific_journal-3703	85	8	:	:	PUNCT
american_scientific_journal-3703	85	9	)	)	PUNCT
american_scientific_journal-3703	85	10	,	,	PUNCT
american_scientific_journal-3703	85	11	(	(	PUNCT
american_scientific_journal-3703	85	12	)	)	PUNCT
american_scientific_journal-3703	85	13	,	,	PUNCT
american_scientific_journal-3703	85	14	,	,	PUNCT
american_scientific_journal-3703	85	15	(	(	PUNCT
american_scientific_journal-3703	85	16	εε	εε	ADP
american_scientific_journal-3703	85	17	xnyxnandxx	xnyxnandxx	NOUN
american_scientific_journal-3703	85	18	∈∃∀∈∀	∈∃∀∈∀	PROPN
american_scientific_journal-3703	85	19	and	and	CCONJ
american_scientific_journal-3703	85	20	0≤∃	0≤∃	NUM
american_scientific_journal-3703	86	1	k	k	PRON
american_scientific_journal-3703	86	2	such	such	ADJ
american_scientific_journal-3703	86	3	that	that	PRON
american_scientific_journal-3703	86	4	[	[	X
american_scientific_journal-3703	86	5	]	]	X
american_scientific_journal-3703	86	6	(	(	PUNCT
american_scientific_journal-3703	86	7	(	(	PUNCT
american_scientific_journal-3703	86	8	)	)	PUNCT
american_scientific_journal-3703	86	9	,	,	PUNCT
american_scientific_journal-3703	86	10	(	(	PUNCT
american_scientific_journal-3703	86	11	)	)	PUNCT
american_scientific_journal-3703	86	12	)	)	PUNCT
american_scientific_journal-3703	86	13	4	4	NUM
american_scientific_journal-3703	86	14	.k	.k	NOUN
american_scientific_journal-3703	87	1	kd	kd	PROPN
american_scientific_journal-3703	87	2	f	f	PROPN
american_scientific_journal-3703	87	3	x	x	PROPN
american_scientific_journal-3703	87	4	f	f	PROPN
american_scientific_journal-3703	87	5	y	y	PROPN
american_scientific_journal-3703	87	6	δ	δ	PROPN
american_scientific_journal-3703	87	7	>	>	X
american_scientific_journal-3703	87	8	in	in	ADP
american_scientific_journal-3703	87	9	other	other	ADJ
american_scientific_journal-3703	87	10	words	word	NOUN
american_scientific_journal-3703	87	11	,	,	PUNCT
american_scientific_journal-3703	87	12	a	a	DET
american_scientific_journal-3703	87	13	continuous	continuous	ADJ
american_scientific_journal-3703	87	14	map	map	NOUN
american_scientific_journal-3703	87	15	:	:	PUNCT
american_scientific_journal-3703	87	16	f	f	X
american_scientific_journal-3703	87	17	x	x	X
american_scientific_journal-3703	87	18	x→	x→	PUNCT
american_scientific_journal-3703	87	19	on	on	ADP
american_scientific_journal-3703	87	20	a	a	DET
american_scientific_journal-3703	87	21	compact	compact	ADJ
american_scientific_journal-3703	87	22	metric	metric	ADJ
american_scientific_journal-3703	87	23	space	space	NOUN
american_scientific_journal-3703	87	24	x	x	PUNCT
american_scientific_journal-3703	87	25	is	be	AUX
american_scientific_journal-3703	87	26	called	call	VERB
american_scientific_journal-3703	87	27	chaotic	chaotic	ADJ
american_scientific_journal-3703	87	28	in	in	ADP
american_scientific_journal-3703	87	29	the	the	DET
american_scientific_journal-3703	87	30	sense	sense	NOUN
american_scientific_journal-3703	87	31	of	of	ADP
american_scientific_journal-3703	87	32	devaney	devaney	PROPN
american_scientific_journal-3703	87	33	–	–	PUNCT
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american_scientific_journal-3703	87	35	just	just	ADV
american_scientific_journal-3703	87	36	d	d	ADJ
american_scientific_journal-3703	87	37	-	-	PUNCT
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american_scientific_journal-3703	87	39	if	if	SCONJ
american_scientific_journal-3703	87	40	there	there	PRON
american_scientific_journal-3703	87	41	exists	exist	VERB
american_scientific_journal-3703	87	42	a	a	DET
american_scientific_journal-3703	87	43	compact	compact	ADJ
american_scientific_journal-3703	87	44	invariant	invariant	NOUN
american_scientific_journal-3703	87	45	subset	subset	NOUN
american_scientific_journal-3703	87	46	y	y	PROPN
american_scientific_journal-3703	87	47	(	(	PUNCT
american_scientific_journal-3703	87	48	called	call	VERB
american_scientific_journal-3703	87	49	a	a	DET
american_scientific_journal-3703	87	50	d	d	ADJ
american_scientific_journal-3703	87	51	-	-	ADJ
american_scientific_journal-3703	87	52	chaotic	chaotic	ADJ
american_scientific_journal-3703	87	53	set	set	NOUN
american_scientific_journal-3703	87	54	)	)	PUNCT
american_scientific_journal-3703	87	55	of	of	ADP
american_scientific_journal-3703	87	56	x	x	PUNCT
american_scientific_journal-3703	87	57	with	with	ADP
american_scientific_journal-3703	87	58	the	the	DET
american_scientific_journal-3703	87	59	following	follow	VERB
american_scientific_journal-3703	87	60	properties	property	NOUN
american_scientific_journal-3703	87	61	:	:	PUNCT
american_scientific_journal-3703	87	62	(	(	PUNCT
american_scientific_journal-3703	87	63	)	)	PUNCT
american_scientific_journal-3703	87	64	|	|	ADV
american_scientific_journal-3703	87	65	i	i	PRON
american_scientific_journal-3703	87	66	f	f	PROPN
american_scientific_journal-3703	87	67	y	y	PROPN
american_scientific_journal-3703	87	68	is	be	AUX
american_scientific_journal-3703	87	69	transitive	transitive	ADJ
american_scientific_journal-3703	87	70	,	,	PUNCT
american_scientific_journal-3703	87	71	(	(	PUNCT
american_scientific_journal-3703	87	72	)	)	PUNCT
american_scientific_journal-3703	87	73	(	(	PUNCT
american_scientific_journal-3703	87	74	)	)	PUNCT
american_scientific_journal-3703	88	1	|	|	ADV
american_scientific_journal-3703	88	2	ii	ii	NOUN
american_scientific_journal-3703	89	1	p	p	X
american_scientific_journal-3703	89	2	f	f	PROPN
american_scientific_journal-3703	89	3	y	y	PROPN
american_scientific_journal-3703	89	4	y=	y=	PROPN
american_scientific_journal-3703	89	5	,	,	PUNCT
american_scientific_journal-3703	89	6	(	(	PUNCT
american_scientific_journal-3703	89	7	)	)	PUNCT
american_scientific_journal-3703	89	8	|	|	ADV
american_scientific_journal-3703	89	9	iii	iii	X
american_scientific_journal-3703	89	10	f	f	X
american_scientific_journal-3703	89	11	y	y	PROPN
american_scientific_journal-3703	89	12	has	have	VERB
american_scientific_journal-3703	89	13	sensitive	sensitive	ADJ
american_scientific_journal-3703	89	14	dependence	dependence	NOUN
american_scientific_journal-3703	89	15	on	on	ADP
american_scientific_journal-3703	89	16	initial	initial	ADJ
american_scientific_journal-3703	89	17	conditions	condition	NOUN
american_scientific_journal-3703	89	18	.	.	PUNCT
american_scientific_journal-3703	90	1	3.2.2	3.2.2	NUM
american_scientific_journal-3703	90	2	li	li	NOUN
american_scientific_journal-3703	90	3	and	and	CCONJ
american_scientific_journal-3703	90	4	yorke	yorke	PROPN
american_scientific_journal-3703	90	5	definition	definition	NOUN
american_scientific_journal-3703	90	6	[	[	X
american_scientific_journal-3703	90	7	7	7	X
american_scientific_journal-3703	90	8	]	]	X
american_scientific_journal-3703	90	9	a	a	DET
american_scientific_journal-3703	90	10	continuous	continuous	ADJ
american_scientific_journal-3703	90	11	map	map	NOUN
american_scientific_journal-3703	90	12	:	:	PUNCT
american_scientific_journal-3703	90	13	f	f	X
american_scientific_journal-3703	90	14	x	x	X
american_scientific_journal-3703	90	15	x→	x→	PUNCT
american_scientific_journal-3703	90	16	on	on	ADP
american_scientific_journal-3703	90	17	a	a	DET
american_scientific_journal-3703	90	18	compact	compact	ADJ
american_scientific_journal-3703	90	19	metric	metric	ADJ
american_scientific_journal-3703	90	20	space	space	NOUN
american_scientific_journal-3703	90	21	(	(	PUNCT
american_scientific_journal-3703	90	22	)	)	PUNCT
american_scientific_journal-3703	90	23	,	,	PUNCT
american_scientific_journal-3703	90	24	x	x	X
american_scientific_journal-3703	90	25	d	d	NOUN
american_scientific_journal-3703	90	26	is	be	AUX
american_scientific_journal-3703	90	27	called	call	VERB
american_scientific_journal-3703	90	28	chaotic	chaotic	ADJ
american_scientific_journal-3703	90	29	in	in	ADP
american_scientific_journal-3703	90	30	the	the	DET
american_scientific_journal-3703	90	31	sense	sense	NOUN
american_scientific_journal-3703	90	32	of	of	ADP
american_scientific_journal-3703	90	33	li	li	PROPN
american_scientific_journal-3703	90	34	and	and	CCONJ
american_scientific_journal-3703	90	35	yorke	yorke	PROPN
american_scientific_journal-3703	90	36	–	–	PUNCT
american_scientific_journal-3703	90	37	or	or	CCONJ
american_scientific_journal-3703	90	38	just	just	ADV
american_scientific_journal-3703	90	39	l	l	NOUN
american_scientific_journal-3703	90	40	/	/	SYM
american_scientific_journal-3703	90	41	y	y	NOUN
american_scientific_journal-3703	90	42	-	-	NOUN
american_scientific_journal-3703	90	43	chaotic	chaotic	ADJ
american_scientific_journal-3703	90	44	–	–	PUNCT
american_scientific_journal-3703	90	45	if	if	SCONJ
american_scientific_journal-3703	90	46	there	there	PRON
american_scientific_journal-3703	90	47	exists	exist	VERB
american_scientific_journal-3703	90	48	an	an	DET
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american_scientific_journal-3703	90	50	subset	subset	NOUN
american_scientific_journal-3703	90	51	s	s	X
american_scientific_journal-3703	90	52	(	(	PUNCT
american_scientific_journal-3703	90	53	called	call	VERB
american_scientific_journal-3703	90	54	a	a	DET
american_scientific_journal-3703	90	55	scrambled	scramble	VERB
american_scientific_journal-3703	90	56	set	set	NOUN
american_scientific_journal-3703	90	57	)	)	PUNCT
american_scientific_journal-3703	90	58	of	of	ADP
american_scientific_journal-3703	90	59	x	x	PUNCT
american_scientific_journal-3703	90	60	with	with	ADP
american_scientific_journal-3703	90	61	the	the	DET
american_scientific_journal-3703	90	62	following	follow	VERB
american_scientific_journal-3703	90	63	properties	property	NOUN
american_scientific_journal-3703	90	64	:	:	PUNCT
american_scientific_journal-3703	90	65	(	(	PUNCT
american_scientific_journal-3703	90	66	)	)	PUNCT
american_scientific_journal-3703	90	67	(	(	PUNCT
american_scientific_journal-3703	90	68	)	)	PUNCT
american_scientific_journal-3703	90	69	(	(	PUNCT
american_scientific_journal-3703	90	70	)	)	PUNCT
american_scientific_journal-3703	90	71	(	(	PUNCT
american_scientific_journal-3703	90	72	)	)	PUNCT
american_scientific_journal-3703	90	73	lim	lim	PROPN
american_scientific_journal-3703	90	74	,	,	PUNCT
american_scientific_journal-3703	90	75	0	0	NUM
american_scientific_journal-3703	90	76	for	for	ADP
american_scientific_journal-3703	90	77	all	all	PRON
american_scientific_journal-3703	90	78	,	,	PUNCT
american_scientific_journal-3703	90	79	,	,	PUNCT
american_scientific_journal-3703	90	80	,	,	PUNCT
american_scientific_journal-3703	90	81	n	n	CCONJ
american_scientific_journal-3703	90	82	n	n	NOUN
american_scientific_journal-3703	90	83	i	i	PRON
american_scientific_journal-3703	90	84	sup	sup	VERB
american_scientific_journal-3703	91	1	d	d	NOUN
american_scientific_journal-3703	91	2	f	f	X
american_scientific_journal-3703	91	3	x	x	SYM
american_scientific_journal-3703	91	4	f	f	PROPN
american_scientific_journal-3703	91	5	n	n	CCONJ
american_scientific_journal-3703	91	6	y	y	PROPN
american_scientific_journal-3703	91	7	x	x	PUNCT
american_scientific_journal-3703	91	8	y	y	PROPN
american_scientific_journal-3703	91	9	s	s	PROPN
american_scientific_journal-3703	91	10	x	x	VERB
american_scientific_journal-3703	91	11	y	y	PROPN
american_scientific_journal-3703	91	12	→∞	→∞	PROPN
american_scientific_journal-3703	91	13	>	>	SYM
american_scientific_journal-3703	91	14	∈	∈	PROPN
american_scientific_journal-3703	91	15	≠	≠	PROPN
american_scientific_journal-3703	91	16	(	(	PUNCT
american_scientific_journal-3703	91	17	)	)	PUNCT
american_scientific_journal-3703	91	18	(	(	PUNCT
american_scientific_journal-3703	91	19	)	)	PUNCT
american_scientific_journal-3703	91	20	(	(	PUNCT
american_scientific_journal-3703	91	21	)	)	PUNCT
american_scientific_journal-3703	91	22	(	(	PUNCT
american_scientific_journal-3703	91	23	)	)	PUNCT
american_scientific_journal-3703	91	24	lim	lim	PROPN
american_scientific_journal-3703	91	25	inf	inf	PROPN
american_scientific_journal-3703	91	26	,	,	PUNCT
american_scientific_journal-3703	91	27	0	0	NUM
american_scientific_journal-3703	91	28	for	for	ADP
american_scientific_journal-3703	91	29	all	all	PRON
american_scientific_journal-3703	91	30	,	,	PUNCT
american_scientific_journal-3703	91	31	,	,	PUNCT
american_scientific_journal-3703	91	32	,	,	PUNCT
american_scientific_journal-3703	91	33	n	n	CCONJ
american_scientific_journal-3703	91	34	n	n	CCONJ
american_scientific_journal-3703	91	35	n	n	NOUN
american_scientific_journal-3703	91	36	ii	ii	NOUN
american_scientific_journal-3703	92	1	d	d	X
american_scientific_journal-3703	92	2	f	f	PROPN
american_scientific_journal-3703	92	3	x	x	X
american_scientific_journal-3703	92	4	f	f	PROPN
american_scientific_journal-3703	92	5	y	y	PROPN
american_scientific_journal-3703	92	6	x	x	PUNCT
american_scientific_journal-3703	92	7	y	y	PROPN
american_scientific_journal-3703	92	8	s	s	PROPN
american_scientific_journal-3703	92	9	x	x	VERB
american_scientific_journal-3703	92	10	y	y	PROPN
american_scientific_journal-3703	92	11	→∞	→∞	PROPN
american_scientific_journal-3703	92	12	∈=	∈=	PUNCT
american_scientific_journal-3703	92	13	≠	≠	PROPN
american_scientific_journal-3703	92	14	(	(	PUNCT
american_scientific_journal-3703	92	15	)	)	PUNCT
american_scientific_journal-3703	92	16	(	(	PUNCT
american_scientific_journal-3703	92	17	)	)	PUNCT
american_scientific_journal-3703	92	18	(	(	PUNCT
american_scientific_journal-3703	92	19	)	)	PUNCT
american_scientific_journal-3703	92	20	(	(	PUNCT
american_scientific_journal-3703	92	21	)	)	PUNCT
american_scientific_journal-3703	92	22	>	>	PUNCT
american_scientific_journal-3703	92	23	0	0	PUNCT
american_scientific_journal-3703	93	1	lim	lim	PROPN
american_scientific_journal-3703	93	2	sup	sup	NOUN
american_scientific_journal-3703	93	3	,	,	PUNCT
american_scientific_journal-3703	93	4	for	for	ADP
american_scientific_journal-3703	93	5	all	all	PRON
american_scientific_journal-3703	93	6	,	,	PUNCT
american_scientific_journal-3703	93	7	,	,	PUNCT
american_scientific_journal-3703	93	8	periodic	periodic	NOUN
american_scientific_journal-3703	93	9	.	.	PUNCT
american_scientific_journal-3703	94	1	n	n	CCONJ
american_scientific_journal-3703	94	2	n	n	CCONJ
american_scientific_journal-3703	94	3	n	n	NOUN
american_scientific_journal-3703	94	4	iii	iii	X
american_scientific_journal-3703	95	1	d	d	NOUN
american_scientific_journal-3703	95	2	f	f	X
american_scientific_journal-3703	95	3	x	x	X
american_scientific_journal-3703	95	4	f	f	PROPN
american_scientific_journal-3703	95	5	y	y	PROPN
american_scientific_journal-3703	95	6	x	x	PROPN
american_scientific_journal-3703	95	7	s	s	X
american_scientific_journal-3703	95	8	p	p	X
american_scientific_journal-3703	95	9	x	x	X
american_scientific_journal-3703	95	10	p	p	X
american_scientific_journal-3703	95	11	→∞	→∞	PROPN
american_scientific_journal-3703	95	12	∈	∈	PROPN
american_scientific_journal-3703	95	13	∈	∈	PROPN
american_scientific_journal-3703	95	14	american	american	PROPN
american_scientific_journal-3703	95	15	scientific	scientific	PROPN
american_scientific_journal-3703	95	16	research	research	PROPN
american_scientific_journal-3703	95	17	journal	journal	NOUN
american_scientific_journal-3703	95	18	for	for	ADP
american_scientific_journal-3703	95	19	engineering	engineering	NOUN
american_scientific_journal-3703	95	20	,	,	PUNCT
american_scientific_journal-3703	95	21	technology	technology	NOUN
american_scientific_journal-3703	95	22	,	,	PUNCT
american_scientific_journal-3703	95	23	and	and	CCONJ
american_scientific_journal-3703	95	24	sciences	science	NOUN
american_scientific_journal-3703	95	25	(	(	PUNCT
american_scientific_journal-3703	95	26	asrjets	asrjet	NOUN
american_scientific_journal-3703	95	27	)	)	PUNCT
american_scientific_journal-3703	95	28	(	(	PUNCT
american_scientific_journal-3703	95	29	2018	2018	NUM
american_scientific_journal-3703	95	30	)	)	PUNCT
american_scientific_journal-3703	95	31	volume	volume	NOUN
american_scientific_journal-3703	95	32	43	43	NUM
american_scientific_journal-3703	95	33	,	,	PUNCT
american_scientific_journal-3703	95	34	no	no	DET
american_scientific_journal-3703	95	35	1	1	NUM
american_scientific_journal-3703	95	36	,	,	PUNCT
american_scientific_journal-3703	95	37	pp	pp	ADV
american_scientific_journal-3703	95	38	110	110	NUM
american_scientific_journal-3703	95	39	-	-	SYM
american_scientific_journal-3703	95	40	133	133	NUM
american_scientific_journal-3703	95	41	115	115	NUM
american_scientific_journal-3703	95	42	in	in	ADP
american_scientific_journal-3703	95	43	other	other	ADJ
american_scientific_journal-3703	95	44	words	word	NOUN
american_scientific_journal-3703	95	45	,	,	PUNCT
american_scientific_journal-3703	95	46	let	let	VERB
american_scientific_journal-3703	95	47	𝐼𝐼	𝐼𝐼	PROPN
american_scientific_journal-3703	95	48	be	be	AUX
american_scientific_journal-3703	95	49	an	an	DET
american_scientific_journal-3703	95	50	interval	interval	NOUN
american_scientific_journal-3703	95	51	and	and	CCONJ
american_scientific_journal-3703	95	52	let	let	VERB
american_scientific_journal-3703	95	53	:	:	PUNCT
american_scientific_journal-3703	95	54	f	f	X
american_scientific_journal-3703	96	1	i	i	PRON
american_scientific_journal-3703	96	2	i→	i→	AUX
american_scientific_journal-3703	96	3	be	be	AUX
american_scientific_journal-3703	96	4	a	a	DET
american_scientific_journal-3703	96	5	continuous	continuous	ADJ
american_scientific_journal-3703	96	6	map	map	NOUN
american_scientific_journal-3703	96	7	with	with	ADP
american_scientific_journal-3703	96	8	a	a	DET
american_scientific_journal-3703	96	9	periodic	periodic	ADJ
american_scientific_journal-3703	96	10	point	point	NOUN
american_scientific_journal-3703	96	11	of	of	ADP
american_scientific_journal-3703	96	12	period	period	NOUN
american_scientific_journal-3703	96	13	three	three	NUM
american_scientific_journal-3703	96	14	.	.	PUNCT
american_scientific_journal-3703	97	1	then	then	ADV
american_scientific_journal-3703	97	2	f	f	PROPN
american_scientific_journal-3703	97	3	is	be	AUX
american_scientific_journal-3703	97	4	said	say	VERB
american_scientific_journal-3703	97	5	to	to	PART
american_scientific_journal-3703	97	6	be	be	AUX
american_scientific_journal-3703	97	7	chaotic	chaotic	ADJ
american_scientific_journal-3703	97	8	in	in	ADP
american_scientific_journal-3703	97	9	the	the	DET
american_scientific_journal-3703	97	10	sense	sense	NOUN
american_scientific_journal-3703	97	11	of	of	ADP
american_scientific_journal-3703	97	12	li	li	PROPN
american_scientific_journal-3703	97	13	-	-	PROPN
american_scientific_journal-3703	97	14	yorke	yorke	PROPN
american_scientific_journal-3703	97	15	or	or	CCONJ
american_scientific_journal-3703	97	16	l	l	PROPN
american_scientific_journal-3703	97	17	-	-	PROPN
american_scientific_journal-3703	97	18	y	y	NOUN
american_scientific_journal-3703	97	19	chaotic	chaotic	ADJ
american_scientific_journal-3703	97	20	if	if	SCONJ
american_scientific_journal-3703	97	21	f	f	PROPN
american_scientific_journal-3703	97	22	has	have	VERB
american_scientific_journal-3703	97	23	an	an	DET
american_scientific_journal-3703	97	24	uncountable	uncountable	ADJ
american_scientific_journal-3703	97	25	scrambled	scramble	VERB
american_scientific_journal-3703	97	26	set	set	NOUN
american_scientific_journal-3703	97	27	.	.	PUNCT
american_scientific_journal-3703	98	1	3.2.3	3.2.3	NUM
american_scientific_journal-3703	98	2	lyapunov	lyapunov	ADJ
american_scientific_journal-3703	98	3	definition	definition	NOUN
american_scientific_journal-3703	98	4	[	[	X
american_scientific_journal-3703	98	5	1	1	X
american_scientific_journal-3703	98	6	]	]	PUNCT
american_scientific_journal-3703	98	7	consider	consider	VERB
american_scientific_journal-3703	98	8	the	the	DET
american_scientific_journal-3703	98	9	continuous	continuous	ADJ
american_scientific_journal-3703	98	10	and	and	CCONJ
american_scientific_journal-3703	98	11	differentiable	differentiable	ADJ
american_scientific_journal-3703	98	12	map	map	NOUN
american_scientific_journal-3703	98	13	:	:	PUNCT
american_scientific_journal-3703	98	14	f	f	PROPN
american_scientific_journal-3703	98	15	→	→	SYM
american_scientific_journal-3703	98	16	¡	¡	PROPN
american_scientific_journal-3703	98	17	¡	¡	PROPN
american_scientific_journal-3703	98	18	.then	.then	PUNCT
american_scientific_journal-3703	99	1	f	f	PROPN
american_scientific_journal-3703	99	2	is	be	AUX
american_scientific_journal-3703	99	3	said	say	VERB
american_scientific_journal-3703	99	4	to	to	PART
american_scientific_journal-3703	99	5	be	be	AUX
american_scientific_journal-3703	99	6	chaotic	chaotic	ADJ
american_scientific_journal-3703	99	7	according	accord	VERB
american_scientific_journal-3703	99	8	to	to	ADP
american_scientific_journal-3703	99	9	lyapunov	lyapunov	NOUN
american_scientific_journal-3703	99	10	or	or	CCONJ
american_scientific_journal-3703	99	11	l	l	NOUN
american_scientific_journal-3703	99	12	-	-	ADJ
american_scientific_journal-3703	99	13	chaotic	chaotic	ADJ
american_scientific_journal-3703	99	14	if	if	SCONJ
american_scientific_journal-3703	99	15	:	:	PUNCT
american_scientific_journal-3703	99	16	1	1	X
american_scientific_journal-3703	99	17	.	.	X
american_scientific_journal-3703	99	18	f	f	PROPN
american_scientific_journal-3703	99	19	is	be	AUX
american_scientific_journal-3703	99	20	topologically	topologically	ADV
american_scientific_journal-3703	99	21	transitive	transitive	ADJ
american_scientific_journal-3703	99	22	.	.	PUNCT
american_scientific_journal-3703	100	1	2	2	X
american_scientific_journal-3703	100	2	.	.	X
american_scientific_journal-3703	100	3	f	f	PROPN
american_scientific_journal-3703	100	4	has	have	VERB
american_scientific_journal-3703	100	5	a	a	DET
american_scientific_journal-3703	100	6	positive	positive	ADJ
american_scientific_journal-3703	100	7	lyapunov	lyapunov	NOUN
american_scientific_journal-3703	100	8	exponent	exponent	NOUN
american_scientific_journal-3703	100	9	.	.	PUNCT
american_scientific_journal-3703	101	1	3.2.4	3.2.4	NUM
american_scientific_journal-3703	101	2	wiggin	wiggin	NOUN
american_scientific_journal-3703	101	3	’s	’s	PART
american_scientific_journal-3703	101	4	definition	definition	NOUN
american_scientific_journal-3703	101	5	[	[	X
american_scientific_journal-3703	101	6	13	13	NUM
american_scientific_journal-3703	101	7	]	]	PUNCT
american_scientific_journal-3703	101	8	let	let	VERB
american_scientific_journal-3703	101	9	:	:	PUNCT
american_scientific_journal-3703	101	10	f	f	X
american_scientific_journal-3703	101	11	x	x	PUNCT
american_scientific_journal-3703	101	12	x→	x→	AUX
american_scientific_journal-3703	101	13	be	be	AUX
american_scientific_journal-3703	101	14	a	a	DET
american_scientific_journal-3703	101	15	continuous	continuous	ADJ
american_scientific_journal-3703	101	16	map	map	NOUN
american_scientific_journal-3703	101	17	and	and	CCONJ
american_scientific_journal-3703	101	18	x	x	PART
american_scientific_journal-3703	101	19	be	be	AUX
american_scientific_journal-3703	101	20	a	a	DET
american_scientific_journal-3703	101	21	metric	metric	ADJ
american_scientific_journal-3703	101	22	space	space	NOUN
american_scientific_journal-3703	101	23	.then	.then	PUNCT
american_scientific_journal-3703	102	1	the	the	DET
american_scientific_journal-3703	102	2	map	map	NOUN
american_scientific_journal-3703	102	3	f	f	NOUN
american_scientific_journal-3703	102	4	is	be	AUX
american_scientific_journal-3703	102	5	said	say	VERB
american_scientific_journal-3703	102	6	to	to	PART
american_scientific_journal-3703	102	7	be	be	AUX
american_scientific_journal-3703	102	8	chaotic	chaotic	ADJ
american_scientific_journal-3703	102	9	according	accord	VERB
american_scientific_journal-3703	102	10	to	to	ADP
american_scientific_journal-3703	102	11	wiggins	wiggins	PROPN
american_scientific_journal-3703	102	12	or	or	CCONJ
american_scientific_journal-3703	102	13	w	w	NOUN
american_scientific_journal-3703	102	14	-	-	PUNCT
american_scientific_journal-3703	102	15	chaotic	chaotic	ADJ
american_scientific_journal-3703	102	16	if	if	SCONJ
american_scientific_journal-3703	102	17	:	:	PUNCT
american_scientific_journal-3703	102	18	1	1	X
american_scientific_journal-3703	102	19	.	.	X
american_scientific_journal-3703	102	20	f	f	PROPN
american_scientific_journal-3703	102	21	is	be	AUX
american_scientific_journal-3703	102	22	topologically	topologically	ADV
american_scientific_journal-3703	102	23	transitive	transitive	ADJ
american_scientific_journal-3703	102	24	.	.	PUNCT
american_scientific_journal-3703	103	1	2	2	X
american_scientific_journal-3703	103	2	.	.	X
american_scientific_journal-3703	103	3	f	f	PROPN
american_scientific_journal-3703	103	4	exhibits	exhibit	VERB
american_scientific_journal-3703	103	5	sensitive	sensitive	ADJ
american_scientific_journal-3703	103	6	dependence	dependence	NOUN
american_scientific_journal-3703	103	7	on	on	ADP
american_scientific_journal-3703	103	8	initial	initial	ADJ
american_scientific_journal-3703	103	9	conditions	condition	NOUN
american_scientific_journal-3703	103	10	.	.	PUNCT
american_scientific_journal-3703	104	1	4	4	X
american_scientific_journal-3703	104	2	.	.	NUM
american_scientific_journal-3703	104	3	theorems	theorem	NOUN
american_scientific_journal-3703	104	4	and	and	CCONJ
american_scientific_journal-3703	104	5	propositions	proposition	NOUN
american_scientific_journal-3703	104	6	4.1	4.1	NUM
american_scientific_journal-3703	104	7	theorem	theorem	NOUN
american_scientific_journal-3703	104	8	(	(	PUNCT
american_scientific_journal-3703	104	9	period	period	NOUN
american_scientific_journal-3703	104	10	three	three	NUM
american_scientific_journal-3703	104	11	implies	imply	VERB
american_scientific_journal-3703	104	12	chaos	chaos	NOUN
american_scientific_journal-3703	104	13	)	)	PUNCT
american_scientific_journal-3703	104	14	.	.	PUNCT
american_scientific_journal-3703	105	1	suppose	suppose	VERB
american_scientific_journal-3703	105	2	:	:	PUNCT
american_scientific_journal-3703	105	3	f	f	PROPN
american_scientific_journal-3703	105	4	→	→	SYM
american_scientific_journal-3703	105	5	¡	¡	PROPN
american_scientific_journal-3703	105	6	¡	¡	PROPN
american_scientific_journal-3703	105	7	is	be	AUX
american_scientific_journal-3703	105	8	continuous	continuous	ADJ
american_scientific_journal-3703	105	9	.	.	PUNCT
american_scientific_journal-3703	106	1	if	if	SCONJ
american_scientific_journal-3703	106	2	f	f	PROPN
american_scientific_journal-3703	106	3	has	have	VERB
american_scientific_journal-3703	106	4	a	a	DET
american_scientific_journal-3703	106	5	periodic	periodic	ADJ
american_scientific_journal-3703	106	6	point	point	NOUN
american_scientific_journal-3703	106	7	of	of	ADP
american_scientific_journal-3703	106	8	prime	prime	ADJ
american_scientific_journal-3703	106	9	period	period	NOUN
american_scientific_journal-3703	106	10	3	3	NUM
american_scientific_journal-3703	106	11	,	,	PUNCT
american_scientific_journal-3703	106	12	then	then	ADV
american_scientific_journal-3703	106	13	f	f	PROPN
american_scientific_journal-3703	106	14	has	have	VERB
american_scientific_journal-3703	106	15	periodic	periodic	ADJ
american_scientific_journal-3703	106	16	points	point	NOUN
american_scientific_journal-3703	106	17	of	of	ADP
american_scientific_journal-3703	106	18	all	all	DET
american_scientific_journal-3703	106	19	other	other	ADJ
american_scientific_journal-3703	106	20	periods	period	NOUN
american_scientific_journal-3703	106	21	.	.	PUNCT
american_scientific_journal-3703	107	1	proof	proof	NOUN
american_scientific_journal-3703	107	2	.	.	PUNCT
american_scientific_journal-3703	108	1	first	first	ADV
american_scientific_journal-3703	108	2	we	we	PRON
american_scientific_journal-3703	108	3	need	need	VERB
american_scientific_journal-3703	108	4	to	to	PART
american_scientific_journal-3703	108	5	established	establish	VERB
american_scientific_journal-3703	108	6	two	two	NUM
american_scientific_journal-3703	108	7	lemma	lemma	PROPN
american_scientific_journal-3703	108	8	that	that	PRON
american_scientific_journal-3703	108	9	follows	follow	VERB
american_scientific_journal-3703	108	10	from	from	ADP
american_scientific_journal-3703	108	11	the	the	DET
american_scientific_journal-3703	108	12	continuity	continuity	NOUN
american_scientific_journal-3703	108	13	of	of	ADP
american_scientific_journal-3703	108	14	f	f	PROPN
american_scientific_journal-3703	108	15	.	.	PUNCT
american_scientific_journal-3703	109	1	fixed	fix	VERB
american_scientific_journal-3703	109	2	point	point	NOUN
american_scientific_journal-3703	109	3	lemma	lemma	PROPN
american_scientific_journal-3703	109	4	:	:	PUNCT
american_scientific_journal-3703	109	5	suppose	suppose	VERB
american_scientific_journal-3703	109	6	i	i	PRON
american_scientific_journal-3703	109	7	and	and	CCONJ
american_scientific_journal-3703	109	8	j	j	PROPN
american_scientific_journal-3703	109	9	are	be	AUX
american_scientific_journal-3703	109	10	closed	close	VERB
american_scientific_journal-3703	109	11	intervals	interval	NOUN
american_scientific_journal-3703	109	12	such	such	ADJ
american_scientific_journal-3703	109	13	that	that	SCONJ
american_scientific_journal-3703	109	14	i	i	PRON
american_scientific_journal-3703	109	15	j⊂	j⊂	PROPN
american_scientific_journal-3703	109	16	.if	.if	PUNCT
american_scientific_journal-3703	110	1	(	(	PUNCT
american_scientific_journal-3703	110	2	)	)	PUNCT
american_scientific_journal-3703	110	3	j	j	PROPN
american_scientific_journal-3703	110	4	f	f	PROPN
american_scientific_journal-3703	110	5	i⊂	i⊂	PROPN
american_scientific_journal-3703	110	6	then	then	ADV
american_scientific_journal-3703	110	7	f	f	PROPN
american_scientific_journal-3703	110	8	has	have	AUX
american_scientific_journal-3703	110	9	fixed	fix	VERB
american_scientific_journal-3703	110	10	point	point	NOUN
american_scientific_journal-3703	110	11	in	in	ADP
american_scientific_journal-3703	110	12	i	i	PRON
american_scientific_journal-3703	110	13	pre	pre	ADJ
american_scientific_journal-3703	110	14	-	-	ADJ
american_scientific_journal-3703	110	15	image	image	ADJ
american_scientific_journal-3703	110	16	lemma	lemma	PROPN
american_scientific_journal-3703	110	17	:	:	PUNCT
american_scientific_journal-3703	110	18	suppose	suppose	VERB
american_scientific_journal-3703	110	19	i	i	PRON
american_scientific_journal-3703	110	20	and	and	CCONJ
american_scientific_journal-3703	110	21	j	j	PROPN
american_scientific_journal-3703	110	22	are	be	AUX
american_scientific_journal-3703	110	23	closed	close	VERB
american_scientific_journal-3703	110	24	intervals	interval	NOUN
american_scientific_journal-3703	110	25	such	such	ADJ
american_scientific_journal-3703	110	26	that	that	PRON
american_scientific_journal-3703	110	27	(	(	PUNCT
american_scientific_journal-3703	110	28	)	)	PUNCT
american_scientific_journal-3703	110	29	j	j	PROPN
american_scientific_journal-3703	110	30	f	f	PROPN
american_scientific_journal-3703	110	31	i⊂	i⊂	PROPN
american_scientific_journal-3703	110	32	.	.	PUNCT
american_scientific_journal-3703	111	1	then	then	ADV
american_scientific_journal-3703	111	2	there	there	PRON
american_scientific_journal-3703	111	3	exists	exist	VERB
american_scientific_journal-3703	111	4	a	a	DET
american_scientific_journal-3703	111	5	closed	closed	ADJ
american_scientific_journal-3703	111	6	subinterval	subinterval	NOUN
american_scientific_journal-3703	111	7	i	i	PRON
american_scientific_journal-3703	111	8	i′	i′	VERB
american_scientific_journal-3703	111	9	⊂	⊂	PRON
american_scientific_journal-3703	111	10	such	such	ADJ
american_scientific_journal-3703	111	11	that	that	SCONJ
american_scientific_journal-3703	111	12	(	(	PUNCT
american_scientific_journal-3703	111	13	)	)	PUNCT
american_scientific_journal-3703	111	14	j	j	PROPN
american_scientific_journal-3703	111	15	f	f	NOUN
american_scientific_journal-3703	112	1	i	i	PRON
american_scientific_journal-3703	112	2	′=	′=	PROPN
american_scientific_journal-3703	112	3	.	.	PUNCT
american_scientific_journal-3703	113	1	let	let	VERB
american_scientific_journal-3703	113	2	f	f	PROPN
american_scientific_journal-3703	113	3	has	have	VERB
american_scientific_journal-3703	113	4	a	a	DET
american_scientific_journal-3703	113	5	3	3	NUM
american_scientific_journal-3703	113	6	-	-	PUNCT
american_scientific_journal-3703	113	7	cycle	cycle	NOUN
american_scientific_journal-3703	113	8	given	give	VERB
american_scientific_journal-3703	113	9	by	by	ADP
american_scientific_journal-3703	113	10	a	a	DET
american_scientific_journal-3703	113	11	b	b	PROPN
american_scientific_journal-3703	113	12	c	c	X
american_scientific_journal-3703	113	13	a→	a→	X
american_scientific_journal-3703	113	14	→	→	SYM
american_scientific_journal-3703	113	15	→	→	SYM
american_scientific_journal-3703	113	16	.	.	PUNCT
american_scientific_journal-3703	114	1	we	we	PRON
american_scientific_journal-3703	114	2	will	will	AUX
american_scientific_journal-3703	114	3	assume	assume	VERB
american_scientific_journal-3703	114	4	a	a	DET
american_scientific_journal-3703	114	5	b	b	NOUN
american_scientific_journal-3703	114	6	c	c	X
american_scientific_journal-3703	114	7	<	<	X
american_scientific_journal-3703	114	8	<	<	X
american_scientific_journal-3703	114	9	,	,	PUNCT
american_scientific_journal-3703	114	10	the	the	DET
american_scientific_journal-3703	114	11	other	other	ADJ
american_scientific_journal-3703	114	12	cases	case	NOUN
american_scientific_journal-3703	114	13	are	be	AUX
american_scientific_journal-3703	114	14	handled	handle	VERB
american_scientific_journal-3703	114	15	similarly	similarly	ADV
american_scientific_journal-3703	114	16	.	.	PUNCT
american_scientific_journal-3703	115	1	let	let	VERB
american_scientific_journal-3703	115	2	[	[	PUNCT
american_scientific_journal-3703	115	3	]	]	X
american_scientific_journal-3703	115	4	0	0	NUM
american_scientific_journal-3703	115	5	,	,	PUNCT
american_scientific_journal-3703	115	6	i	i	PRON
american_scientific_journal-3703	115	7	a	a	DET
american_scientific_journal-3703	115	8	b=	b=	NOUN
american_scientific_journal-3703	115	9	and	and	CCONJ
american_scientific_journal-3703	115	10	[	[	PUNCT
american_scientific_journal-3703	115	11	]	]	X
american_scientific_journal-3703	115	12	1	1	NUM
american_scientific_journal-3703	115	13	,	,	PUNCT
american_scientific_journal-3703	115	14	i	i	PRON
american_scientific_journal-3703	115	15	b	b	PROPN
american_scientific_journal-3703	115	16	c=	c=	NOUN
american_scientific_journal-3703	115	17	.	.	PUNCT
american_scientific_journal-3703	116	1	then	then	ADV
american_scientific_journal-3703	116	2	we	we	PRON
american_scientific_journal-3703	116	3	have	have	VERB
american_scientific_journal-3703	116	4	(	(	PUNCT
american_scientific_journal-3703	116	5	)	)	PUNCT
american_scientific_journal-3703	116	6	1	1	NUM
american_scientific_journal-3703	116	7	0i	0i	X
american_scientific_journal-3703	116	8	f	f	PROPN
american_scientific_journal-3703	116	9	i⊂	i⊂	PROPN
american_scientific_journal-3703	116	10	and	and	CCONJ
american_scientific_journal-3703	116	11	(	(	PUNCT
american_scientific_journal-3703	116	12	)	)	PUNCT
american_scientific_journal-3703	116	13	0	0	NUM
american_scientific_journal-3703	116	14	1	1	NUM
american_scientific_journal-3703	116	15	1i	1i	NOUN
american_scientific_journal-3703	117	1	i	i	PRON
american_scientific_journal-3703	117	2	f	f	PROPN
american_scientific_journal-3703	117	3	i∪	i∪	AUX
american_scientific_journal-3703	117	4	⊂	⊂	X
american_scientific_journal-3703	117	5	.first	.first	NUM
american_scientific_journal-3703	117	6	we	we	PRON
american_scientific_journal-3703	117	7	note	note	VERB
american_scientific_journal-3703	117	8	that	that	SCONJ
american_scientific_journal-3703	117	9	since	since	SCONJ
american_scientific_journal-3703	117	10	(	(	PUNCT
american_scientific_journal-3703	117	11	)	)	PUNCT
american_scientific_journal-3703	117	12	1	1	NUM
american_scientific_journal-3703	117	13	1i	1i	NUM
american_scientific_journal-3703	117	14	f	f	X
american_scientific_journal-3703	117	15	i⊂	i⊂	PROPN
american_scientific_journal-3703	117	16	,	,	PUNCT
american_scientific_journal-3703	117	17	f	f	PROPN
american_scientific_journal-3703	117	18	has	have	VERB
american_scientific_journal-3703	117	19	a	a	DET
american_scientific_journal-3703	117	20	fixed	fix	VERB
american_scientific_journal-3703	117	21	point	point	NOUN
american_scientific_journal-3703	117	22	in	in	ADP
american_scientific_journal-3703	117	23	1i	1i	NOUN
american_scientific_journal-3703	117	24	,	,	PUNCT
american_scientific_journal-3703	117	25	by	by	ADP
american_scientific_journal-3703	117	26	the	the	DET
american_scientific_journal-3703	117	27	fixed	fix	VERB
american_scientific_journal-3703	117	28	point	point	NOUN
american_scientific_journal-3703	117	29	lemma	lemma	PROPN
american_scientific_journal-3703	117	30	.	.	PUNCT
american_scientific_journal-3703	118	1	now	now	ADV
american_scientific_journal-3703	118	2	we	we	PRON
american_scientific_journal-3703	118	3	will	will	AUX
american_scientific_journal-3703	118	4	find	find	VERB
american_scientific_journal-3703	118	5	a	a	DET
american_scientific_journal-3703	118	6	period	period	NOUN
american_scientific_journal-3703	118	7	2	2	NUM
american_scientific_journal-3703	118	8	-	-	PUNCT
american_scientific_journal-3703	118	9	cycle	cycle	NOUN
american_scientific_journal-3703	118	10	.	.	PUNCT
american_scientific_journal-3703	119	1	first	first	ADV
american_scientific_journal-3703	119	2	we	we	PRON
american_scientific_journal-3703	119	3	have	have	VERB
american_scientific_journal-3703	119	4	that	that	PRON
american_scientific_journal-3703	119	5	(	(	PUNCT
american_scientific_journal-3703	119	6	)	)	PUNCT
american_scientific_journal-3703	119	7	1	1	NUM
american_scientific_journal-3703	119	8	0i	0i	X
american_scientific_journal-3703	119	9	f	f	PROPN
american_scientific_journal-3703	119	10	i⊂	i⊂	PROPN
american_scientific_journal-3703	119	11	,	,	PUNCT
american_scientific_journal-3703	119	12	so	so	CCONJ
american_scientific_journal-3703	119	13	by	by	ADP
american_scientific_journal-3703	119	14	the	the	DET
american_scientific_journal-3703	119	15	pre	pre	ADJ
american_scientific_journal-3703	119	16	-	-	ADJ
american_scientific_journal-3703	119	17	image	image	ADJ
american_scientific_journal-3703	119	18	lemma	lemma	PROPN
american_scientific_journal-3703	119	19	,	,	PUNCT
american_scientific_journal-3703	119	20	there	there	PRON
american_scientific_journal-3703	119	21	exists	exist	VERB
american_scientific_journal-3703	119	22	a	a	DET
american_scientific_journal-3703	119	23	subset	subset	NOUN
american_scientific_journal-3703	119	24	0	0	NUM
american_scientific_journal-3703	119	25	0a	0a	PROPN
american_scientific_journal-3703	119	26	i⊂	i⊂	NOUN
american_scientific_journal-3703	119	27	such	such	ADJ
american_scientific_journal-3703	119	28	that	that	SCONJ
american_scientific_journal-3703	119	29	(	(	PUNCT
american_scientific_journal-3703	119	30	)	)	PUNCT
american_scientific_journal-3703	119	31	1	1	NUM
american_scientific_journal-3703	119	32	0i	0i	X
american_scientific_journal-3703	119	33	f	f	PROPN
american_scientific_journal-3703	119	34	a=	a=	VERB
american_scientific_journal-3703	119	35	.	.	PUNCT
american_scientific_journal-3703	120	1	on	on	ADP
american_scientific_journal-3703	120	2	the	the	DET
american_scientific_journal-3703	120	3	other	other	ADJ
american_scientific_journal-3703	120	4	hand	hand	NOUN
american_scientific_journal-3703	120	5	(	(	PUNCT
american_scientific_journal-3703	120	6	)	)	PUNCT
american_scientific_journal-3703	120	7	0	0	NUM
american_scientific_journal-3703	120	8	1i	1i	NUM
american_scientific_journal-3703	120	9	f	f	X
american_scientific_journal-3703	120	10	i⊂	i⊂	NOUN
american_scientific_journal-3703	120	11	,	,	PUNCT
american_scientific_journal-3703	120	12	so	so	CCONJ
american_scientific_journal-3703	120	13	in	in	ADP
american_scientific_journal-3703	120	14	fact	fact	NOUN
american_scientific_journal-3703	120	15	(	(	PUNCT
american_scientific_journal-3703	120	16	)	)	PUNCT
american_scientific_journal-3703	120	17	2	2	NUM
american_scientific_journal-3703	120	18	0	0	NUM
american_scientific_journal-3703	120	19	0i	0i	X
american_scientific_journal-3703	120	20	f	f	PROPN
american_scientific_journal-3703	120	21	a⊂	a⊂	VERB
american_scientific_journal-3703	120	22	.	.	PUNCT
american_scientific_journal-3703	121	1	then	then	ADV
american_scientific_journal-3703	121	2	by	by	ADP
american_scientific_journal-3703	121	3	the	the	DET
american_scientific_journal-3703	121	4	fixed	fix	VERB
american_scientific_journal-3703	121	5	point	point	NOUN
american_scientific_journal-3703	121	6	lemma	lemma	PROPN
american_scientific_journal-3703	121	7	,	,	PUNCT
american_scientific_journal-3703	121	8	there	there	PRON
american_scientific_journal-3703	121	9	is	be	VERB
american_scientific_journal-3703	121	10	a	a	DET
american_scientific_journal-3703	121	11	fixed	fix	VERB
american_scientific_journal-3703	121	12	point	point	NOUN
american_scientific_journal-3703	121	13	for	for	ADP
american_scientific_journal-3703	121	14	2f	2f	NUM
american_scientific_journal-3703	121	15	in	in	ADP
american_scientific_journal-3703	121	16	0i	0i	NOUN
american_scientific_journal-3703	121	17	.	.	PUNCT
american_scientific_journal-3703	122	1	so	so	ADV
american_scientific_journal-3703	122	2	we	we	PRON
american_scientific_journal-3703	122	3	have	have	VERB
american_scientific_journal-3703	122	4	a	a	DET
american_scientific_journal-3703	122	5	point	point	NOUN
american_scientific_journal-3703	122	6	of	of	ADP
american_scientific_journal-3703	122	7	period	period	NOUN
american_scientific_journal-3703	122	8	2	2	NUM
american_scientific_journal-3703	122	9	for	for	ADP
american_scientific_journal-3703	122	10	f.	f.	PROPN
american_scientific_journal-3703	122	11	in	in	ADP
american_scientific_journal-3703	122	12	fact	fact	NOUN
american_scientific_journal-3703	122	13	,	,	PUNCT
american_scientific_journal-3703	122	14	since	since	SCONJ
american_scientific_journal-3703	122	15	the	the	DET
american_scientific_journal-3703	122	16	iteration	iteration	NOUN
american_scientific_journal-3703	122	17	of	of	ADP
american_scientific_journal-3703	122	18	this	this	DET
american_scientific_journal-3703	122	19	american	american	ADJ
american_scientific_journal-3703	122	20	scientific	scientific	ADJ
american_scientific_journal-3703	122	21	research	research	NOUN
american_scientific_journal-3703	122	22	journal	journal	NOUN
american_scientific_journal-3703	122	23	for	for	ADP
american_scientific_journal-3703	122	24	engineering	engineering	NOUN
american_scientific_journal-3703	122	25	,	,	PUNCT
american_scientific_journal-3703	122	26	technology	technology	NOUN
american_scientific_journal-3703	122	27	,	,	PUNCT
american_scientific_journal-3703	122	28	and	and	CCONJ
american_scientific_journal-3703	122	29	sciences	science	NOUN
american_scientific_journal-3703	122	30	(	(	PUNCT
american_scientific_journal-3703	122	31	asrjets	asrjet	NOUN
american_scientific_journal-3703	122	32	)	)	PUNCT
american_scientific_journal-3703	122	33	(	(	PUNCT
american_scientific_journal-3703	122	34	2018	2018	NUM
american_scientific_journal-3703	122	35	)	)	PUNCT
american_scientific_journal-3703	122	36	volume	volume	NOUN
american_scientific_journal-3703	122	37	43	43	NUM
american_scientific_journal-3703	122	38	,	,	PUNCT
american_scientific_journal-3703	122	39	no	no	DET
american_scientific_journal-3703	122	40	1	1	NUM
american_scientific_journal-3703	122	41	,	,	PUNCT
american_scientific_journal-3703	122	42	pp	pp	ADV
american_scientific_journal-3703	122	43	110	110	NUM
american_scientific_journal-3703	122	44	-	-	SYM
american_scientific_journal-3703	122	45	133	133	NUM
american_scientific_journal-3703	122	46	116	116	NUM
american_scientific_journal-3703	122	47	point	point	NOUN
american_scientific_journal-3703	122	48	leaves	leave	VERB
american_scientific_journal-3703	122	49	0i	0i	VERB
american_scientific_journal-3703	122	50	it	it	PRON
american_scientific_journal-3703	122	51	can	can	AUX
american_scientific_journal-3703	122	52	not	not	PART
american_scientific_journal-3703	122	53	be	be	AUX
american_scientific_journal-3703	122	54	a	a	DET
american_scientific_journal-3703	122	55	fixed	fix	VERB
american_scientific_journal-3703	122	56	point	point	NOUN
american_scientific_journal-3703	122	57	for	for	ADP
american_scientific_journal-3703	122	58	f	f	PROPN
american_scientific_journal-3703	122	59	,	,	PUNCT
american_scientific_journal-3703	122	60	so	so	ADV
american_scientific_journal-3703	122	61	it	it	PRON
american_scientific_journal-3703	122	62	has	have	VERB
american_scientific_journal-3703	122	63	prime	prime	ADJ
american_scientific_journal-3703	122	64	period	period	NOUN
american_scientific_journal-3703	122	65	2	2	NUM
american_scientific_journal-3703	122	66	.	.	PUNCT
american_scientific_journal-3703	123	1	we	we	PRON
american_scientific_journal-3703	123	2	will	will	AUX
american_scientific_journal-3703	123	3	find	find	VERB
american_scientific_journal-3703	123	4	a	a	DET
american_scientific_journal-3703	123	5	periodic	periodic	ADJ
american_scientific_journal-3703	123	6	cycle	cycle	NOUN
american_scientific_journal-3703	123	7	of	of	ADP
american_scientific_journal-3703	123	8	period	period	NOUN
american_scientific_journal-3703	123	9	n	n	X
american_scientific_journal-3703	123	10	for	for	ADP
american_scientific_journal-3703	123	11	all	all	DET
american_scientific_journal-3703	123	12	n>3	n>3	NOUN
american_scientific_journal-3703	123	13	by	by	ADP
american_scientific_journal-3703	123	14	involving	involve	VERB
american_scientific_journal-3703	123	15	the	the	DET
american_scientific_journal-3703	123	16	pre	pre	ADJ
american_scientific_journal-3703	123	17	-	-	ADJ
american_scientific_journal-3703	123	18	image	image	ADJ
american_scientific_journal-3703	123	19	lemma	lemma	PROPN
american_scientific_journal-3703	123	20	n	n	PROPN
american_scientific_journal-3703	123	21	times	time	NOUN
american_scientific_journal-3703	123	22	.	.	PUNCT
american_scientific_journal-3703	124	1	since	since	SCONJ
american_scientific_journal-3703	124	2	(	(	PUNCT
american_scientific_journal-3703	124	3	)	)	PUNCT
american_scientific_journal-3703	124	4	1	1	NUM
american_scientific_journal-3703	124	5	1i	1i	NUM
american_scientific_journal-3703	124	6	f	f	X
american_scientific_journal-3703	124	7	i⊂	i⊂	NOUN
american_scientific_journal-3703	124	8	,	,	PUNCT
american_scientific_journal-3703	124	9	there	there	PRON
american_scientific_journal-3703	124	10	is	be	VERB
american_scientific_journal-3703	124	11	a	a	DET
american_scientific_journal-3703	124	12	closed	closed	ADJ
american_scientific_journal-3703	124	13	subinterval	subinterval	NOUN
american_scientific_journal-3703	124	14	1	1	NUM
american_scientific_journal-3703	124	15	1a	1a	NOUN
american_scientific_journal-3703	124	16	i⊂	i⊂	NOUN
american_scientific_journal-3703	124	17	such	such	ADJ
american_scientific_journal-3703	124	18	that	that	PRON
american_scientific_journal-3703	124	19	(	(	PUNCT
american_scientific_journal-3703	124	20	)	)	SYM
american_scientific_journal-3703	124	21	1	1	NUM
american_scientific_journal-3703	124	22	1i	1i	NOUN
american_scientific_journal-3703	124	23	f	f	NOUN
american_scientific_journal-3703	124	24	a=	a=	VERB
american_scientific_journal-3703	124	25	.	.	PUNCT
american_scientific_journal-3703	125	1	now	now	ADV
american_scientific_journal-3703	125	2	again	again	ADV
american_scientific_journal-3703	125	3	we	we	PRON
american_scientific_journal-3703	125	4	have	have	VERB
american_scientific_journal-3703	125	5	(	(	PUNCT
american_scientific_journal-3703	125	6	)	)	PUNCT
american_scientific_journal-3703	125	7	1	1	NUM
american_scientific_journal-3703	125	8	1a	1a	X
american_scientific_journal-3703	125	9	f	f	X
american_scientific_journal-3703	125	10	a⊂	a⊂	VERB
american_scientific_journal-3703	125	11	,	,	PUNCT
american_scientific_journal-3703	125	12	so	so	CCONJ
american_scientific_journal-3703	125	13	there	there	PRON
american_scientific_journal-3703	125	14	is	be	VERB
american_scientific_journal-3703	125	15	a	a	DET
american_scientific_journal-3703	125	16	closed	closed	ADJ
american_scientific_journal-3703	125	17	interval	interval	NOUN
american_scientific_journal-3703	125	18	2	2	NUM
american_scientific_journal-3703	125	19	1a	1a	NOUN
american_scientific_journal-3703	125	20	a⊂	a⊂	PRON
american_scientific_journal-3703	125	21	such	such	ADJ
american_scientific_journal-3703	125	22	that	that	SCONJ
american_scientific_journal-3703	125	23	(	(	PUNCT
american_scientific_journal-3703	125	24	)	)	SYM
american_scientific_journal-3703	125	25	1	1	NUM
american_scientific_journal-3703	125	26	2a	2a	NUM
american_scientific_journal-3703	125	27	f	f	X
american_scientific_journal-3703	125	28	a=	a=	VERB
american_scientific_journal-3703	125	29	.	.	PUNCT
american_scientific_journal-3703	126	1	thus	thus	ADV
american_scientific_journal-3703	126	2	(	(	PUNCT
american_scientific_journal-3703	126	3	)	)	SYM
american_scientific_journal-3703	126	4	2	2	NUM
american_scientific_journal-3703	126	5	1	1	NUM
american_scientific_journal-3703	126	6	2i	2i	NUM
american_scientific_journal-3703	126	7	f	f	PROPN
american_scientific_journal-3703	126	8	a=	a=	VERB
american_scientific_journal-3703	126	9	.	.	PUNCT
american_scientific_journal-3703	127	1	continue	continue	VERB
american_scientific_journal-3703	127	2	this	this	DET
american_scientific_journal-3703	127	3	process	process	NOUN
american_scientific_journal-3703	127	4	for	for	ADP
american_scientific_journal-3703	127	5	n-2	n-2	NOUN
american_scientific_journal-3703	127	6	steps	step	NOUN
american_scientific_journal-3703	127	7	to	to	PART
american_scientific_journal-3703	127	8	produce	produce	VERB
american_scientific_journal-3703	127	9	the	the	DET
american_scientific_journal-3703	127	10	following	follow	VERB
american_scientific_journal-3703	127	11	nested	nested	ADJ
american_scientific_journal-3703	127	12	collection	collection	NOUN
american_scientific_journal-3703	127	13	of	of	ADP
american_scientific_journal-3703	127	14	closed	closed	ADJ
american_scientific_journal-3703	127	15	subintervals	subinterval	NOUN
american_scientific_journal-3703	127	16	:	:	PUNCT
american_scientific_journal-3703	127	17	2	2	NUM
american_scientific_journal-3703	127	18	3	3	NUM
american_scientific_journal-3703	127	19	2	2	NUM
american_scientific_journal-3703	127	20	1	1	NUM
american_scientific_journal-3703	127	21	1	1	NUM
american_scientific_journal-3703	127	22	...	...	PUNCT
american_scientific_journal-3703	127	23	n	n	CCONJ
american_scientific_journal-3703	127	24	na	na	ADP
american_scientific_journal-3703	127	25	a	a	DET
american_scientific_journal-3703	127	26	a	a	DET
american_scientific_journal-3703	127	27	a	a	DET
american_scientific_journal-3703	127	28	i−	i−	NOUN
american_scientific_journal-3703	127	29	−⊂	−⊂	NOUN
american_scientific_journal-3703	127	30	⊂	⊂	PRON
american_scientific_journal-3703	127	31	⊂	⊂	PROPN
american_scientific_journal-3703	127	32	⊂	⊂	PROPN
american_scientific_journal-3703	128	1	⊂	⊂	X
american_scientific_journal-3703	128	2	,	,	PUNCT
american_scientific_journal-3703	128	3	such	such	ADJ
american_scientific_journal-3703	128	4	that	that	SCONJ
american_scientific_journal-3703	128	5	(	(	PUNCT
american_scientific_journal-3703	128	6	)	)	PUNCT
american_scientific_journal-3703	128	7	1i	1i	NOUN
american_scientific_journal-3703	128	8	ia	ia	NOUN
american_scientific_journal-3703	128	9	f	f	PROPN
american_scientific_journal-3703	128	10	a=	a=	VERB
american_scientific_journal-3703	128	11	+	+	CCONJ
american_scientific_journal-3703	128	12	and	and	CCONJ
american_scientific_journal-3703	128	13	(	(	PUNCT
american_scientific_journal-3703	128	14	)	)	SYM
american_scientific_journal-3703	128	15	2	2	NUM
american_scientific_journal-3703	128	16	1	1	NUM
american_scientific_journal-3703	128	17	2	2	NUM
american_scientific_journal-3703	128	18	.n	.n	NOUN
american_scientific_journal-3703	128	19	ni	ni	PROPN
american_scientific_journal-3703	128	20	f	f	PROPN
american_scientific_journal-3703	128	21	a−	a−	PROPN
american_scientific_journal-3703	128	22	−=	−=	PUNCT
american_scientific_journal-3703	128	23	now	now	ADV
american_scientific_journal-3703	128	24	let	let	VERB
american_scientific_journal-3703	128	25	’s	’s	NOUN
american_scientific_journal-3703	128	26	bring	bring	VERB
american_scientific_journal-3703	128	27	in	in	ADP
american_scientific_journal-3703	128	28	0i	0i	NOUN
american_scientific_journal-3703	128	29	.	.	PUNCT
american_scientific_journal-3703	129	1	we	we	PRON
american_scientific_journal-3703	129	2	have	have	VERB
american_scientific_journal-3703	129	3	(	(	PUNCT
american_scientific_journal-3703	129	4	)	)	SYM
american_scientific_journal-3703	129	5	2	2	NUM
american_scientific_journal-3703	129	6	1	1	NUM
american_scientific_journal-3703	129	7	0na	0na	NOUN
american_scientific_journal-3703	130	1	i	i	PRON
american_scientific_journal-3703	130	2	f	f	PROPN
american_scientific_journal-3703	130	3	i−	i−	PROPN
american_scientific_journal-3703	130	4	⊂	⊂	PROPN
american_scientific_journal-3703	130	5	⊂	⊂	PROPN
american_scientific_journal-3703	130	6	,	,	PUNCT
american_scientific_journal-3703	130	7	so	so	CCONJ
american_scientific_journal-3703	130	8	there	there	PRON
american_scientific_journal-3703	130	9	is	be	VERB
american_scientific_journal-3703	130	10	a	a	DET
american_scientific_journal-3703	130	11	closed	close	VERB
american_scientific_journal-3703	130	12	subintervals	subinterval	NOUN
american_scientific_journal-3703	130	13	1	1	NUM
american_scientific_journal-3703	130	14	0na	0na	NOUN
american_scientific_journal-3703	130	15	i−	i−	PROPN
american_scientific_journal-3703	131	1	⊂	⊂	PROPN
american_scientific_journal-3703	131	2	such	such	ADJ
american_scientific_journal-3703	131	3	that	that	SCONJ
american_scientific_journal-3703	131	4	(	(	PUNCT
american_scientific_journal-3703	131	5	)	)	PUNCT
american_scientific_journal-3703	131	6	2	2	NUM
american_scientific_journal-3703	131	7	1n	1n	NUM
american_scientific_journal-3703	131	8	na	na	ADP
american_scientific_journal-3703	131	9	f	f	PROPN
american_scientific_journal-3703	131	10	a−	a−	PROPN
american_scientific_journal-3703	131	11	−=	−=	PROPN
american_scientific_journal-3703	131	12	.	.	PUNCT
american_scientific_journal-3703	132	1	finally	finally	ADV
american_scientific_journal-3703	132	2	we	we	PRON
american_scientific_journal-3703	132	3	also	also	ADV
american_scientific_journal-3703	132	4	have	have	VERB
american_scientific_journal-3703	132	5	(	(	PUNCT
american_scientific_journal-3703	132	6	)	)	PUNCT
american_scientific_journal-3703	132	7	1	1	NUM
american_scientific_journal-3703	132	8	0	0	NUM
american_scientific_journal-3703	132	9	1na	1na	NOUN
american_scientific_journal-3703	133	1	i	i	PRON
american_scientific_journal-3703	133	2	f	f	PROPN
american_scientific_journal-3703	133	3	i−	i−	PROPN
american_scientific_journal-3703	133	4	⊂	⊂	PROPN
american_scientific_journal-3703	133	5	⊂	⊂	PROPN
american_scientific_journal-3703	133	6	,	,	PUNCT
american_scientific_journal-3703	133	7	so	so	CCONJ
american_scientific_journal-3703	133	8	there	there	PRON
american_scientific_journal-3703	133	9	is	be	VERB
american_scientific_journal-3703	133	10	a	a	DET
american_scientific_journal-3703	133	11	closed	closed	ADJ
american_scientific_journal-3703	133	12	subinterval	subinterval	NOUN
american_scientific_journal-3703	133	13	1na	1na	NOUN
american_scientific_journal-3703	133	14	i⊂	i⊂	NOUN
american_scientific_journal-3703	133	15	such	such	ADJ
american_scientific_journal-3703	133	16	that	that	PRON
american_scientific_journal-3703	133	17	(	(	PUNCT
american_scientific_journal-3703	133	18	)	)	PUNCT
american_scientific_journal-3703	133	19	1n	1n	NOUN
american_scientific_journal-3703	133	20	na	na	ADP
american_scientific_journal-3703	133	21	f	f	PROPN
american_scientific_journal-3703	133	22	a−	a−	PROPN
american_scientific_journal-3703	133	23	=	=	PUNCT
american_scientific_journal-3703	133	24	.	.	PUNCT
american_scientific_journal-3703	134	1	what	what	PRON
american_scientific_journal-3703	134	2	we	we	PRON
american_scientific_journal-3703	134	3	have	have	AUX
american_scientific_journal-3703	134	4	accomplished	accomplish	VERB
american_scientific_journal-3703	134	5	is	be	AUX
american_scientific_journal-3703	134	6	the	the	DET
american_scientific_journal-3703	134	7	following	following	NOUN
american_scientific_journal-3703	134	8	:	:	PUNCT
american_scientific_journal-3703	134	9	1	1	NUM
american_scientific_journal-3703	134	10	1	1	NUM
american_scientific_journal-3703	134	11	1	1	NUM
american_scientific_journal-3703	134	12	...	...	PUNCT
american_scientific_journal-3703	134	13	f	f	PROPN
american_scientific_journal-3703	134	14	f	f	X
american_scientific_journal-3703	134	15	f	f	PROPN
american_scientific_journal-3703	134	16	f	f	PROPN
american_scientific_journal-3703	134	17	n	n	INTJ
american_scientific_journal-3703	134	18	na	na	INTJ
american_scientific_journal-3703	134	19	a	a	DET
american_scientific_journal-3703	134	20	a	a	DET
american_scientific_journal-3703	134	21	i−→	i−→	NOUN
american_scientific_journal-3703	134	22	→	→	NOUN
american_scientific_journal-3703	134	23	→	→	NOUN
american_scientific_journal-3703	134	24	→	→	NOUN
american_scientific_journal-3703	134	25	where	where	SCONJ
american_scientific_journal-3703	134	26	1na	1na	ADJ
american_scientific_journal-3703	134	27	i⊂	i⊂	NOUN
american_scientific_journal-3703	134	28	and	and	CCONJ
american_scientific_journal-3703	134	29	(	(	PUNCT
american_scientific_journal-3703	134	30	)	)	SYM
american_scientific_journal-3703	134	31	1	1	NUM
american_scientific_journal-3703	134	32	n	n	NUM
american_scientific_journal-3703	134	33	ni	ni	PROPN
american_scientific_journal-3703	134	34	f	f	PROPN
american_scientific_journal-3703	134	35	a=	a=	VERB
american_scientific_journal-3703	134	36	.	.	PUNCT
american_scientific_journal-3703	135	1	but	but	CCONJ
american_scientific_journal-3703	135	2	by	by	ADP
american_scientific_journal-3703	135	3	the	the	DET
american_scientific_journal-3703	135	4	fixed	fix	VERB
american_scientific_journal-3703	135	5	point	point	NOUN
american_scientific_journal-3703	135	6	lemma	lemma	PROPN
american_scientific_journal-3703	135	7	,	,	PUNCT
american_scientific_journal-3703	135	8	this	this	PRON
american_scientific_journal-3703	135	9	means	mean	VERB
american_scientific_journal-3703	135	10	that	that	SCONJ
american_scientific_journal-3703	135	11	there	there	PRON
american_scientific_journal-3703	135	12	is	be	VERB
american_scientific_journal-3703	135	13	a	a	DET
american_scientific_journal-3703	135	14	fixed	fix	VERB
american_scientific_journal-3703	135	15	point	point	NOUN
american_scientific_journal-3703	135	16	for	for	ADP
american_scientific_journal-3703	135	17	nf	nf	NOUN
american_scientific_journal-3703	135	18	in	in	ADP
american_scientific_journal-3703	135	19	na	na	ADP
american_scientific_journal-3703	135	20	.lets	.let	NOUN
american_scientific_journal-3703	135	21	call	call	VERB
american_scientific_journal-3703	135	22	this	this	DET
american_scientific_journal-3703	135	23	fixed	fix	VERB
american_scientific_journal-3703	135	24	point	point	NOUN
american_scientific_journal-3703	135	25	0x	0x	NOUN
american_scientific_journal-3703	135	26	.	.	PUNCT
american_scientific_journal-3703	136	1	then	then	ADV
american_scientific_journal-3703	136	2	0x	0x	NOUN
american_scientific_journal-3703	136	3	is	be	AUX
american_scientific_journal-3703	136	4	a	a	DET
american_scientific_journal-3703	136	5	periodic	periodic	ADJ
american_scientific_journal-3703	136	6	point	point	NOUN
american_scientific_journal-3703	136	7	of	of	ADP
american_scientific_journal-3703	136	8	period	period	NOUN
american_scientific_journal-3703	136	9	n	n	X
american_scientific_journal-3703	136	10	for	for	ADP
american_scientific_journal-3703	136	11	f	f	PROPN
american_scientific_journal-3703	136	12	.	.	PUNCT
american_scientific_journal-3703	137	1	in	in	ADP
american_scientific_journal-3703	137	2	fact	fact	NOUN
american_scientific_journal-3703	137	3	,	,	PUNCT
american_scientific_journal-3703	137	4	since	since	SCONJ
american_scientific_journal-3703	137	5	the	the	DET
american_scientific_journal-3703	137	6	first	first	ADJ
american_scientific_journal-3703	137	7	iterate	iterate	NOUN
american_scientific_journal-3703	137	8	of	of	ADP
american_scientific_journal-3703	137	9	0x	0x	NOUN
american_scientific_journal-3703	137	10	lies	lie	VERB
american_scientific_journal-3703	137	11	in	in	ADP
american_scientific_journal-3703	137	12	1i	1i	NOUN
american_scientific_journal-3703	137	13	,	,	PUNCT
american_scientific_journal-3703	137	14	while	while	SCONJ
american_scientific_journal-3703	137	15	the	the	DET
american_scientific_journal-3703	137	16	next	next	ADJ
american_scientific_journal-3703	137	17	1n	1n	NUM
american_scientific_journal-3703	137	18	−	−	NOUN
american_scientific_journal-3703	137	19	iterates	iterate	VERB
american_scientific_journal-3703	137	20	lie	lie	VERB
american_scientific_journal-3703	137	21	in	in	ADP
american_scientific_journal-3703	137	22	1i	1i	NOUN
american_scientific_journal-3703	137	23	we	we	PRON
american_scientific_journal-3703	137	24	know	know	VERB
american_scientific_journal-3703	137	25	that	that	SCONJ
american_scientific_journal-3703	137	26	0x	0x	NOUN
american_scientific_journal-3703	137	27	has	have	VERB
american_scientific_journal-3703	137	28	prime	prime	ADJ
american_scientific_journal-3703	137	29	period	period	NOUN
american_scientific_journal-3703	137	30	.	.	PUNCT
american_scientific_journal-3703	138	1	4.2	4.2	NUM
american_scientific_journal-3703	138	2	proposition	proposition	NOUN
american_scientific_journal-3703	138	3	the	the	DET
american_scientific_journal-3703	138	4	doubling	double	VERB
american_scientific_journal-3703	138	5	map	map	NOUN
american_scientific_journal-3703	138	6	(	(	PUNCT
american_scientific_journal-3703	138	7	)	)	PUNCT
american_scientific_journal-3703	138	8	12	12	NUM
american_scientific_journal-3703	138	9	for	for	ADP
american_scientific_journal-3703	138	10	0	0	NUM
american_scientific_journal-3703	138	11	2	2	NUM
american_scientific_journal-3703	138	12	12	12	NUM
american_scientific_journal-3703	138	13	1	1	NUM
american_scientific_journal-3703	138	14	for	for	ADP
american_scientific_journal-3703	138	15	1	1	NUM
american_scientific_journal-3703	138	16	2	2	NUM
american_scientific_journal-3703	138	17	x	x	SYM
american_scientific_journal-3703	138	18	x	x	PUNCT
american_scientific_journal-3703	138	19	d	d	NOUN
american_scientific_journal-3703	138	20	x	x	X
american_scientific_journal-3703	138	21	x	x	X
american_scientific_journal-3703	138	22	x	x	PUNCT
american_scientific_journal-3703	138	23			VERB
american_scientific_journal-3703	138	24	≤	≤	X
american_scientific_journal-3703	138	25	<	<	X
american_scientific_journal-3703	138	26	=	=	PROPN
american_scientific_journal-3703	138	27			PRON
american_scientific_journal-3703	138	28			PROPN
american_scientific_journal-3703	138	29	−	−	PROPN
american_scientific_journal-3703	138	30	≤	≤	X
american_scientific_journal-3703	138	31	<	<	X
american_scientific_journal-3703	138	32			NOUN
american_scientific_journal-3703	138	33	is	be	AUX
american_scientific_journal-3703	138	34	chaotic	chaotic	ADJ
american_scientific_journal-3703	138	35	on	on	ADP
american_scientific_journal-3703	138	36	[	[	PUNCT
american_scientific_journal-3703	138	37	)	)	PUNCT
american_scientific_journal-3703	138	38	0,1	0,1	NUM
american_scientific_journal-3703	138	39	in	in	ADP
american_scientific_journal-3703	138	40	the	the	DET
american_scientific_journal-3703	138	41	sense	sense	NOUN
american_scientific_journal-3703	138	42	of	of	ADP
american_scientific_journal-3703	138	43	devaney	devaney	PROPN
american_scientific_journal-3703	138	44	.	.	PUNCT
american_scientific_journal-3703	139	1	proof	proof	NOUN
american_scientific_journal-3703	139	2	.	.	PUNCT
american_scientific_journal-3703	140	1	first	first	ADV
american_scientific_journal-3703	140	2	,	,	PUNCT
american_scientific_journal-3703	140	3	we	we	PRON
american_scientific_journal-3703	140	4	check	check	VERB
american_scientific_journal-3703	140	5	that	that	SCONJ
american_scientific_journal-3703	140	6	d	d	NOUN
american_scientific_journal-3703	140	7	has	have	VERB
american_scientific_journal-3703	140	8	a	a	DET
american_scientific_journal-3703	140	9	dense	dense	ADJ
american_scientific_journal-3703	140	10	set	set	NOUN
american_scientific_journal-3703	140	11	of	of	ADP
american_scientific_journal-3703	140	12	periodic	periodic	ADJ
american_scientific_journal-3703	140	13	points	point	NOUN
american_scientific_journal-3703	140	14	.	.	PUNCT
american_scientific_journal-3703	141	1	we	we	PRON
american_scientific_journal-3703	141	2	claim	claim	VERB
american_scientific_journal-3703	141	3	that	that	SCONJ
american_scientific_journal-3703	141	4	every	every	DET
american_scientific_journal-3703	141	5	rational	rational	ADJ
american_scientific_journal-3703	141	6	number	number	NOUN
american_scientific_journal-3703	141	7	px	px	X
american_scientific_journal-3703	141	8	q	q	NOUN
american_scientific_journal-3703	141	9	=	=	PUNCT
american_scientific_journal-3703	141	10	with	with	ADP
american_scientific_journal-3703	141	11	q	q	NOUN
american_scientific_journal-3703	141	12	odd	odd	ADJ
american_scientific_journal-3703	141	13	is	be	AUX
american_scientific_journal-3703	141	14	a	a	DET
american_scientific_journal-3703	141	15	periodic	periodic	ADJ
american_scientific_journal-3703	141	16	point	point	NOUN
american_scientific_journal-3703	141	17	for	for	ADP
american_scientific_journal-3703	141	18	d	d	PROPN
american_scientific_journal-3703	141	19	.this	.this	PRON
american_scientific_journal-3703	141	20	follows	follow	VERB
american_scientific_journal-3703	141	21	by	by	ADP
american_scientific_journal-3703	141	22	observing	observe	VERB
american_scientific_journal-3703	141	23	that	that	SCONJ
american_scientific_journal-3703	141	24	d	d	PROPN
american_scientific_journal-3703	141	25	is	be	AUX
american_scientific_journal-3703	141	26	a	a	DET
american_scientific_journal-3703	141	27	bijection	bijection	NOUN
american_scientific_journal-3703	141	28	from	from	ADP
american_scientific_journal-3703	141	29	the	the	DET
american_scientific_journal-3703	141	30	set	set	NOUN
american_scientific_journal-3703	141	31	1	1	NUM
american_scientific_journal-3703	141	32	2	2	NUM
american_scientific_journal-3703	141	33	1	1	NUM
american_scientific_journal-3703	141	34	,	,	PUNCT
american_scientific_journal-3703	141	35	,	,	PUNCT
american_scientific_journal-3703	141	36	...	...	PUNCT
american_scientific_journal-3703	141	37	,	,	PUNCT
american_scientific_journal-3703	141	38	q	q	X
american_scientific_journal-3703	141	39	q	q	X
american_scientific_journal-3703	141	40	q	q	X
american_scientific_journal-3703	141	41	q	q	X
american_scientific_journal-3703	141	42			NOUN
american_scientific_journal-3703	141	43	−	−	X
american_scientific_journal-3703	141	44			ADP
american_scientific_journal-3703	141	45			PROPN
american_scientific_journal-3703	141	46			ADJ
american_scientific_journal-3703	141	47			NOUN
american_scientific_journal-3703	141	48	to	to	ADP
american_scientific_journal-3703	141	49	itself	itself	PRON
american_scientific_journal-3703	141	50	:	:	PUNCT
american_scientific_journal-3703	141	51	clearly	clearly	ADV
american_scientific_journal-3703	141	52	d	d	X
american_scientific_journal-3703	141	53	maps	map	VERB
american_scientific_journal-3703	141	54	this	this	PRON
american_scientific_journal-3703	141	55	set	set	NOUN
american_scientific_journal-3703	141	56	into	into	ADP
american_scientific_journal-3703	141	57	itself	itself	PRON
american_scientific_journal-3703	141	58	,	,	PUNCT
american_scientific_journal-3703	141	59	and	and	CCONJ
american_scientific_journal-3703	141	60	it	it	PRON
american_scientific_journal-3703	141	61	is	be	AUX
american_scientific_journal-3703	141	62	also	also	ADV
american_scientific_journal-3703	141	63	surjective	surjective	ADJ
american_scientific_journal-3703	141	64	because	because	SCONJ
american_scientific_journal-3703	141	65	2k	2k	NUM
american_scientific_journal-3703	141	66	kd	kd	PROPN
american_scientific_journal-3703	141	67	q	q	X
american_scientific_journal-3703	141	68	q	q	PROPN
american_scientific_journal-3703	141	69			PROPN
american_scientific_journal-3703	141	70			PUNCT
american_scientific_journal-3703	142	1	=	=	NOUN
american_scientific_journal-3703	142	2			NOUN
american_scientific_journal-3703	142	3			VERB
american_scientific_journal-3703	142	4			PRON
american_scientific_journal-3703	142	5			PUNCT
american_scientific_journal-3703	142	6	and	and	CCONJ
american_scientific_journal-3703	142	7	(	(	PUNCT
american_scientific_journal-3703	142	8	)	)	SYM
american_scientific_journal-3703	142	9	1	1	NUM
american_scientific_journal-3703	142	10	/	/	SYM
american_scientific_journal-3703	142	11	22	22	NUM
american_scientific_journal-3703	142	12	1	1	NUM
american_scientific_journal-3703	142	13	k	k	NOUN
american_scientific_journal-3703	142	14	qk	qk	NOUN
american_scientific_journal-3703	142	15	d	d	NOUN
american_scientific_journal-3703	142	16	q	q	X
american_scientific_journal-3703	142	17	q	q	PROPN
american_scientific_journal-3703	142	18			PROPN
american_scientific_journal-3703	142	19	+	+	NOUN
american_scientific_journal-3703	142	20	−−	−−	NOUN
american_scientific_journal-3703	142	21	=	=	SYM
american_scientific_journal-3703	142	22			NOUN
american_scientific_journal-3703	142	23			NOUN
american_scientific_journal-3703	142	24			VERB
american_scientific_journal-3703	142	25			PRON
american_scientific_journal-3703	142	26			PUNCT
american_scientific_journal-3703	143	1	but	but	CCONJ
american_scientific_journal-3703	143	2	the	the	DET
american_scientific_journal-3703	143	3	rational	rational	ADJ
american_scientific_journal-3703	143	4	numbers	number	NOUN
american_scientific_journal-3703	143	5	with	with	ADP
american_scientific_journal-3703	143	6	odd	odd	ADJ
american_scientific_journal-3703	143	7	denominator	denominator	NOUN
american_scientific_journal-3703	143	8	are	be	AUX
american_scientific_journal-3703	143	9	dense	dense	ADJ
american_scientific_journal-3703	143	10	in	in	ADP
american_scientific_journal-3703	143	11	[	[	PUNCT
american_scientific_journal-3703	143	12	)	)	SYM
american_scientific_journal-3703	143	13	0,1	0,1	NUM
american_scientific_journal-3703	144	1	so	so	ADV
american_scientific_journal-3703	144	2	d	d	NOUN
american_scientific_journal-3703	144	3	has	have	VERB
american_scientific_journal-3703	144	4	a	a	DET
american_scientific_journal-3703	144	5	dense	dense	ADJ
american_scientific_journal-3703	144	6	set	set	NOUN
american_scientific_journal-3703	144	7	of	of	ADP
american_scientific_journal-3703	144	8	periodic	periodic	ADJ
american_scientific_journal-3703	144	9	points	point	NOUN
american_scientific_journal-3703	144	10	.	.	PUNCT
american_scientific_journal-3703	145	1	second	second	ADJ
american_scientific_journal-3703	145	2	,	,	PUNCT
american_scientific_journal-3703	145	3	we	we	PRON
american_scientific_journal-3703	145	4	claim	claim	VERB
american_scientific_journal-3703	145	5	that	that	SCONJ
american_scientific_journal-3703	145	6	d	d	NOUN
american_scientific_journal-3703	145	7	has	have	VERB
american_scientific_journal-3703	145	8	a	a	DET
american_scientific_journal-3703	145	9	dense	dense	ADJ
american_scientific_journal-3703	145	10	orbit	orbit	NOUN
american_scientific_journal-3703	145	11	,	,	PUNCT
american_scientific_journal-3703	145	12	so	so	CCONJ
american_scientific_journal-3703	145	13	(	(	PUNCT
american_scientific_journal-3703	145	14	in	in	ADP
american_scientific_journal-3703	145	15	particular	particular	ADJ
american_scientific_journal-3703	145	16	)	)	PUNCT
american_scientific_journal-3703	145	17	it	it	PRON
american_scientific_journal-3703	145	18	is	be	AUX
american_scientific_journal-3703	145	19	transitive	transitive	ADJ
american_scientific_journal-3703	145	20	.	.	PUNCT
american_scientific_journal-3703	146	1	to	to	PART
american_scientific_journal-3703	146	2	do	do	VERB
american_scientific_journal-3703	146	3	this	this	PRON
american_scientific_journal-3703	146	4	,	,	PUNCT
american_scientific_journal-3703	146	5	let	let	VERB
american_scientific_journal-3703	146	6	{	{	PUNCT
american_scientific_journal-3703	146	7	1	1	NUM
american_scientific_journal-3703	146	8	2	2	NUM
american_scientific_journal-3703	146	9	3	3	NUM
american_scientific_journal-3703	146	10	0	0	NUM
american_scientific_journal-3703	146	11	.	.	PROPN
american_scientific_journal-3703	147	1	01	01	NUM
american_scientific_journal-3703	147	2	00011011000001	00011011000001	NUM
american_scientific_journal-3703	147	3	...	...	PUNCT
american_scientific_journal-3703	148	1	111	111	NUM
american_scientific_journal-3703	148	2	...	...	PUNCT
american_scientific_journal-3703	148	3	length	length	NOUN
american_scientific_journal-3703	148	4	length	length	NOUN
american_scientific_journal-3703	148	5	length	length	NOUN
american_scientific_journal-3703	148	6	α	α	X
american_scientific_journal-3703	148	7	=	=	SYM
american_scientific_journal-3703	148	8	14	14	NUM
american_scientific_journal-3703	148	9	2	2	NUM
american_scientific_journal-3703	148	10	43	43	NUM
american_scientific_journal-3703	148	11	1	1	NUM
american_scientific_journal-3703	148	12	44	44	NUM
american_scientific_journal-3703	148	13	2	2	NUM
american_scientific_journal-3703	148	14	4	4	NUM
american_scientific_journal-3703	148	15	43	43	NUM
american_scientific_journal-3703	148	16	be	be	AUX
american_scientific_journal-3703	148	17	the	the	DET
american_scientific_journal-3703	148	18	base-2	base-2	PROPN
american_scientific_journal-3703	148	19	decimal	decimal	NOUN
american_scientific_journal-3703	148	20	constructed	construct	VERB
american_scientific_journal-3703	148	21	by	by	ADP
american_scientific_journal-3703	148	22	listing	list	VERB
american_scientific_journal-3703	148	23	all	all	DET
american_scientific_journal-3703	148	24	sequences	sequence	NOUN
american_scientific_journal-3703	148	25	of	of	ADP
american_scientific_journal-3703	148	26	length	length	NOUN
american_scientific_journal-3703	148	27	1	1	NUM
american_scientific_journal-3703	148	28	,	,	PUNCT
american_scientific_journal-3703	148	29	then	then	ADV
american_scientific_journal-3703	148	30	all	all	DET
american_scientific_journal-3703	148	31	sequences	sequence	NOUN
american_scientific_journal-3703	148	32	of	of	ADP
american_scientific_journal-3703	148	33	length	length	NOUN
american_scientific_journal-3703	148	34	2	2	NUM
american_scientific_journal-3703	148	35	,	,	PUNCT
american_scientific_journal-3703	148	36	then	then	ADV
american_scientific_journal-3703	148	37	all	all	DET
american_scientific_journal-3703	148	38	sequences	sequence	NOUN
american_scientific_journal-3703	148	39	of	of	ADP
american_scientific_journal-3703	148	40	length	length	NOUN
american_scientific_journal-3703	148	41	3	3	NUM
american_scientific_journal-3703	148	42	,	,	PUNCT
american_scientific_journal-3703	148	43	and	and	CCONJ
american_scientific_journal-3703	148	44	so	so	ADV
american_scientific_journal-3703	148	45	forth	forth	ADV
american_scientific_journal-3703	148	46	.	.	PUNCT
american_scientific_journal-3703	149	1	note	note	VERB
american_scientific_journal-3703	149	2	that	that	SCONJ
american_scientific_journal-3703	149	3	,	,	PUNCT
american_scientific_journal-3703	149	4	in	in	ADP
american_scientific_journal-3703	149	5	base	base	NOUN
american_scientific_journal-3703	149	6	(	(	PUNCT
american_scientific_journal-3703	149	7	)	)	PUNCT
american_scientific_journal-3703	149	8	2	2	NUM
american_scientific_journal-3703	149	9	,	,	PUNCT
american_scientific_journal-3703	149	10	d	d	NOUN
american_scientific_journal-3703	149	11	x	x	VERB
american_scientific_journal-3703	149	12	is	be	AUX
american_scientific_journal-3703	149	13	obtained	obtain	VERB
american_scientific_journal-3703	149	14	simply	simply	ADV
american_scientific_journal-3703	149	15	by	by	ADP
american_scientific_journal-3703	149	16	deleting	delete	VERB
american_scientific_journal-3703	149	17	the	the	DET
american_scientific_journal-3703	149	18	first	first	ADJ
american_scientific_journal-3703	149	19	digit	digit	NOUN
american_scientific_journal-3703	149	20	of	of	ADP
american_scientific_journal-3703	149	21	the	the	DET
american_scientific_journal-3703	149	22	base-2	base-2	PROPN
american_scientific_journal-3703	149	23	decimal	decimal	ADJ
american_scientific_journal-3703	149	24	expansion	expansion	NOUN
american_scientific_journal-3703	149	25	of	of	ADP
american_scientific_journal-3703	149	26	α	α	PROPN
american_scientific_journal-3703	149	27	(	(	PUNCT
american_scientific_journal-3703	149	28	i.e.	i.e.	X
american_scientific_journal-3703	149	29	,	,	PUNCT
american_scientific_journal-3703	149	30	it	it	PRON
american_scientific_journal-3703	149	31	acts	act	VERB
american_scientific_journal-3703	149	32	essentially	essentially	ADV
american_scientific_journal-3703	149	33	as	as	SCONJ
american_scientific_journal-3703	149	34	the	the	DET
american_scientific_journal-3703	149	35	shift	shift	NOUN
american_scientific_journal-3703	149	36	map).so	map).so	PROPN
american_scientific_journal-3703	149	37	in	in	ADP
american_scientific_journal-3703	149	38	particular	particular	ADJ
american_scientific_journal-3703	149	39	,	,	PUNCT
american_scientific_journal-3703	149	40	for	for	ADP
american_scientific_journal-3703	149	41	any	any	DET
american_scientific_journal-3703	149	42	sequence	sequence	NOUN
american_scientific_journal-3703	149	43	of	of	ADP
american_scientific_journal-3703	149	44	digits	digit	NOUN
american_scientific_journal-3703	149	45	,	,	PUNCT
american_scientific_journal-3703	149	46	there	there	PRON
american_scientific_journal-3703	149	47	is	be	VERB
american_scientific_journal-3703	149	48	a	a	DET
american_scientific_journal-3703	149	49	shift	shift	NOUN
american_scientific_journal-3703	149	50	of	of	ADP
american_scientific_journal-3703	149	51	α	α	PRON
american_scientific_journal-3703	149	52	that	that	PRON
american_scientific_journal-3703	149	53	begins	begin	VERB
american_scientific_journal-3703	149	54	with	with	ADP
american_scientific_journal-3703	149	55	that	that	DET
american_scientific_journal-3703	149	56	sequence	sequence	NOUN
american_scientific_journal-3703	149	57	of	of	ADP
american_scientific_journal-3703	149	58	digits	digit	NOUN
american_scientific_journal-3703	149	59	.	.	PUNCT
american_scientific_journal-3703	150	1	now	now	ADV
american_scientific_journal-3703	150	2	let	let	VERB
american_scientific_journal-3703	150	3	1	1	NUM
american_scientific_journal-3703	150	4	2	2	NUM
american_scientific_journal-3703	150	5	30	30	NUM
american_scientific_journal-3703	150	6	.	.	PUNCT
american_scientific_journal-3703	150	7	...	...	PUNCT
american_scientific_journal-3703	151	1	x	x	PUNCT
american_scientific_journal-3703	151	2	d	d	X
american_scientific_journal-3703	151	3	d	d	X
american_scientific_journal-3703	151	4	d=	d=	NOUN
american_scientific_journal-3703	151	5	and	and	CCONJ
american_scientific_journal-3703	151	6	0ε	0ε	NOUN
american_scientific_journal-3703	151	7	>	>	PUNCT
american_scientific_journal-3703	151	8	.	.	PUNCT
american_scientific_journal-3703	152	1	we	we	PRON
american_scientific_journal-3703	152	2	will	will	AUX
american_scientific_journal-3703	152	3	show	show	VERB
american_scientific_journal-3703	152	4	there	there	PRON
american_scientific_journal-3703	152	5	is	be	VERB
american_scientific_journal-3703	152	6	some	some	DET
american_scientific_journal-3703	152	7	shift	shift	NOUN
american_scientific_journal-3703	152	8	of	of	ADP
american_scientific_journal-3703	152	9	α	α	NOUN
american_scientific_journal-3703	152	10	within	within	ADP
american_scientific_journal-3703	152	11	ε	ε	PROPN
american_scientific_journal-3703	152	12	of	of	ADP
american_scientific_journal-3703	152	13	x.	x.	PROPN
american_scientific_journal-3703	152	14	choose	choose	VERB
american_scientific_journal-3703	152	15	n	n	NOUN
american_scientific_journal-3703	152	16	with	with	ADP
american_scientific_journal-3703	152	17	2	2	NUM
american_scientific_journal-3703	152	18	n	n	CCONJ
american_scientific_journal-3703	152	19	ε−	ε−	PROPN
american_scientific_journal-3703	152	20	<	<	X
american_scientific_journal-3703	152	21	.	.	PUNCT
american_scientific_journal-3703	153	1	american	american	PROPN
american_scientific_journal-3703	153	2	scientific	scientific	ADJ
american_scientific_journal-3703	153	3	research	research	PROPN
american_scientific_journal-3703	153	4	journal	journal	NOUN
american_scientific_journal-3703	153	5	for	for	ADP
american_scientific_journal-3703	153	6	engineering	engineering	NOUN
american_scientific_journal-3703	153	7	,	,	PUNCT
american_scientific_journal-3703	153	8	technology	technology	NOUN
american_scientific_journal-3703	153	9	,	,	PUNCT
american_scientific_journal-3703	153	10	and	and	CCONJ
american_scientific_journal-3703	153	11	sciences	science	NOUN
american_scientific_journal-3703	153	12	(	(	PUNCT
american_scientific_journal-3703	153	13	asrjets	asrjet	NOUN
american_scientific_journal-3703	153	14	)	)	PUNCT
american_scientific_journal-3703	153	15	(	(	PUNCT
american_scientific_journal-3703	153	16	2018	2018	NUM
american_scientific_journal-3703	153	17	)	)	PUNCT
american_scientific_journal-3703	153	18	volume	volume	NOUN
american_scientific_journal-3703	153	19	43	43	NUM
american_scientific_journal-3703	153	20	,	,	PUNCT
american_scientific_journal-3703	153	21	no	no	DET
american_scientific_journal-3703	153	22	1	1	NUM
american_scientific_journal-3703	153	23	,	,	PUNCT
american_scientific_journal-3703	153	24	pp	pp	ADV
american_scientific_journal-3703	153	25	110	110	NUM
american_scientific_journal-3703	153	26	-	-	SYM
american_scientific_journal-3703	153	27	133	133	NUM
american_scientific_journal-3703	153	28	117	117	NUM
american_scientific_journal-3703	153	29	then	then	ADV
american_scientific_journal-3703	153	30	there	there	PRON
american_scientific_journal-3703	153	31	is	be	VERB
american_scientific_journal-3703	153	32	a	a	DET
american_scientific_journal-3703	153	33	positive	positive	ADJ
american_scientific_journal-3703	153	34	integer	integer	NOUN
american_scientific_journal-3703	153	35	k	k	PROPN
american_scientific_journal-3703	153	36	such	such	ADJ
american_scientific_journal-3703	153	37	that	that	PRON
american_scientific_journal-3703	153	38	(	(	PUNCT
american_scientific_journal-3703	153	39	)	)	PUNCT
american_scientific_journal-3703	153	40	kd	kd	PROPN
american_scientific_journal-3703	153	41	α	α	PROPN
american_scientific_journal-3703	153	42	begins	begin	VERB
american_scientific_journal-3703	153	43	as	as	ADP
american_scientific_journal-3703	153	44	1	1	NUM
american_scientific_journal-3703	153	45	2	2	NUM
american_scientific_journal-3703	153	46	10	10	NUM
american_scientific_journal-3703	153	47	.	.	PUNCT
american_scientific_journal-3703	153	48	...	...	PUNCT
american_scientific_journal-3703	154	1	n	n	CCONJ
american_scientific_journal-3703	155	1	nd	nd	NOUN
american_scientific_journal-3703	155	2	d	d	NOUN
american_scientific_journal-3703	155	3	d	d	PROPN
american_scientific_journal-3703	155	4	d	d	PROPN
american_scientific_journal-3703	155	5	+	+	CCONJ
american_scientific_journal-3703	155	6	,	,	PUNCT
american_scientific_journal-3703	155	7	so	so	SCONJ
american_scientific_journal-3703	155	8	that	that	SCONJ
american_scientific_journal-3703	155	9	(	(	PUNCT
american_scientific_journal-3703	155	10	)	)	PUNCT
american_scientific_journal-3703	155	11	kd	kd	PROPN
american_scientific_journal-3703	155	12	α	α	PROPN
american_scientific_journal-3703	155	13	and	and	CCONJ
american_scientific_journal-3703	155	14	x	x	PRON
american_scientific_journal-3703	155	15	can	can	AUX
american_scientific_journal-3703	155	16	only	only	ADV
american_scientific_journal-3703	155	17	differ	differ	VERB
american_scientific_journal-3703	155	18	past	past	ADP
american_scientific_journal-3703	155	19	the	the	DET
american_scientific_journal-3703	155	20	n	n	NOUN
american_scientific_journal-3703	155	21	+	+	CCONJ
american_scientific_journal-3703	155	22	2nd	2nd	ADJ
american_scientific_journal-3703	155	23	decimal	decimal	ADJ
american_scientific_journal-3703	155	24	place	place	NOUN
american_scientific_journal-3703	155	25	.	.	PUNCT
american_scientific_journal-3703	156	1	then	then	ADV
american_scientific_journal-3703	156	2	(	(	PUNCT
american_scientific_journal-3703	156	3	)	)	PUNCT
american_scientific_journal-3703	156	4	2	2	NUM
american_scientific_journal-3703	156	5	2	2	NUM
american_scientific_journal-3703	156	6	2	2	NUM
american_scientific_journal-3703	156	7	2	2	NUM
american_scientific_journal-3703	156	8	k	k	NOUN
american_scientific_journal-3703	156	9	n	n	CCONJ
american_scientific_journal-3703	156	10	i	i	PRON
american_scientific_journal-3703	156	11	i	i	PRON
american_scientific_journal-3703	156	12	n	n	VERB
american_scientific_journal-3703	156	13	d	d	X
american_scientific_journal-3703	156	14	xα	xα	INTJ
american_scientific_journal-3703	156	15	ε	ε	PROPN
american_scientific_journal-3703	156	16	∞	∞	NUM
american_scientific_journal-3703	156	17	−	−	PROPN
american_scientific_journal-3703	157	1	=	=	PUNCT
american_scientific_journal-3703	158	1	+	+	NUM
american_scientific_journal-3703	158	2	−	−	PROPN
american_scientific_journal-3703	158	3	≤	≤	NOUN
american_scientific_journal-3703	158	4	<	<	X
american_scientific_journal-3703	158	5	<	<	X
american_scientific_journal-3703	158	6	∑	∑	PUNCT
american_scientific_journal-3703	158	7	as	as	SCONJ
american_scientific_journal-3703	158	8	required	require	VERB
american_scientific_journal-3703	158	9	.	.	PUNCT
american_scientific_journal-3703	159	1	finally	finally	ADV
american_scientific_journal-3703	159	2	,	,	PUNCT
american_scientific_journal-3703	159	3	we	we	PRON
american_scientific_journal-3703	159	4	show	show	VERB
american_scientific_journal-3703	159	5	that	that	SCONJ
american_scientific_journal-3703	159	6	d	d	NOUN
american_scientific_journal-3703	159	7	has	have	VERB
american_scientific_journal-3703	159	8	sensitive	sensitive	ADJ
american_scientific_journal-3703	159	9	dependence	dependence	NOUN
american_scientific_journal-3703	159	10	.	.	PUNCT
american_scientific_journal-3703	160	1	we	we	PRON
american_scientific_journal-3703	160	2	will	will	AUX
american_scientific_journal-3703	160	3	show	show	VERB
american_scientific_journal-3703	160	4	that	that	SCONJ
american_scientific_journal-3703	160	5	the	the	DET
american_scientific_journal-3703	160	6	value	value	NOUN
american_scientific_journal-3703	160	7	1	1	NUM
american_scientific_journal-3703	160	8	3	3	NUM
american_scientific_journal-3703	160	9	β	β	X
american_scientific_journal-3703	160	10	=	=	PUNCT
american_scientific_journal-3703	160	11	will	will	AUX
american_scientific_journal-3703	160	12	satisfy	satisfy	VERB
american_scientific_journal-3703	160	13	the	the	DET
american_scientific_journal-3703	160	14	requirements	requirement	NOUN
american_scientific_journal-3703	160	15	of	of	ADP
american_scientific_journal-3703	160	16	the	the	DET
american_scientific_journal-3703	160	17	definition	definition	NOUN
american_scientific_journal-3703	160	18	.	.	PUNCT
american_scientific_journal-3703	161	1	first	first	ADV
american_scientific_journal-3703	161	2	,	,	PUNCT
american_scientific_journal-3703	161	3	observe	observe	VERB
american_scientific_journal-3703	161	4	that	that	SCONJ
american_scientific_journal-3703	161	5	if	if	SCONJ
american_scientific_journal-3703	161	6	,	,	PUNCT
american_scientific_journal-3703	161	7	a	a	DET
american_scientific_journal-3703	161	8	b	b	NOUN
american_scientific_journal-3703	161	9	are	be	AUX
american_scientific_journal-3703	161	10	both	both	PRON
american_scientific_journal-3703	161	11	in	in	ADP
american_scientific_journal-3703	161	12	10	10	NUM
american_scientific_journal-3703	161	13	,	,	PUNCT
american_scientific_journal-3703	161	14	2	2	NUM
american_scientific_journal-3703	161	15			NOUN
american_scientific_journal-3703	161	16			PROPN
american_scientific_journal-3703	161	17			NOUN
american_scientific_journal-3703	161	18			PUNCT
american_scientific_journal-3703	161	19	or	or	CCONJ
american_scientific_journal-3703	161	20	1	1	NUM
american_scientific_journal-3703	161	21	,	,	PUNCT
american_scientific_journal-3703	161	22	1	1	NUM
american_scientific_journal-3703	161	23	2	2	NUM
american_scientific_journal-3703	161	24			NOUN
american_scientific_journal-3703	161	25			PROPN
american_scientific_journal-3703	161	26			NOUN
american_scientific_journal-3703	162	1			PUNCT
american_scientific_journal-3703	163	1	,	,	PUNCT
american_scientific_journal-3703	163	2	then	then	ADV
american_scientific_journal-3703	163	3	(	(	PUNCT
american_scientific_journal-3703	163	4	)	)	PUNCT
american_scientific_journal-3703	163	5	(	(	PUNCT
american_scientific_journal-3703	163	6	)	)	PUNCT
american_scientific_journal-3703	163	7	2d	2d	PROPN
american_scientific_journal-3703	164	1	b	b	PROPN
american_scientific_journal-3703	164	2	d	d	NOUN
american_scientific_journal-3703	164	3	a	a	DET
american_scientific_journal-3703	164	4	b	b	X
american_scientific_journal-3703	164	5	a−	a−	NOUN
american_scientific_journal-3703	164	6	=	=	PUNCT
american_scientific_journal-3703	164	7	−	−	PROPN
american_scientific_journal-3703	164	8	.	.	PUNCT
american_scientific_journal-3703	165	1	also	also	ADV
american_scientific_journal-3703	165	2	,	,	PUNCT
american_scientific_journal-3703	165	3	if	if	SCONJ
american_scientific_journal-3703	165	4	10	10	NUM
american_scientific_journal-3703	165	5	,	,	PUNCT
american_scientific_journal-3703	165	6	2	2	NUM
american_scientific_journal-3703	165	7	a	a	DET
american_scientific_journal-3703	165	8			NOUN
american_scientific_journal-3703	165	9	∈	∈	X
american_scientific_journal-3703	165	10			NOUN
american_scientific_journal-3703	165	11			PUNCT
american_scientific_journal-3703	165	12	and	and	CCONJ
american_scientific_journal-3703	165	13	1	1	NUM
american_scientific_journal-3703	165	14	,	,	PUNCT
american_scientific_journal-3703	165	15	1	1	NUM
american_scientific_journal-3703	165	16	2	2	NUM
american_scientific_journal-3703	165	17	b	b	NOUN
american_scientific_journal-3703	165	18			NOUN
american_scientific_journal-3703	165	19	∈	∈	PROPN
american_scientific_journal-3703	165	20			NOUN
american_scientific_journal-3703	165	21			PUNCT
american_scientific_journal-3703	166	1	then	then	ADV
american_scientific_journal-3703	166	2	one	one	NUM
american_scientific_journal-3703	166	3	of	of	ADP
american_scientific_journal-3703	166	4	b	b	NOUN
american_scientific_journal-3703	166	5	a−	a−	PROPN
american_scientific_journal-3703	166	6	and	and	CCONJ
american_scientific_journal-3703	166	7	(	(	PUNCT
american_scientific_journal-3703	166	8	)	)	PUNCT
american_scientific_journal-3703	166	9	(	(	PUNCT
american_scientific_journal-3703	166	10	)	)	PUNCT
american_scientific_journal-3703	166	11	d	d	X
american_scientific_journal-3703	166	12	b	b	PROPN
american_scientific_journal-3703	166	13	d	d	X
american_scientific_journal-3703	166	14	a−	a−	PROPN
american_scientific_journal-3703	166	15	is	be	AUX
american_scientific_journal-3703	166	16	at	at	ADV
american_scientific_journal-3703	166	17	least	least	ADJ
american_scientific_journal-3703	166	18	1	1	NUM
american_scientific_journal-3703	166	19	3	3	NUM
american_scientific_journal-3703	166	20	,	,	PUNCT
american_scientific_journal-3703	166	21	since	since	SCONJ
american_scientific_journal-3703	166	22	if	if	SCONJ
american_scientific_journal-3703	166	23	1	1	NUM
american_scientific_journal-3703	166	24	3	3	NUM
american_scientific_journal-3703	166	25	b	b	X
american_scientific_journal-3703	166	26	a−	a−	X
american_scientific_journal-3703	166	27	<	<	X
american_scientific_journal-3703	166	28	then	then	ADV
american_scientific_journal-3703	166	29	(	(	PUNCT
american_scientific_journal-3703	166	30	)	)	PUNCT
american_scientific_journal-3703	166	31	(	(	PUNCT
american_scientific_journal-3703	166	32	)	)	PUNCT
american_scientific_journal-3703	166	33	(	(	PUNCT
american_scientific_journal-3703	166	34	)	)	PUNCT
american_scientific_journal-3703	166	35	1	1	NUM
american_scientific_journal-3703	166	36	2d	2d	NUM
american_scientific_journal-3703	166	37	b	b	PROPN
american_scientific_journal-3703	166	38	d	d	NOUN
american_scientific_journal-3703	166	39	a	a	DET
american_scientific_journal-3703	166	40	b	b	X
american_scientific_journal-3703	166	41	a−	a−	NOUN
american_scientific_journal-3703	166	42	=	=	PUNCT
american_scientific_journal-3703	167	1	−	−	PROPN
american_scientific_journal-3703	167	2	−	−	NOUN
american_scientific_journal-3703	167	3	is	be	AUX
american_scientific_journal-3703	167	4	larger	large	ADJ
american_scientific_journal-3703	167	5	than	than	ADP
american_scientific_journal-3703	167	6	1	1	NUM
american_scientific_journal-3703	167	7	3	3	NUM
american_scientific_journal-3703	167	8	.therefore	.therefore	NOUN
american_scientific_journal-3703	167	9	,	,	PUNCT
american_scientific_journal-3703	167	10	if	if	SCONJ
american_scientific_journal-3703	167	11	x	x	PRON
american_scientific_journal-3703	167	12	,	,	PUNCT
american_scientific_journal-3703	167	13	y	y	PROPN
american_scientific_journal-3703	167	14	are	be	AUX
american_scientific_journal-3703	167	15	any	any	DET
american_scientific_journal-3703	167	16	two	two	NUM
american_scientific_journal-3703	167	17	distinct	distinct	ADJ
american_scientific_journal-3703	167	18	points	point	NOUN
american_scientific_journal-3703	167	19	,	,	PUNCT
american_scientific_journal-3703	167	20	the	the	DET
american_scientific_journal-3703	167	21	value	value	NOUN
american_scientific_journal-3703	167	22	of	of	ADP
american_scientific_journal-3703	167	23	(	(	PUNCT
american_scientific_journal-3703	167	24	)	)	PUNCT
american_scientific_journal-3703	167	25	(	(	PUNCT
american_scientific_journal-3703	167	26	)	)	PUNCT
american_scientific_journal-3703	167	27	n	n	CCONJ
american_scientific_journal-3703	167	28	nd	nd	NOUN
american_scientific_journal-3703	167	29	y	y	PROPN
american_scientific_journal-3703	167	30	d	d	PROPN
american_scientific_journal-3703	167	31	x−	x−	PROPN
american_scientific_journal-3703	167	32	will	will	AUX
american_scientific_journal-3703	167	33	double	double	VERB
american_scientific_journal-3703	167	34	at	at	ADP
american_scientific_journal-3703	167	35	each	each	DET
american_scientific_journal-3703	167	36	stage	stage	NOUN
american_scientific_journal-3703	167	37	until	until	ADP
american_scientific_journal-3703	167	38	the	the	DET
american_scientific_journal-3703	167	39	points	point	NOUN
american_scientific_journal-3703	167	40	x	x	PUNCT
american_scientific_journal-3703	167	41	and	and	CCONJ
american_scientific_journal-3703	167	42	y	y	PROPN
american_scientific_journal-3703	167	43	land	land	NOUN
american_scientific_journal-3703	167	44	in	in	ADP
american_scientific_journal-3703	167	45	opposite	opposite	ADJ
american_scientific_journal-3703	167	46	halves	half	NOUN
american_scientific_journal-3703	167	47	of	of	ADP
american_scientific_journal-3703	167	48	[	[	PUNCT
american_scientific_journal-3703	167	49	)	)	SYM
american_scientific_journal-3703	167	50	0,1	0,1	NUM
american_scientific_journal-3703	167	51	,	,	PUNCT
american_scientific_journal-3703	167	52	at	at	ADP
american_scientific_journal-3703	167	53	which	which	DET
american_scientific_journal-3703	167	54	point	point	NOUN
american_scientific_journal-3703	167	55	either	either	CCONJ
american_scientific_journal-3703	167	56	(	(	PUNCT
american_scientific_journal-3703	167	57	)	)	PUNCT
american_scientific_journal-3703	167	58	(	(	PUNCT
american_scientific_journal-3703	167	59	)	)	PUNCT
american_scientific_journal-3703	167	60	n	n	CCONJ
american_scientific_journal-3703	167	61	nd	nd	NOUN
american_scientific_journal-3703	167	62	y	y	PROPN
american_scientific_journal-3703	167	63	d	d	PROPN
american_scientific_journal-3703	167	64	x−	x−	PROPN
american_scientific_journal-3703	167	65	will	will	AUX
american_scientific_journal-3703	167	66	exceed	exceed	VERB
american_scientific_journal-3703	167	67	1	1	NUM
american_scientific_journal-3703	167	68	3	3	NUM
american_scientific_journal-3703	167	69	or	or	CCONJ
american_scientific_journal-3703	167	70	(	(	PUNCT
american_scientific_journal-3703	167	71	)	)	PUNCT
american_scientific_journal-3703	167	72	(	(	PUNCT
american_scientific_journal-3703	167	73	)	)	PUNCT
american_scientific_journal-3703	167	74	1	1	NUM
american_scientific_journal-3703	167	75	1n	1n	NUM
american_scientific_journal-3703	167	76	nd	nd	NOUN
american_scientific_journal-3703	168	1	y	y	NOUN
american_scientific_journal-3703	168	2	d	d	NOUN
american_scientific_journal-3703	168	3	x+	x+	PUNCT
american_scientific_journal-3703	169	1	+	+	ADP
american_scientific_journal-3703	169	2	−	−	NOUN
american_scientific_journal-3703	169	3	will	will	NOUN
american_scientific_journal-3703	169	4	.	.	PUNCT
american_scientific_journal-3703	170	1	thus	thus	ADV
american_scientific_journal-3703	170	2	,	,	PUNCT
american_scientific_journal-3703	170	3	for	for	ADP
american_scientific_journal-3703	170	4	any	any	DET
american_scientific_journal-3703	170	5	two	two	NUM
american_scientific_journal-3703	170	6	distinct	distinct	ADJ
american_scientific_journal-3703	170	7	points	point	NOUN
american_scientific_journal-3703	170	8	x	x	PUNCT
american_scientific_journal-3703	170	9	and	and	CCONJ
american_scientific_journal-3703	170	10	y	y	PROPN
american_scientific_journal-3703	170	11	,	,	PUNCT
american_scientific_journal-3703	170	12	their	their	PRON
american_scientific_journal-3703	170	13	orbits	orbit	NOUN
american_scientific_journal-3703	170	14	will	will	AUX
american_scientific_journal-3703	170	15	eventually	eventually	ADV
american_scientific_journal-3703	170	16	be	be	AUX
american_scientific_journal-3703	170	17	a	a	DET
american_scientific_journal-3703	170	18	distance	distance	NOUN
american_scientific_journal-3703	170	19	of	of	ADP
american_scientific_journal-3703	170	20	at	at	ADV
american_scientific_journal-3703	170	21	least	least	ADJ
american_scientific_journal-3703	170	22	apart	apart	ADV
american_scientific_journal-3703	170	23	after	after	ADP
american_scientific_journal-3703	170	24	iterating	iterate	VERB
american_scientific_journal-3703	170	25	some	some	DET
american_scientific_journal-3703	170	26	number	number	NOUN
american_scientific_journal-3703	170	27	of	of	ADP
american_scientific_journal-3703	170	28	times	time	NOUN
american_scientific_journal-3703	170	29	[	[	X
american_scientific_journal-3703	170	30	3	3	NUM
american_scientific_journal-3703	170	31	]	]	PUNCT
american_scientific_journal-3703	170	32	.	.	PUNCT
american_scientific_journal-3703	171	1	4.3	4.3	NUM
american_scientific_journal-3703	171	2	proposition	proposition	NOUN
american_scientific_journal-3703	171	3	the	the	DET
american_scientific_journal-3703	171	4	doubling	double	VERB
american_scientific_journal-3703	171	5	map	map	NOUN
american_scientific_journal-3703	171	6	(	(	PUNCT
american_scientific_journal-3703	171	7	)	)	PUNCT
american_scientific_journal-3703	171	8	12	12	NUM
american_scientific_journal-3703	171	9	for	for	ADP
american_scientific_journal-3703	171	10	0	0	NUM
american_scientific_journal-3703	171	11	2	2	NUM
american_scientific_journal-3703	171	12	12	12	NUM
american_scientific_journal-3703	171	13	1	1	NUM
american_scientific_journal-3703	171	14	for	for	ADP
american_scientific_journal-3703	171	15	1	1	NUM
american_scientific_journal-3703	171	16	2	2	NUM
american_scientific_journal-3703	171	17	x	x	SYM
american_scientific_journal-3703	171	18	x	x	PUNCT
american_scientific_journal-3703	171	19	d	d	NOUN
american_scientific_journal-3703	171	20	x	x	X
american_scientific_journal-3703	171	21	x	x	X
american_scientific_journal-3703	171	22	x	x	PUNCT
american_scientific_journal-3703	171	23			VERB
american_scientific_journal-3703	171	24	≤	≤	X
american_scientific_journal-3703	171	25	<	<	X
american_scientific_journal-3703	171	26	=	=	PROPN
american_scientific_journal-3703	171	27			PRON
american_scientific_journal-3703	171	28			PROPN
american_scientific_journal-3703	171	29	−	−	PROPN
american_scientific_journal-3703	171	30	≤	≤	X
american_scientific_journal-3703	171	31	<	<	X
american_scientific_journal-3703	171	32			NOUN
american_scientific_journal-3703	171	33	is	be	AUX
american_scientific_journal-3703	171	34	chaotic	chaotic	ADJ
american_scientific_journal-3703	171	35	on	on	ADP
american_scientific_journal-3703	171	36	[	[	PUNCT
american_scientific_journal-3703	171	37	)	)	PUNCT
american_scientific_journal-3703	171	38	0,1	0,1	NUM
american_scientific_journal-3703	171	39	in	in	ADP
american_scientific_journal-3703	171	40	the	the	DET
american_scientific_journal-3703	171	41	sense	sense	NOUN
american_scientific_journal-3703	171	42	of	of	ADP
american_scientific_journal-3703	171	43	lyapunov	lyapunov	PROPN
american_scientific_journal-3703	171	44	exponent	exponent	NOUN
american_scientific_journal-3703	171	45	.	.	PUNCT
american_scientific_journal-3703	172	1	proof	proof	NOUN
american_scientific_journal-3703	172	2	.	.	PUNCT
american_scientific_journal-3703	173	1	the	the	DET
american_scientific_journal-3703	173	2	give	give	NOUN
american_scientific_journal-3703	173	3	doubling	doubling	NOUN
american_scientific_journal-3703	173	4	map	map	NOUN
american_scientific_journal-3703	173	5	is	be	AUX
american_scientific_journal-3703	173	6	(	(	PUNCT
american_scientific_journal-3703	173	7	)	)	PUNCT
american_scientific_journal-3703	173	8	2	2	NUM
american_scientific_journal-3703	173	9	;	;	PUNCT
american_scientific_journal-3703	173	10	0	0	NUM
american_scientific_journal-3703	173	11	0.5	0.5	NUM
american_scientific_journal-3703	173	12	2	2	NUM
american_scientific_journal-3703	173	13	1	1	NUM
american_scientific_journal-3703	173	14	;	;	PUNCT
american_scientific_journal-3703	173	15	0.5	0.5	NUM
american_scientific_journal-3703	173	16	x	x	SYM
american_scientific_journal-3703	173	17	1	1	NUM
american_scientific_journal-3703	173	18	x	x	SYM
american_scientific_journal-3703	173	19	x	x	SYM
american_scientific_journal-3703	173	20	d	d	NOUN
american_scientific_journal-3703	173	21	x	x	X
american_scientific_journal-3703	173	22	x	x	SYM
american_scientific_journal-3703	173	23	≤	≤	NOUN
american_scientific_journal-3703	173	24	<	<	X
american_scientific_journal-3703	173	25			NOUN
american_scientific_journal-3703	173	26	=	=	PUNCT
american_scientific_journal-3703	173	27			ADP
american_scientific_journal-3703	173	28	−	−	PROPN
american_scientific_journal-3703	173	29	≤	≤	NOUN
american_scientific_journal-3703	173	30	<	<	X
american_scientific_journal-3703	173	31			NOUN
american_scientific_journal-3703	173	32	in	in	ADP
american_scientific_journal-3703	173	33	this	this	DET
american_scientific_journal-3703	173	34	case	case	NOUN
american_scientific_journal-3703	173	35	,	,	PUNCT
american_scientific_journal-3703	173	36	(	(	PUNCT
american_scientific_journal-3703	173	37	)	)	PUNCT
american_scientific_journal-3703	173	38	2	2	NUM
american_scientific_journal-3703	173	39	1d	1d	NUM
american_scientific_journal-3703	173	40	x′	x′	X
american_scientific_journal-3703	174	1	=	=	PUNCT
american_scientific_journal-3703	174	2	>	>	X
american_scientific_journal-3703	174	3	,	,	PUNCT
american_scientific_journal-3703	174	4	so	so	CCONJ
american_scientific_journal-3703	174	5	the	the	DET
american_scientific_journal-3703	174	6	doubling	double	VERB
american_scientific_journal-3703	174	7	map	map	NOUN
american_scientific_journal-3703	174	8	is	be	AUX
american_scientific_journal-3703	174	9	not	not	PART
american_scientific_journal-3703	174	10	attracted	attract	VERB
american_scientific_journal-3703	174	11	to	to	ADP
american_scientific_journal-3703	174	12	a	a	DET
american_scientific_journal-3703	174	13	sink	sink	NOUN
american_scientific_journal-3703	174	14	and	and	CCONJ
american_scientific_journal-3703	174	15	this	this	PRON
american_scientific_journal-3703	174	16	is	be	AUX
american_scientific_journal-3703	174	17	not	not	PART
american_scientific_journal-3703	174	18	asymptotically	asymptotically	ADV
american_scientific_journal-3703	174	19	periodic	periodic	ADJ
american_scientific_journal-3703	174	20	.	.	PUNCT
american_scientific_journal-3703	175	1	it	it	PRON
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american_scientific_journal-3703	175	17	1	1	NUM
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american_scientific_journal-3703	175	19	ln	ln	ADJ
american_scientific_journal-3703	175	20	lim	lim	PROPN
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american_scientific_journal-3703	181	20	0h	0h	NUM
american_scientific_journal-3703	181	21	x	x	SYM
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american_scientific_journal-3703	184	4	x	x	SYM
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american_scientific_journal-3703	187	11	2	2	NUM
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american_scientific_journal-3703	187	20	.........	.........	PUNCT
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american_scientific_journal-3703	187	24	3	3	NUM
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american_scientific_journal-3703	187	26	3	3	NUM
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american_scientific_journal-3703	187	34	,	,	PUNCT
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american_scientific_journal-3703	188	1	1when	1when	NUM
american_scientific_journal-3703	188	2	;	;	PUNCT
american_scientific_journal-3703	188	3	5	5	NUM
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american_scientific_journal-3703	188	20	.........	.........	PUNCT
american_scientific_journal-3703	188	21	5	5	NUM
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american_scientific_journal-3703	188	23	5	5	NUM
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american_scientific_journal-3703	188	25	5	5	NUM
american_scientific_journal-3703	188	26	5	5	NUM
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american_scientific_journal-3703	188	31			PROPN
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american_scientific_journal-3703	188	34	0	0	NUM
american_scientific_journal-3703	188	35	1when	1when	NUM
american_scientific_journal-3703	188	36	;	;	PUNCT
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american_scientific_journal-3703	188	45	1	1	NUM
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american_scientific_journal-3703	188	47	1	1	NUM
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american_scientific_journal-3703	188	117	1	1	NUM
american_scientific_journal-3703	188	118	2	2	NUM
american_scientific_journal-3703	188	119	4	4	NUM
american_scientific_journal-3703	188	120	1	1	NUM
american_scientific_journal-3703	188	121	2	2	NUM
american_scientific_journal-3703	188	122	4	4	NUM
american_scientific_journal-3703	188	123	1	1	NUM
american_scientific_journal-3703	188	124	2	2	NUM
american_scientific_journal-3703	188	125	,	,	PUNCT
american_scientific_journal-3703	188	126	,	,	PUNCT
american_scientific_journal-3703	188	127	,	,	PUNCT
american_scientific_journal-3703	188	128	,	,	PUNCT
american_scientific_journal-3703	188	129	,	,	PUNCT
american_scientific_journal-3703	188	130	,	,	PUNCT
american_scientific_journal-3703	188	131	,	,	PUNCT
american_scientific_journal-3703	188	132	,	,	PUNCT
american_scientific_journal-3703	188	133	.........	.........	PUNCT
american_scientific_journal-3703	188	134	7	7	NUM
american_scientific_journal-3703	188	135	7	7	NUM
american_scientific_journal-3703	188	136	7	7	NUM
american_scientific_journal-3703	188	137	7	7	NUM
american_scientific_journal-3703	188	138	7	7	NUM
american_scientific_journal-3703	188	139	7	7	NUM
american_scientific_journal-3703	188	140	7	7	NUM
american_scientific_journal-3703	188	141	7	7	NUM
american_scientific_journal-3703	188	142	v	v	NOUN
american_scientific_journal-3703	188	143			NOUN
american_scientific_journal-3703	188	144			NOUN
american_scientific_journal-3703	188	145			PRON
american_scientific_journal-3703	188	146			PROPN
american_scientific_journal-3703	188	147			ADJ
american_scientific_journal-3703	188	148			NOUN
american_scientific_journal-3703	188	149	,	,	PUNCT
american_scientific_journal-3703	188	150	0	0	NUM
american_scientific_journal-3703	189	1	1when	1when	NUM
american_scientific_journal-3703	189	2	;	;	PUNCT
american_scientific_journal-3703	189	3	11	11	NUM
american_scientific_journal-3703	189	4	x	x	X
american_scientific_journal-3703	189	5	=	=	PRON
american_scientific_journal-3703	189	6	(	(	PUNCT
american_scientific_journal-3703	189	7	)	)	PUNCT
american_scientific_journal-3703	189	8	1	1	NUM
american_scientific_journal-3703	189	9	2	2	NUM
american_scientific_journal-3703	189	10	4	4	NUM
american_scientific_journal-3703	189	11	8	8	NUM
american_scientific_journal-3703	189	12	5	5	NUM
american_scientific_journal-3703	189	13	10	10	NUM
american_scientific_journal-3703	189	14	9	9	NUM
american_scientific_journal-3703	189	15	7	7	NUM
american_scientific_journal-3703	189	16	3	3	NUM
american_scientific_journal-3703	189	17	6	6	NUM
american_scientific_journal-3703	189	18	1	1	NUM
american_scientific_journal-3703	189	19	,	,	PUNCT
american_scientific_journal-3703	189	20	,	,	PUNCT
american_scientific_journal-3703	189	21	,	,	PUNCT
american_scientific_journal-3703	189	22	,	,	PUNCT
american_scientific_journal-3703	189	23	,	,	PUNCT
american_scientific_journal-3703	189	24	,	,	PUNCT
american_scientific_journal-3703	189	25	,	,	PUNCT
american_scientific_journal-3703	189	26	,	,	PUNCT
american_scientific_journal-3703	189	27	,	,	PUNCT
american_scientific_journal-3703	189	28	,	,	PUNCT
american_scientific_journal-3703	189	29	,	,	PUNCT
american_scientific_journal-3703	189	30	.........	.........	PUNCT
american_scientific_journal-3703	189	31	11	11	NUM
american_scientific_journal-3703	189	32	11	11	NUM
american_scientific_journal-3703	189	33	11	11	NUM
american_scientific_journal-3703	189	34	11	11	NUM
american_scientific_journal-3703	189	35	11	11	NUM
american_scientific_journal-3703	189	36	11	11	NUM
american_scientific_journal-3703	189	37	11	11	NUM
american_scientific_journal-3703	189	38	11	11	NUM
american_scientific_journal-3703	189	39	11	11	NUM
american_scientific_journal-3703	189	40	11	11	NUM
american_scientific_journal-3703	189	41	11	11	NUM
american_scientific_journal-3703	189	42	vi	vi	NOUN
american_scientific_journal-3703	189	43			NOUN
american_scientific_journal-3703	189	44			NOUN
american_scientific_journal-3703	189	45			PRON
american_scientific_journal-3703	189	46			PROPN
american_scientific_journal-3703	189	47			ADJ
american_scientific_journal-3703	189	48			NOUN
american_scientific_journal-3703	189	49	we	we	PRON
american_scientific_journal-3703	189	50	see	see	VERB
american_scientific_journal-3703	189	51	that	that	SCONJ
american_scientific_journal-3703	189	52	(	(	PUNCT
american_scientific_journal-3703	189	53	i	i	NOUN
american_scientific_journal-3703	189	54	)	)	PUNCT
american_scientific_journal-3703	189	55	,	,	PUNCT
american_scientific_journal-3703	189	56	(	(	PUNCT
american_scientific_journal-3703	189	57	ii	ii	NOUN
american_scientific_journal-3703	189	58	)	)	PUNCT
american_scientific_journal-3703	189	59	,	,	PUNCT
american_scientific_journal-3703	189	60	(	(	PUNCT
american_scientific_journal-3703	189	61	iii	iii	NOUN
american_scientific_journal-3703	189	62	)	)	PUNCT
american_scientific_journal-3703	189	63	,	,	PUNCT
american_scientific_journal-3703	189	64	(	(	PUNCT
american_scientific_journal-3703	189	65	iv	iv	X
american_scientific_journal-3703	189	66	)	)	PUNCT
american_scientific_journal-3703	189	67	,	,	PUNCT
american_scientific_journal-3703	189	68	(	(	PUNCT
american_scientific_journal-3703	189	69	vi	vi	X
american_scientific_journal-3703	189	70	)	)	PUNCT
american_scientific_journal-3703	189	71	have	have	VERB
american_scientific_journal-3703	189	72	the	the	DET
american_scientific_journal-3703	189	73	period	period	NOUN
american_scientific_journal-3703	189	74	2	2	NUM
american_scientific_journal-3703	189	75	,	,	PUNCT
american_scientific_journal-3703	189	76	4	4	NUM
american_scientific_journal-3703	189	77	,	,	PUNCT
american_scientific_journal-3703	189	78	2	2	NUM
american_scientific_journal-3703	189	79	,	,	PUNCT
american_scientific_journal-3703	189	80	6	6	NUM
american_scientific_journal-3703	189	81	,	,	PUNCT
american_scientific_journal-3703	189	82	9	9	NUM
american_scientific_journal-3703	189	83	respectively	respectively	ADV
american_scientific_journal-3703	189	84	but	but	CCONJ
american_scientific_journal-3703	189	85	(	(	PUNCT
american_scientific_journal-3703	189	86	v	v	NOUN
american_scientific_journal-3703	189	87	)	)	PUNCT
american_scientific_journal-3703	189	88	has	have	VERB
american_scientific_journal-3703	189	89	prime	prime	ADJ
american_scientific_journal-3703	189	90	period	period	NOUN
american_scientific_journal-3703	189	91	3	3	NUM
american_scientific_journal-3703	189	92	.	.	PUNCT
american_scientific_journal-3703	190	1	so	so	ADV
american_scientific_journal-3703	190	2	the	the	DET
american_scientific_journal-3703	190	3	doubling	double	VERB
american_scientific_journal-3703	190	4	map	map	NOUN
american_scientific_journal-3703	190	5	is	be	AUX
american_scientific_journal-3703	190	6	chaotic	chaotic	ADJ
american_scientific_journal-3703	190	7	in	in	ADP
american_scientific_journal-3703	190	8	the	the	DET
american_scientific_journal-3703	190	9	sense	sense	NOUN
american_scientific_journal-3703	190	10	of	of	ADP
american_scientific_journal-3703	190	11	li	li	PROPN
american_scientific_journal-3703	190	12	-	-	PROPN
american_scientific_journal-3703	190	13	yorke	yorke	NOUN
american_scientific_journal-3703	190	14	[	[	X
american_scientific_journal-3703	190	15	7	7	NUM
american_scientific_journal-3703	190	16	]	]	PUNCT
american_scientific_journal-3703	190	17	.	.	PUNCT
american_scientific_journal-3703	191	1	4.5	4.5	NUM
american_scientific_journal-3703	191	2	proposition	proposition	NOUN
american_scientific_journal-3703	191	3	doubling	doubling	NOUN
american_scientific_journal-3703	191	4	map	map	NOUN
american_scientific_journal-3703	191	5	is	be	AUX
american_scientific_journal-3703	191	6	chaotic	chaotic	ADJ
american_scientific_journal-3703	191	7	in	in	ADP
american_scientific_journal-3703	191	8	the	the	DET
american_scientific_journal-3703	191	9	sense	sense	NOUN
american_scientific_journal-3703	191	10	of	of	ADP
american_scientific_journal-3703	191	11	wiggin	wiggin	PROPN
american_scientific_journal-3703	191	12	.	.	PUNCT
american_scientific_journal-3703	192	1	proof	proof	NOUN
american_scientific_journal-3703	192	2	.	.	PUNCT
american_scientific_journal-3703	193	1	consider	consider	VERB
american_scientific_journal-3703	193	2	the	the	DET
american_scientific_journal-3703	193	3	doubling	double	VERB
american_scientific_journal-3703	193	4	map	map	NOUN
american_scientific_journal-3703	193	5	(	(	PUNCT
american_scientific_journal-3703	193	6	)	)	PUNCT
american_scientific_journal-3703	193	7	[	[	PUNCT
american_scientific_journal-3703	193	8	)	)	PUNCT
american_scientific_journal-3703	193	9	[	[	PUNCT
american_scientific_journal-3703	193	10	):	):	PUNCT
american_scientific_journal-3703	193	11	0,1	0,1	NUM
american_scientific_journal-3703	193	12	0,1d	0,1d	NOUN
american_scientific_journal-3703	193	13	x	x	X
american_scientific_journal-3703	193	14	→	→	PUNCT
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american_scientific_journal-3703	193	17	(	(	PUNCT
american_scientific_journal-3703	193	18	)	)	PUNCT
american_scientific_journal-3703	193	19	2	2	NUM
american_scientific_journal-3703	193	20	;	;	PUNCT
american_scientific_journal-3703	193	21	0	0	NUM
american_scientific_journal-3703	193	22	0.5	0.5	NUM
american_scientific_journal-3703	193	23	2	2	NUM
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american_scientific_journal-3703	193	25	2	2	NUM
american_scientific_journal-3703	193	26	1	1	NUM
american_scientific_journal-3703	193	27	;	;	PUNCT
american_scientific_journal-3703	193	28	0,5	0,5	NUM
american_scientific_journal-3703	193	29	1	1	NUM
american_scientific_journal-3703	193	30	x	x	SYM
american_scientific_journal-3703	193	31	x	x	PUNCT
american_scientific_journal-3703	193	32	d	d	NOUN
american_scientific_journal-3703	193	33	x	x	X
american_scientific_journal-3703	193	34	x	x	X
american_scientific_journal-3703	193	35	x	x	PUNCT
american_scientific_journal-3703	193	36	x	x	SYM
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american_scientific_journal-3703	193	38	<	<	X
american_scientific_journal-3703	193	39			NOUN
american_scientific_journal-3703	193	40	=	=	SYM
american_scientific_journal-3703	193	41	=	=	PUNCT
american_scientific_journal-3703	193	42			ADP
american_scientific_journal-3703	193	43	−	−	PROPN
american_scientific_journal-3703	193	44	≤	≤	NUM
american_scientific_journal-3703	193	45	≤	≤	NOUN
american_scientific_journal-3703	193	46	first	first	ADV
american_scientific_journal-3703	193	47	i	i	PRON
american_scientific_journal-3703	193	48	will	will	AUX
american_scientific_journal-3703	193	49	prove	prove	VERB
american_scientific_journal-3703	193	50	that	that	PRON
american_scientific_journal-3703	193	51	(	(	PUNCT
american_scientific_journal-3703	193	52	)	)	PUNCT
american_scientific_journal-3703	193	53	d	d	X
american_scientific_journal-3703	193	54	x	x	PUNCT
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american_scientific_journal-3703	194	2	∑	∑	PART
american_scientific_journal-3703	194	3	be	be	AUX
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american_scientific_journal-3703	194	12	0	0	PROPN
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american_scientific_journal-3703	194	15	1	1	NUM
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american_scientific_journal-3703	194	24	)	)	PUNCT
american_scientific_journal-3703	194	25	0	0	NUM
american_scientific_journal-3703	194	26	1	1	NUM
american_scientific_journal-3703	194	27	2	2	NUM
american_scientific_journal-3703	194	28	1	1	NUM
american_scientific_journal-3703	194	29	,	,	PUNCT
american_scientific_journal-3703	194	30	.......	.......	PUNCT
american_scientific_journal-3703	195	1	2	2	NUM
american_scientific_journal-3703	195	2	i	i	PRON
american_scientific_journal-3703	195	3	iis	iis	VERB
american_scientific_journal-3703	195	4	s	s	X
american_scientific_journal-3703	196	1	s	s	NOUN
american_scientific_journal-3703	197	1	s	s	X
american_scientific_journal-3703	197	2	s	s	X
american_scientific_journal-3703	197	3	sρ	sρ	ADP
american_scientific_journal-3703	197	4	τ	τ	PROPN
american_scientific_journal-3703	197	5	τ=	τ=	PRON
american_scientific_journal-3703	197	6	−	−	NOUN
american_scientific_journal-3703	197	7	∀	∀	NOUN
american_scientific_journal-3703	197	8	=	=	PUNCT
american_scientific_journal-3703	197	9	and	and	CCONJ
american_scientific_journal-3703	197	10	(	(	PUNCT
american_scientific_journal-3703	197	11	)	)	PUNCT
american_scientific_journal-3703	197	12	0	0	NUM
american_scientific_journal-3703	197	13	1	1	NUM
american_scientific_journal-3703	197	14	2	2	NUM
american_scientific_journal-3703	197	15	......	......	PUNCT
american_scientific_journal-3703	197	16	τ	τ	PROPN
american_scientific_journal-3703	197	17	τ	τ	PROPN
american_scientific_journal-3703	197	18	τ	τ	PROPN
american_scientific_journal-3703	197	19	τ=	τ=	PROPN
american_scientific_journal-3703	197	20	∈σ	∈σ	PROPN
american_scientific_journal-3703	197	21	and	and	CCONJ
american_scientific_journal-3703	197	22	we	we	PRON
american_scientific_journal-3703	197	23	define	define	VERB
american_scientific_journal-3703	197	24	:	:	PUNCT
american_scientific_journal-3703	197	25	σ	σ	PROPN
american_scientific_journal-3703	197	26	σ	σ	PROPN
american_scientific_journal-3703	197	27	→	→	PROPN
american_scientific_journal-3703	197	28	σ	σ	PROPN
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american_scientific_journal-3703	197	30	by	by	ADP
american_scientific_journal-3703	197	31	(	(	PUNCT
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american_scientific_journal-3703	197	33	(	(	PUNCT
american_scientific_journal-3703	197	34	)	)	PUNCT
american_scientific_journal-3703	197	35	0	0	NUM
american_scientific_journal-3703	198	1	1	1	NUM
american_scientific_journal-3703	198	2	2	2	NUM
american_scientific_journal-3703	198	3	1	1	NUM
american_scientific_journal-3703	198	4	2	2	NUM
american_scientific_journal-3703	198	5	3	3	NUM
american_scientific_journal-3703	198	6	........	........	PUNCT
american_scientific_journal-3703	198	7	........	........	PUNCT
american_scientific_journal-3703	199	1	s	s	PART
american_scientific_journal-3703	199	2	s	s	X
american_scientific_journal-3703	199	3	s	s	X
american_scientific_journal-3703	199	4	s	s	NOUN
american_scientific_journal-3703	199	5	s	s	NOUN
american_scientific_journal-3703	199	6	sσ	sσ	NOUN
american_scientific_journal-3703	199	7	=	=	PUNCT
american_scientific_journal-3703	199	8	.	.	PUNCT
american_scientific_journal-3703	200	1	then	then	ADV
american_scientific_journal-3703	200	2	there	there	PRON
american_scientific_journal-3703	200	3	exist	exist	VERB
american_scientific_journal-3703	200	4	a	a	DET
american_scientific_journal-3703	200	5	point	point	NOUN
american_scientific_journal-3703	200	6	(	(	PUNCT
american_scientific_journal-3703	200	7	)	)	PUNCT
american_scientific_journal-3703	200	8	0100011011000001	0100011011000001	NUM
american_scientific_journal-3703	200	9	....	....	PUNCT
american_scientific_journal-3703	201	1	x	x	X
american_scientific_journal-3703	201	2	=	=	PUNCT
american_scientific_journal-3703	201	3	created	create	VERB
american_scientific_journal-3703	201	4	by	by	ADP
american_scientific_journal-3703	201	5	blocks	block	NOUN
american_scientific_journal-3703	201	6	of	of	ADP
american_scientific_journal-3703	201	7	0	0	NUM
american_scientific_journal-3703	201	8	'	'	PUNCT
american_scientific_journal-3703	201	9	and	and	CCONJ
american_scientific_journal-3703	201	10	1	1	NUM
american_scientific_journal-3703	201	11	's	's	PART
american_scientific_journal-3703	201	12	s	s	NOUN
american_scientific_journal-3703	201	13	which	which	PRON
american_scientific_journal-3703	201	14	has	have	VERB
american_scientific_journal-3703	201	15	a	a	DET
american_scientific_journal-3703	201	16	dense	dense	ADJ
american_scientific_journal-3703	201	17	orbit	orbit	NOUN
american_scientific_journal-3703	201	18	.	.	PUNCT
american_scientific_journal-3703	202	1	so	so	ADV
american_scientific_journal-3703	202	2	σ	σ	PROPN
american_scientific_journal-3703	202	3	is	be	AUX
american_scientific_journal-3703	202	4	transitive	transitive	ADJ
american_scientific_journal-3703	202	5	and	and	CCONJ
american_scientific_journal-3703	202	6	then	then	ADV
american_scientific_journal-3703	202	7	(	(	PUNCT
american_scientific_journal-3703	202	8	)	)	PUNCT
american_scientific_journal-3703	202	9	b	b	X
american_scientific_journal-3703	202	10	x	x	PUNCT
american_scientific_journal-3703	202	11	is	be	AUX
american_scientific_journal-3703	202	12	transitive	transitive	ADJ
american_scientific_journal-3703	203	1	[	[	PUNCT
american_scientific_journal-3703	203	2	13	13	NUM
american_scientific_journal-3703	203	3	]	]	PUNCT
american_scientific_journal-3703	203	4	.	.	PUNCT
american_scientific_journal-3703	204	1	now	now	ADV
american_scientific_journal-3703	204	2	i	i	PRON
american_scientific_journal-3703	204	3	will	will	AUX
american_scientific_journal-3703	204	4	prove	prove	VERB
american_scientific_journal-3703	204	5	that	that	PRON
american_scientific_journal-3703	204	6	(	(	PUNCT
american_scientific_journal-3703	204	7	)	)	PUNCT
american_scientific_journal-3703	204	8	b	b	X
american_scientific_journal-3703	204	9	x	x	PUNCT
american_scientific_journal-3703	204	10	has	have	VERB
american_scientific_journal-3703	204	11	a	a	DET
american_scientific_journal-3703	204	12	dense	dense	ADJ
american_scientific_journal-3703	204	13	set	set	NOUN
american_scientific_journal-3703	204	14	of	of	ADP
american_scientific_journal-3703	204	15	periodic	periodic	ADJ
american_scientific_journal-3703	204	16	points	point	NOUN
american_scientific_journal-3703	204	17	.	.	PUNCT
american_scientific_journal-3703	205	1	we	we	PRON
american_scientific_journal-3703	205	2	have	have	VERB
american_scientific_journal-3703	205	3	that	that	PRON
american_scientific_journal-3703	205	4	(	(	PUNCT
american_scientific_journal-3703	205	5	)	)	PUNCT
american_scientific_journal-3703	205	6	(	(	PUNCT
american_scientific_journal-3703	205	7	)	)	PUNCT
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american_scientific_journal-3703	205	9	}	}	PUNCT
american_scientific_journal-3703	205	10	(	(	PUNCT
american_scientific_journal-3703	205	11	)	)	PUNCT
american_scientific_journal-3703	205	12	1	1	NUM
american_scientific_journal-3703	205	13	1fix	1fix	NUM
american_scientific_journal-3703	205	14	0	0	NUM
american_scientific_journal-3703	205	15	1	1	NUM
american_scientific_journal-3703	205	16	2	2	NUM
american_scientific_journal-3703	205	17	1.b	1.b	NUM
american_scientific_journal-3703	205	18	per	per	ADP
american_scientific_journal-3703	205	19	b	b	NOUN
american_scientific_journal-3703	205	20	per	per	ADP
american_scientific_journal-3703	205	21	f=	f=	ADJ
american_scientific_journal-3703	205	22	=	=	PUNCT
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american_scientific_journal-3703	205	24	=	=	PUNCT
american_scientific_journal-3703	206	1	=	=	SYM
american_scientific_journal-3703	206	2	−	−	PROPN
american_scientific_journal-3703	206	3	the	the	DET
american_scientific_journal-3703	206	4	second	second	ADJ
american_scientific_journal-3703	206	5	iterated	iterated	ADJ
american_scientific_journal-3703	206	6	map	map	NOUN
american_scientific_journal-3703	206	7	2b	2b	NOUN
american_scientific_journal-3703	206	8	is	be	AUX
american_scientific_journal-3703	206	9	given	give	VERB
american_scientific_journal-3703	206	10	by	by	ADP
american_scientific_journal-3703	206	11	(	(	PUNCT
american_scientific_journal-3703	206	12	)	)	PUNCT
american_scientific_journal-3703	206	13	(	(	PUNCT
american_scientific_journal-3703	206	14	)	)	SYM
american_scientific_journal-3703	206	15	2	2	NUM
american_scientific_journal-3703	206	16	2	2	NUM
american_scientific_journal-3703	206	17	1	1	NUM
american_scientific_journal-3703	206	18	24	24	NUM
american_scientific_journal-3703	206	19	mod1	mod1	NOUN
american_scientific_journal-3703	206	20	and	and	CCONJ
american_scientific_journal-3703	206	21	0	0	NUM
american_scientific_journal-3703	206	22	,	,	PUNCT
american_scientific_journal-3703	206	23	,	,	PUNCT
american_scientific_journal-3703	206	24	3	3	NUM
american_scientific_journal-3703	206	25	3	3	NUM
american_scientific_journal-3703	206	26	b	b	X
american_scientific_journal-3703	206	27	x	x	SYM
american_scientific_journal-3703	206	28	x	x	X
american_scientific_journal-3703	206	29	per	per	ADP
american_scientific_journal-3703	206	30	b	b	NOUN
american_scientific_journal-3703	206	31			NOUN
american_scientific_journal-3703	206	32	=	=	NOUN
american_scientific_journal-3703	206	33	=	=	SYM
american_scientific_journal-3703	206	34			ADP
american_scientific_journal-3703	206	35			PROPN
american_scientific_journal-3703	206	36			ADJ
american_scientific_journal-3703	206	37			NOUN
american_scientific_journal-3703	206	38	(	(	PUNCT
american_scientific_journal-3703	206	39	)	)	PUNCT
american_scientific_journal-3703	206	40	2	2	NUM
american_scientific_journal-3703	206	41	2	2	NUM
american_scientific_journal-3703	206	42	3	3	NUM
american_scientific_journal-3703	206	43	2	2	NUM
american_scientific_journal-3703	206	44	1.per	1.per	NOUN
american_scientific_journal-3703	206	45	b⇒	b⇒	PUNCT
american_scientific_journal-3703	206	46	=	=	PUNCT
american_scientific_journal-3703	207	1	=	=	SYM
american_scientific_journal-3703	207	2	−	−	NOUN
american_scientific_journal-3703	207	3	generalizing	generalize	VERB
american_scientific_journal-3703	207	4	this	this	DET
american_scientific_journal-3703	207	5	result	result	NOUN
american_scientific_journal-3703	207	6	the	the	DET
american_scientific_journal-3703	207	7	n	n	ADV
american_scientific_journal-3703	207	8	-	-	PUNCT
american_scientific_journal-3703	207	9	th	th	ADV
american_scientific_journal-3703	207	10	iterated	iterate	VERB
american_scientific_journal-3703	207	11	american	american	ADJ
american_scientific_journal-3703	207	12	scientific	scientific	ADJ
american_scientific_journal-3703	207	13	research	research	NOUN
american_scientific_journal-3703	207	14	journal	journal	NOUN
american_scientific_journal-3703	207	15	for	for	ADP
american_scientific_journal-3703	207	16	engineering	engineering	NOUN
american_scientific_journal-3703	207	17	,	,	PUNCT
american_scientific_journal-3703	207	18	technology	technology	NOUN
american_scientific_journal-3703	207	19	,	,	PUNCT
american_scientific_journal-3703	207	20	and	and	CCONJ
american_scientific_journal-3703	207	21	sciences	science	NOUN
american_scientific_journal-3703	207	22	(	(	PUNCT
american_scientific_journal-3703	207	23	asrjets	asrjet	NOUN
american_scientific_journal-3703	207	24	)	)	PUNCT
american_scientific_journal-3703	207	25	(	(	PUNCT
american_scientific_journal-3703	207	26	2018	2018	NUM
american_scientific_journal-3703	207	27	)	)	PUNCT
american_scientific_journal-3703	207	28	volume	volume	NOUN
american_scientific_journal-3703	207	29	43	43	NUM
american_scientific_journal-3703	207	30	,	,	PUNCT
american_scientific_journal-3703	207	31	no	no	DET
american_scientific_journal-3703	207	32	1	1	NUM
american_scientific_journal-3703	207	33	,	,	PUNCT
american_scientific_journal-3703	207	34	pp	pp	ADV
american_scientific_journal-3703	207	35	110	110	NUM
american_scientific_journal-3703	207	36	-	-	SYM
american_scientific_journal-3703	207	37	133	133	NUM
american_scientific_journal-3703	207	38	119	119	NUM
american_scientific_journal-3703	207	39	map	map	NOUN
american_scientific_journal-3703	207	40	is	be	AUX
american_scientific_journal-3703	207	41	given	give	VERB
american_scientific_journal-3703	207	42	by	by	ADP
american_scientific_journal-3703	207	43	(	(	PUNCT
american_scientific_journal-3703	207	44	)	)	PUNCT
american_scientific_journal-3703	207	45	2	2	NUM
american_scientific_journal-3703	207	46	mod1.n	mod1.n	NOUN
american_scientific_journal-3703	207	47	nb	nb	NOUN
american_scientific_journal-3703	207	48	x	x	PROPN
american_scientific_journal-3703	207	49	x=	x=	PUNCT
american_scientific_journal-3703	208	1	so	so	ADV
american_scientific_journal-3703	208	2	(	(	PUNCT
american_scientific_journal-3703	208	3	)	)	PUNCT
american_scientific_journal-3703	208	4	1	1	NUM
american_scientific_journal-3703	208	5	2	2	NUM
american_scientific_journal-3703	208	6	2	2	NUM
american_scientific_journal-3703	208	7	20	20	NUM
american_scientific_journal-3703	208	8	,	,	PUNCT
american_scientific_journal-3703	208	9	,	,	PUNCT
american_scientific_journal-3703	208	10	,	,	PUNCT
american_scientific_journal-3703	208	11	......	......	PUNCT
american_scientific_journal-3703	208	12	2	2	NUM
american_scientific_journal-3703	208	13	1	1	NUM
american_scientific_journal-3703	208	14	2	2	NUM
american_scientific_journal-3703	208	15	1	1	NUM
american_scientific_journal-3703	208	16	2	2	NUM
american_scientific_journal-3703	208	17	1	1	NUM
american_scientific_journal-3703	208	18	n	n	CCONJ
american_scientific_journal-3703	208	19	n	n	CCONJ
american_scientific_journal-3703	208	20	n	n	CCONJ
american_scientific_journal-3703	208	21	n	n	ADV
american_scientific_journal-3703	208	22	nper	nper	NOUN
american_scientific_journal-3703	208	23	b	b	NOUN
american_scientific_journal-3703	208	24			PROPN
american_scientific_journal-3703	208	25	−	−	NOUN
american_scientific_journal-3703	208	26	=	=	PROPN
american_scientific_journal-3703	208	27			ADP
american_scientific_journal-3703	208	28			PROPN
american_scientific_journal-3703	208	29	−	−	PROPN
american_scientific_journal-3703	208	30	−	−	PROPN
american_scientific_journal-3703	208	31	−	−	PROPN
american_scientific_journal-3703	208	32			NOUN
american_scientific_journal-3703	208	33			PROPN
american_scientific_journal-3703	208	34	(	(	PUNCT
american_scientific_journal-3703	208	35	)	)	PUNCT
american_scientific_journal-3703	208	36	and	and	CCONJ
american_scientific_journal-3703	208	37	2	2	NUM
american_scientific_journal-3703	208	38	1n	1n	NUM
american_scientific_journal-3703	208	39	nper	nper	NOUN
american_scientific_journal-3703	208	40	b	b	NOUN
american_scientific_journal-3703	208	41	=	=	PUNCT
american_scientific_journal-3703	208	42	−	−	PROPN
american_scientific_journal-3703	208	43	.now	.now	NOUN
american_scientific_journal-3703	209	1	(	(	PUNCT
american_scientific_journal-3703	209	2	)	)	PUNCT
american_scientific_journal-3703	209	3	[	[	PUNCT
american_scientific_journal-3703	209	4	)	)	PUNCT
american_scientific_journal-3703	209	5	(	(	PUNCT
american_scientific_journal-3703	209	6	)	)	PUNCT
american_scientific_journal-3703	209	7	lim	lim	PROPN
american_scientific_journal-3703	209	8	so	so	ADV
american_scientific_journal-3703	209	9	0,1	0,1	NUM
american_scientific_journal-3703	209	10	and	and	CCONJ
american_scientific_journal-3703	209	11	0,nn	0,nn	NOUN
american_scientific_journal-3703	209	12	per	per	ADP
american_scientific_journal-3703	209	13	b	b	PROPN
american_scientific_journal-3703	209	14	x	x	SYM
american_scientific_journal-3703	209	15	n	n	PROPN
american_scientific_journal-3703	209	16	xεε	xεε	INTJ
american_scientific_journal-3703	209	17	→∞	→∞	NOUN
american_scientific_journal-3703	210	1	=	=	SYM
american_scientific_journal-3703	210	2	∞	∞	NUM
american_scientific_journal-3703	210	3	∀	∀	X
american_scientific_journal-3703	210	4	∈	∈	NOUN
american_scientific_journal-3703	210	5	∀	∀	X
american_scientific_journal-3703	210	6	>	>	X
american_scientific_journal-3703	210	7	will	will	AUX
american_scientific_journal-3703	210	8	contains	contain	VERB
american_scientific_journal-3703	210	9	a	a	DET
american_scientific_journal-3703	210	10	periodic	periodic	ADJ
american_scientific_journal-3703	210	11	point	point	NOUN
american_scientific_journal-3703	210	12	.	.	PUNCT
american_scientific_journal-3703	211	1	hence	hence	ADV
american_scientific_journal-3703	211	2	the	the	DET
american_scientific_journal-3703	211	3	periodic	periodic	ADJ
american_scientific_journal-3703	211	4	points	point	NOUN
american_scientific_journal-3703	211	5	of	of	ADP
american_scientific_journal-3703	211	6	b	b	NOUN
american_scientific_journal-3703	211	7	are	be	AUX
american_scientific_journal-3703	211	8	dense	dense	ADJ
american_scientific_journal-3703	211	9	.	.	PUNCT
american_scientific_journal-3703	212	1	since	since	SCONJ
american_scientific_journal-3703	212	2	all	all	DET
american_scientific_journal-3703	212	3	the	the	DET
american_scientific_journal-3703	212	4	conditions	condition	NOUN
american_scientific_journal-3703	212	5	for	for	ADP
american_scientific_journal-3703	212	6	the	the	DET
american_scientific_journal-3703	212	7	three	three	NUM
american_scientific_journal-3703	212	8	chaotic	chaotic	ADJ
american_scientific_journal-3703	212	9	definitions	definition	NOUN
american_scientific_journal-3703	212	10	are	be	AUX
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american_scientific_journal-3703	212	12	,	,	PUNCT
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american_scientific_journal-3703	212	14	the	the	DET
american_scientific_journal-3703	212	15	map	map	NOUN
american_scientific_journal-3703	212	16	(	(	PUNCT
american_scientific_journal-3703	212	17	)	)	PUNCT
american_scientific_journal-3703	212	18	d	d	X
american_scientific_journal-3703	212	19	x	x	X
american_scientific_journal-3703	212	20	is	be	AUX
american_scientific_journal-3703	212	21	wchaotic	wchaotic	ADJ
american_scientific_journal-3703	212	22	[	[	X
american_scientific_journal-3703	212	23	7].note	7].note	NUM
american_scientific_journal-3703	212	24	:	:	PUNCT
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american_scientific_journal-3703	212	26	map	map	NOUN
american_scientific_journal-3703	212	27	can	can	AUX
american_scientific_journal-3703	212	28	be	be	AUX
american_scientific_journal-3703	212	29	stated	state	VERB
american_scientific_journal-3703	212	30	as	as	ADP
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american_scientific_journal-3703	212	32	map	map	NOUN
american_scientific_journal-3703	212	33	in	in	ADP
american_scientific_journal-3703	212	34	the	the	DET
american_scientific_journal-3703	212	35	sense	sense	NOUN
american_scientific_journal-3703	212	36	of	of	ADP
american_scientific_journal-3703	212	37	j.	j.	PROPN
american_scientific_journal-3703	212	38	banks	banks	PROPN
american_scientific_journal-3703	212	39	etc	etc	X
american_scientific_journal-3703	212	40	.	.	PUNCT
american_scientific_journal-3703	213	1	al	al	PROPN
american_scientific_journal-3703	213	2	.	.	PUNCT
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american_scientific_journal-3703	214	2	of	of	ADP
american_scientific_journal-3703	214	3	transitivity	transitivity	NOUN
american_scientific_journal-3703	214	4	+	+	CCONJ
american_scientific_journal-3703	214	5	density	density	NOUN
american_scientific_journal-3703	214	6	implies	imply	VERB
american_scientific_journal-3703	214	7	sensitivity	sensitivity	NOUN
american_scientific_journal-3703	214	8	[	[	X
american_scientific_journal-3703	214	9	6	6	NUM
american_scientific_journal-3703	214	10	]	]	PUNCT
american_scientific_journal-3703	214	11	.	.	PUNCT
american_scientific_journal-3703	215	1	4.6	4.6	NUM
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american_scientific_journal-3703	215	3	let	let	VERB
american_scientific_journal-3703	215	4	d	d	NOUN
american_scientific_journal-3703	215	5	is	be	AUX
american_scientific_journal-3703	215	6	defined	define	VERB
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american_scientific_journal-3703	215	8	(	(	PUNCT
american_scientific_journal-3703	215	9	)	)	PUNCT
american_scientific_journal-3703	215	10	2	2	NUM
american_scientific_journal-3703	215	11	0	0	NUM
american_scientific_journal-3703	215	12	0.5	0.5	NUM
american_scientific_journal-3703	215	13	2	2	NUM
american_scientific_journal-3703	215	14	1	1	NUM
american_scientific_journal-3703	215	15	0.5	0.5	NUM
american_scientific_journal-3703	215	16	1	1	NUM
american_scientific_journal-3703	215	17	x	x	SYM
american_scientific_journal-3703	215	18	if	if	SCONJ
american_scientific_journal-3703	215	19	x	x	X
american_scientific_journal-3703	216	1	d	d	NOUN
american_scientific_journal-3703	216	2	x	x	X
american_scientific_journal-3703	216	3	x	x	X
american_scientific_journal-3703	216	4	if	if	SCONJ
american_scientific_journal-3703	216	5	x	x	SYM
american_scientific_journal-3703	216	6	≤	≤	X
american_scientific_journal-3703	216	7	<	<	X
american_scientific_journal-3703	216	8			NOUN
american_scientific_journal-3703	216	9	=	=	PUNCT
american_scientific_journal-3703	216	10			ADP
american_scientific_journal-3703	216	11	−	−	PROPN
american_scientific_journal-3703	216	12	≤	≤	NOUN
american_scientific_journal-3703	216	13	<	<	X
american_scientific_journal-3703	216	14			NOUN
american_scientific_journal-3703	216	15	(	(	PUNCT
american_scientific_journal-3703	216	16	)	)	PUNCT
american_scientific_journal-3703	216	17	d	d	X
american_scientific_journal-3703	216	18	x	x	X
american_scientific_journal-3703	216	19	is	be	AUX
american_scientific_journal-3703	216	20	conjugate	conjugate	ADJ
american_scientific_journal-3703	216	21	to	to	ADP
american_scientific_journal-3703	216	22	logistic	logistic	ADJ
american_scientific_journal-3703	216	23	map	map	NOUN
american_scientific_journal-3703	216	24	.	.	PUNCT
american_scientific_journal-3703	217	1	let	let	VERB
american_scientific_journal-3703	217	2	h	h	NOUN
american_scientific_journal-3703	217	3	be	be	AUX
american_scientific_journal-3703	217	4	the	the	DET
american_scientific_journal-3703	217	5	homeomorphism	homeomorphism	NOUN
american_scientific_journal-3703	217	6	defined	define	VERB
american_scientific_journal-3703	217	7	by	by	ADP
american_scientific_journal-3703	217	8	(	(	PUNCT
american_scientific_journal-3703	217	9	)	)	PUNCT
american_scientific_journal-3703	217	10	2	2	NUM
american_scientific_journal-3703	217	11	2h	2h	NUM
american_scientific_journal-3703	217	12	x	x	SYM
american_scientific_journal-3703	217	13	sin	sin	VERB
american_scientific_journal-3703	217	14	xπ=	xπ=	PROPN
american_scientific_journal-3703	218	1	and	and	CCONJ
american_scientific_journal-3703	218	2	we	we	PRON
american_scientific_journal-3703	218	3	put	put	VERB
american_scientific_journal-3703	218	4	(	(	PUNCT
american_scientific_journal-3703	218	5	)	)	PUNCT
american_scientific_journal-3703	218	6	(	(	PUNCT
american_scientific_journal-3703	218	7	)	)	PUNCT
american_scientific_journal-3703	218	8	(	(	PUNCT
american_scientific_journal-3703	218	9	)	)	PUNCT
american_scientific_journal-3703	218	10	1x	1x	NUM
american_scientific_journal-3703	219	1	h	h	NOUN
american_scientific_journal-3703	220	1	d	d	NOUN
american_scientific_journal-3703	220	2	h	h	NOUN
american_scientific_journal-3703	220	3	xϕ	xϕ	NOUN
american_scientific_journal-3703	221	1	−=	−=	NOUN
american_scientific_journal-3703	222	1	o	o	NOUN
american_scientific_journal-3703	222	2	o	o	INTJ
american_scientific_journal-3703	222	3	.	.	PUNCT
american_scientific_journal-3703	223	1	then	then	ADV
american_scientific_journal-3703	223	2	we	we	PRON
american_scientific_journal-3703	223	3	have	have	VERB
american_scientific_journal-3703	223	4	,	,	PUNCT
american_scientific_journal-3703	223	5	(	(	PUNCT
american_scientific_journal-3703	223	6	)	)	PUNCT
american_scientific_journal-3703	223	7	(	(	PUNCT
american_scientific_journal-3703	223	8	)	)	PUNCT
american_scientific_journal-3703	223	9	(	(	PUNCT
american_scientific_journal-3703	223	10	)	)	PUNCT
american_scientific_journal-3703	223	11	(	(	PUNCT
american_scientific_journal-3703	223	12	)	)	PUNCT
american_scientific_journal-3703	223	13	(	(	PUNCT
american_scientific_journal-3703	223	14	)	)	PUNCT
american_scientific_journal-3703	223	15	1	1	NUM
american_scientific_journal-3703	223	16	1	1	NUM
american_scientific_journal-3703	223	17	1	1	NUM
american_scientific_journal-3703	223	18	1	1	NUM
american_scientific_journal-3703	223	19	,	,	PUNCT
american_scientific_journal-3703	223	20	0	0	NUM
american_scientific_journal-3703	223	21	1	1	NUM
american_scientific_journal-3703	223	22	.	.	PUNCT
american_scientific_journal-3703	224	1	.0	.0	NUM
american_scientific_journal-3703	224	2	1	1	NUM
american_scientific_journal-3703	224	3	2	2	NUM
american_scientific_journal-3703	224	4	2	2	NUM
american_scientific_journal-3703	224	5	1	1	NUM
american_scientific_journal-3703	224	6	1	1	NUM
american_scientific_journal-3703	224	7	1	1	NUM
american_scientific_journal-3703	224	8	2	2	NUM
american_scientific_journal-3703	224	9	,	,	PUNCT
american_scientific_journal-3703	224	10	0	0	NUM
american_scientific_journal-3703	224	11	.	.	PUNCT
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american_scientific_journal-3703	225	2	2	2	NUM
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american_scientific_journal-3703	241	4	−	−	PROPN
american_scientific_journal-3703	241	5	−	−	NOUN
american_scientific_journal-3703	241	6			VERB
american_scientific_journal-3703	241	7			PROPN
american_scientific_journal-3703	241	8	=	=	PROPN
american_scientific_journal-3703	241	9	−	−	PUNCT
american_scientific_journal-3703	241	10			VERB
american_scientific_journal-3703	241	11			VERB
american_scientific_journal-3703	241	12			NOUN
american_scientific_journal-3703	241	13			ADP
american_scientific_journal-3703	241	14			NOUN
american_scientific_journal-3703	241	15	=	=	SYM
american_scientific_journal-3703	241	16	−	−	PROPN
american_scientific_journal-3703	241	17	(	(	PUNCT
american_scientific_journal-3703	241	18	)	)	PUNCT
american_scientific_journal-3703	241	19	{	{	PUNCT
american_scientific_journal-3703	241	20	}	}	PUNCT
american_scientific_journal-3703	241	21	(	(	PUNCT
american_scientific_journal-3703	241	22	)	)	PUNCT
american_scientific_journal-3703	241	23	(	(	PUNCT
american_scientific_journal-3703	241	24	)	)	PUNCT
american_scientific_journal-3703	241	25	{	{	PUNCT
american_scientific_journal-3703	241	26	}	}	PUNCT
american_scientific_journal-3703	241	27	(	(	PUNCT
american_scientific_journal-3703	241	28	)	)	PUNCT
american_scientific_journal-3703	241	29	(	(	PUNCT
american_scientific_journal-3703	241	30	)	)	PUNCT
american_scientific_journal-3703	241	31	{	{	PUNCT
american_scientific_journal-3703	241	32	}	}	PUNCT
american_scientific_journal-3703	241	33	(	(	PUNCT
american_scientific_journal-3703	241	34	)	)	PUNCT
american_scientific_journal-3703	241	35	2	2	NUM
american_scientific_journal-3703	241	36	1	1	NUM
american_scientific_journal-3703	241	37	2	2	NUM
american_scientific_journal-3703	241	38	1	1	NUM
american_scientific_journal-3703	241	39	1	1	NUM
american_scientific_journal-3703	241	40	2	2	NUM
american_scientific_journal-3703	241	41	2	2	NUM
american_scientific_journal-3703	241	42	1	1	NUM
american_scientific_journal-3703	241	43	2	2	NUM
american_scientific_journal-3703	241	44	2	2	NUM
american_scientific_journal-3703	241	45	.	.	NOUN
american_scientific_journal-3703	241	46	2	2	NUM
american_scientific_journal-3703	241	47	1	1	NUM
american_scientific_journal-3703	241	48	4	4	NUM
american_scientific_journal-3703	241	49	1	1	NUM
american_scientific_journal-3703	241	50	sin	sin	NOUN
american_scientific_journal-3703	241	51	sin	sin	NOUN
american_scientific_journal-3703	241	52	x	x	PUNCT
american_scientific_journal-3703	241	53	sin	sin	VERB
american_scientific_journal-3703	241	54	sin	sin	NOUN
american_scientific_journal-3703	241	55	x	x	X
american_scientific_journal-3703	241	56	cos	cos	ADP
american_scientific_journal-3703	241	57	sin	sin	NOUN
american_scientific_journal-3703	241	58	x	x	X
american_scientific_journal-3703	241	59	x	x	PUNCT
american_scientific_journal-3703	241	60	sin	sin	NOUN
american_scientific_journal-3703	241	61	sin	sin	NOUN
american_scientific_journal-3703	241	62	x	x	X
american_scientific_journal-3703	241	63	x	x	PUNCT
american_scientific_journal-3703	241	64	x	x	PUNCT
american_scientific_journal-3703	242	1	−	−	NOUN
american_scientific_journal-3703	242	2	−	−	NUM
american_scientific_journal-3703	243	1	−	−	NOUN
american_scientific_journal-3703	243	2	−	−	PROPN
american_scientific_journal-3703	244	1	=	=	SYM
american_scientific_journal-3703	244	2	=	=	PUNCT
american_scientific_journal-3703	244	3	=	=	PUNCT
american_scientific_journal-3703	245	1	−	−	PROPN
american_scientific_journal-3703	245	2	=	=	PUNCT
american_scientific_journal-3703	245	3	−	−	PROPN
american_scientific_journal-3703	245	4	hence	hence	ADV
american_scientific_journal-3703	245	5	we	we	PRON
american_scientific_journal-3703	245	6	have	have	AUX
american_scientific_journal-3703	245	7	shown	show	VERB
american_scientific_journal-3703	245	8	that	that	SCONJ
american_scientific_journal-3703	245	9	d	d	NOUN
american_scientific_journal-3703	245	10	is	be	AUX
american_scientific_journal-3703	245	11	chaotic	chaotic	ADJ
american_scientific_journal-3703	245	12	map	map	NOUN
american_scientific_journal-3703	246	1	[	[	X
american_scientific_journal-3703	246	2	9	9	NUM
american_scientific_journal-3703	246	3	]	]	PUNCT
american_scientific_journal-3703	246	4	.	.	PUNCT
american_scientific_journal-3703	247	1	4.7	4.7	NUM
american_scientific_journal-3703	247	2	proposition	proposition	NOUN
american_scientific_journal-3703	247	3	let	let	VERB
american_scientific_journal-3703	247	4	d	d	NOUN
american_scientific_journal-3703	247	5	is	be	AUX
american_scientific_journal-3703	247	6	defined	define	VERB
american_scientific_journal-3703	247	7	by	by	ADP
american_scientific_journal-3703	247	8	(	(	PUNCT
american_scientific_journal-3703	247	9	)	)	PUNCT
american_scientific_journal-3703	247	10	2	2	NUM
american_scientific_journal-3703	247	11	0	0	NUM
american_scientific_journal-3703	247	12	0.5	0.5	NUM
american_scientific_journal-3703	247	13	2	2	NUM
american_scientific_journal-3703	247	14	1	1	NUM
american_scientific_journal-3703	247	15	0.5	0.5	NUM
american_scientific_journal-3703	247	16	1	1	NUM
american_scientific_journal-3703	247	17	x	x	SYM
american_scientific_journal-3703	247	18	if	if	SCONJ
american_scientific_journal-3703	247	19	x	x	X
american_scientific_journal-3703	247	20	d	d	NOUN
american_scientific_journal-3703	247	21	x	x	X
american_scientific_journal-3703	247	22	x	x	X
american_scientific_journal-3703	247	23	if	if	SCONJ
american_scientific_journal-3703	247	24	x	x	SYM
american_scientific_journal-3703	247	25	≤	≤	X
american_scientific_journal-3703	247	26	<	<	X
american_scientific_journal-3703	247	27			NOUN
american_scientific_journal-3703	247	28	=	=	PUNCT
american_scientific_journal-3703	247	29			ADP
american_scientific_journal-3703	247	30	−	−	PROPN
american_scientific_journal-3703	247	31	≤	≤	NOUN
american_scientific_journal-3703	247	32	<	<	X
american_scientific_journal-3703	247	33			NOUN
american_scientific_journal-3703	247	34	(	(	PUNCT
american_scientific_journal-3703	247	35	)	)	PUNCT
american_scientific_journal-3703	247	36	d	d	X
american_scientific_journal-3703	247	37	x	x	X
american_scientific_journal-3703	247	38	is	be	AUX
american_scientific_journal-3703	247	39	semi	semi	ADJ
american_scientific_journal-3703	247	40	-	-	ADJ
american_scientific_journal-3703	247	41	conjugacy	conjugacy	ADJ
american_scientific_journal-3703	247	42	with	with	ADP
american_scientific_journal-3703	247	43	tent	tent	NOUN
american_scientific_journal-3703	247	44	map	map	NOUN
american_scientific_journal-3703	247	45	.	.	PUNCT
american_scientific_journal-3703	248	1	we	we	PRON
american_scientific_journal-3703	248	2	will	will	AUX
american_scientific_journal-3703	248	3	show	show	VERB
american_scientific_journal-3703	248	4	that	that	SCONJ
american_scientific_journal-3703	248	5	the	the	DET
american_scientific_journal-3703	248	6	doubling	double	VERB
american_scientific_journal-3703	248	7	map	map	NOUN
american_scientific_journal-3703	248	8	is	be	AUX
american_scientific_journal-3703	248	9	semi	semi	ADJ
american_scientific_journal-3703	248	10	-	-	ADJ
american_scientific_journal-3703	248	11	conjugate	conjugate	ADJ
american_scientific_journal-3703	248	12	to	to	ADP
american_scientific_journal-3703	248	13	the	the	DET
american_scientific_journal-3703	248	14	tent	tent	NOUN
american_scientific_journal-3703	248	15	map	map	NOUN
american_scientific_journal-3703	248	16	t	t	PROPN
american_scientific_journal-3703	248	17	via	via	ADP
american_scientific_journal-3703	248	18	t	t	PROPN
american_scientific_journal-3703	248	19	itself	itself	PRON
american_scientific_journal-3703	248	20	!	!	PUNCT
american_scientific_journal-3703	249	1	that	that	PRON
american_scientific_journal-3703	249	2	is	be	AUX
american_scientific_journal-3703	249	3	,	,	PUNCT
american_scientific_journal-3703	249	4	we	we	PRON
american_scientific_journal-3703	249	5	will	will	AUX
american_scientific_journal-3703	249	6	show	show	VERB
american_scientific_journal-3703	249	7	that	that	SCONJ
american_scientific_journal-3703	249	8	[	[	X
american_scientific_journal-3703	249	9	]	]	X
american_scientific_journal-3703	249	10	[	[	PUNCT
american_scientific_journal-3703	249	11	]	]	X
american_scientific_journal-3703	249	12	[	[	PUNCT
american_scientific_journal-3703	249	13	]	]	X
american_scientific_journal-3703	249	14	[	[	PUNCT
american_scientific_journal-3703	249	15	]	]	X
american_scientific_journal-3703	249	16	0,1	0,1	NUM
american_scientific_journal-3703	249	17	0,1	0,1	NUM
american_scientific_journal-3703	249	18	0,1	0,1	NUM
american_scientific_journal-3703	249	19	0,1	0,1	NUM
american_scientific_journal-3703	249	20	d	d	NOUN
american_scientific_journal-3703	249	21	t	t	PROPN
american_scientific_journal-3703	249	22	t	t	NOUN
american_scientific_journal-3703	249	23	t	t	PROPN
american_scientific_journal-3703	249	24	→	→	PROPN
american_scientific_journal-3703	249	25	↓	↓	NOUN
american_scientific_journal-3703	249	26	↓	↓	NOUN
american_scientific_journal-3703	249	27	→	→	PROPN
american_scientific_journal-3703	249	28	thus	thus	ADV
american_scientific_journal-3703	249	29	t	t	NOUN
american_scientific_journal-3703	249	30	will	will	AUX
american_scientific_journal-3703	249	31	be	be	AUX
american_scientific_journal-3703	249	32	chaotic	chaotic	ADJ
american_scientific_journal-3703	249	33	.	.	PUNCT
american_scientific_journal-3703	250	1	this	this	PRON
american_scientific_journal-3703	250	2	is	be	AUX
american_scientific_journal-3703	250	3	because	because	SCONJ
american_scientific_journal-3703	250	4	orbits	orbit	NOUN
american_scientific_journal-3703	250	5	under	under	ADP
american_scientific_journal-3703	250	6	iteration	iteration	NOUN
american_scientific_journal-3703	250	7	of	of	ADP
american_scientific_journal-3703	250	8	d	d	PROPN
american_scientific_journal-3703	250	9	map	map	NOUN
american_scientific_journal-3703	250	10	to	to	PART
american_scientific_journal-3703	250	11	dynamically	dynamically	ADV
american_scientific_journal-3703	250	12	equivalent	equivalent	ADJ
american_scientific_journal-3703	250	13	orbits	orbit	NOUN
american_scientific_journal-3703	250	14	under	under	ADP
american_scientific_journal-3703	250	15	t.	t.	PROPN
american_scientific_journal-3703	250	16	in	in	ADP
american_scientific_journal-3703	250	17	fact	fact	NOUN
american_scientific_journal-3703	250	18	we	we	PRON
american_scientific_journal-3703	250	19	now	now	ADV
american_scientific_journal-3703	250	20	prove	prove	VERB
american_scientific_journal-3703	250	21	by	by	ADP
american_scientific_journal-3703	250	22	induction	induction	NOUN
american_scientific_journal-3703	250	23	that	that	SCONJ
american_scientific_journal-3703	250	24	(	(	PUNCT
american_scientific_journal-3703	250	25	)	)	SYM
american_scientific_journal-3703	250	26	1	1	NUM
american_scientific_journal-3703	250	27	1n	1n	NUM
american_scientific_journal-3703	250	28	nt	not	PART
american_scientific_journal-3703	251	1	d	d	X
american_scientific_journal-3703	251	2	t−	t−	PROPN
american_scientific_journal-3703	252	1	=	=	NOUN
american_scientific_journal-3703	252	2	o	o	NOUN
american_scientific_journal-3703	252	3	for	for	ADP
american_scientific_journal-3703	252	4	all	all	DET
american_scientific_journal-3703	252	5	0n	0n	NOUN
american_scientific_journal-3703	252	6	>	>	PUNCT
american_scientific_journal-3703	252	7	.	.	PUNCT
american_scientific_journal-3703	252	8	suppose	suppose	VERB
american_scientific_journal-3703	252	9	equation-1	equation-1	PRON
american_scientific_journal-3703	252	10	is	be	AUX
american_scientific_journal-3703	252	11	true	true	ADJ
american_scientific_journal-3703	252	12	for	for	ADP
american_scientific_journal-3703	252	13	:	:	PUNCT
american_scientific_journal-3703	252	14	.n	.n	PROPN
american_scientific_journal-3703	252	15	k=	k=	X
american_scientific_journal-3703	253	1	then	then	ADV
american_scientific_journal-3703	253	2	1	1	NUM
american_scientific_journal-3703	253	3	1k	1k	NUM
american_scientific_journal-3703	253	4	k	k	PROPN
american_scientific_journal-3703	254	1	k	k	PROPN
american_scientific_journal-3703	255	1	kt	kt	PROPN
american_scientific_journal-3703	256	1	d	d	PROPN
american_scientific_journal-3703	256	2	t	t	PROPN
american_scientific_journal-3703	256	3	t	t	PROPN
american_scientific_journal-3703	256	4	t	t	PROPN
american_scientific_journal-3703	256	5	d	d	X
american_scientific_journal-3703	256	6	t	t	PROPN
american_scientific_journal-3703	256	7	t−	t−	PROPN
american_scientific_journal-3703	256	8	−=	−=	NOUN
american_scientific_journal-3703	256	9	⇒	⇒	NOUN
american_scientific_journal-3703	257	1	=	=	NOUN
american_scientific_journal-3703	258	1	o	o	NOUN
american_scientific_journal-3703	258	2	o	o	X
american_scientific_journal-3703	258	3	o	o	X
american_scientific_journal-3703	258	4	o	o	NOUN
american_scientific_journal-3703	258	5	and	and	CCONJ
american_scientific_journal-3703	258	6	since	since	SCONJ
american_scientific_journal-3703	258	7	t	t	PROPN
american_scientific_journal-3703	258	8	d	d	PROPN
american_scientific_journal-3703	258	9	t	t	PROPN
american_scientific_journal-3703	258	10	t	t	PROPN
american_scientific_journal-3703	258	11	=	=	PROPN
american_scientific_journal-3703	258	12	o	o	NOUN
american_scientific_journal-3703	258	13	o	o	NOUN
american_scientific_journal-3703	258	14	,	,	PUNCT
american_scientific_journal-3703	258	15	we	we	PRON
american_scientific_journal-3703	258	16	have	have	VERB
american_scientific_journal-3703	258	17	1k	1k	NUM
american_scientific_journal-3703	258	18	kt	kt	PROPN
american_scientific_journal-3703	258	19	d	d	PROPN
american_scientific_journal-3703	258	20	t	t	PROPN
american_scientific_journal-3703	259	1	+	+	NOUN
american_scientific_journal-3703	259	2	=	=	ADJ
american_scientific_journal-3703	259	3	o	o	ADJ
american_scientific_journal-3703	259	4	american	american	PROPN
american_scientific_journal-3703	259	5	scientific	scientific	ADJ
american_scientific_journal-3703	259	6	research	research	PROPN
american_scientific_journal-3703	259	7	journal	journal	NOUN
american_scientific_journal-3703	259	8	for	for	ADP
american_scientific_journal-3703	259	9	engineering	engineering	NOUN
american_scientific_journal-3703	259	10	,	,	PUNCT
american_scientific_journal-3703	259	11	technology	technology	NOUN
american_scientific_journal-3703	259	12	,	,	PUNCT
american_scientific_journal-3703	259	13	and	and	CCONJ
american_scientific_journal-3703	259	14	sciences	science	NOUN
american_scientific_journal-3703	259	15	(	(	PUNCT
american_scientific_journal-3703	259	16	asrjets	asrjet	NOUN
american_scientific_journal-3703	259	17	)	)	PUNCT
american_scientific_journal-3703	259	18	(	(	PUNCT
american_scientific_journal-3703	259	19	2018	2018	NUM
american_scientific_journal-3703	259	20	)	)	PUNCT
american_scientific_journal-3703	259	21	volume	volume	NOUN
american_scientific_journal-3703	259	22	43	43	NUM
american_scientific_journal-3703	259	23	,	,	PUNCT
american_scientific_journal-3703	259	24	no	no	DET
american_scientific_journal-3703	259	25	1	1	NUM
american_scientific_journal-3703	259	26	,	,	PUNCT
american_scientific_journal-3703	259	27	pp	pp	ADV
american_scientific_journal-3703	259	28	110	110	NUM
american_scientific_journal-3703	259	29	-	-	SYM
american_scientific_journal-3703	259	30	133	133	NUM
american_scientific_journal-3703	259	31	121	121	NUM
american_scientific_journal-3703	259	32	which	which	PRON
american_scientific_journal-3703	259	33	completes	complete	VERB
american_scientific_journal-3703	259	34	the	the	DET
american_scientific_journal-3703	259	35	inductive	inductive	ADJ
american_scientific_journal-3703	259	36	proof	proof	NOUN
american_scientific_journal-3703	259	37	.	.	PUNCT
american_scientific_journal-3703	260	1	we	we	PRON
american_scientific_journal-3703	260	2	remark	remark	VERB
american_scientific_journal-3703	260	3	that	that	SCONJ
american_scientific_journal-3703	260	4	(	(	PUNCT
american_scientific_journal-3703	260	5	1	1	X
american_scientific_journal-3703	260	6	)	)	PUNCT
american_scientific_journal-3703	260	7	gives	give	VERB
american_scientific_journal-3703	260	8	an	an	DET
american_scientific_journal-3703	260	9	explicit	explicit	ADJ
american_scientific_journal-3703	260	10	formula	formula	NOUN
american_scientific_journal-3703	260	11	for	for	ADP
american_scientific_journal-3703	260	12	(	(	PUNCT
american_scientific_journal-3703	260	13	)	)	PUNCT
american_scientific_journal-3703	260	14	nt	not	PART
american_scientific_journal-3703	260	15	x	x	VERB
american_scientific_journal-3703	260	16	since	since	SCONJ
american_scientific_journal-3703	260	17	we	we	PRON
american_scientific_journal-3703	260	18	already	already	ADV
american_scientific_journal-3703	260	19	know	know	VERB
american_scientific_journal-3703	260	20	that	that	DET
american_scientific_journal-3703	260	21	(	(	PUNCT
american_scientific_journal-3703	260	22	)	)	SYM
american_scientific_journal-3703	260	23	1	1	NUM
american_scientific_journal-3703	260	24	12	12	NUM
american_scientific_journal-3703	260	25	mod1n	mod1n	PROPN
american_scientific_journal-3703	260	26	nd	nd	PROPN
american_scientific_journal-3703	260	27	x	x	SYM
american_scientific_journal-3703	260	28	x−	x−	PROPN
american_scientific_journal-3703	260	29	−=	−=	PROPN
american_scientific_journal-3703	260	30	.	.	PUNCT
american_scientific_journal-3703	261	1	we	we	PRON
american_scientific_journal-3703	261	2	now	now	ADV
american_scientific_journal-3703	261	3	show	show	VERB
american_scientific_journal-3703	261	4	that	that	SCONJ
american_scientific_journal-3703	261	5	d	d	NOUN
american_scientific_journal-3703	261	6	is	be	AUX
american_scientific_journal-3703	261	7	semi	semi	ADV
american_scientific_journal-3703	261	8	conjugate	conjugate	ADJ
american_scientific_journal-3703	261	9	to	to	ADP
american_scientific_journal-3703	261	10	t	t	PROPN
american_scientific_journal-3703	261	11	via	via	ADP
american_scientific_journal-3703	261	12	t	t	PROPN
american_scientific_journal-3703	261	13	,	,	PUNCT
american_scientific_journal-3703	261	14	or	or	CCONJ
american_scientific_journal-3703	261	15	in	in	ADP
american_scientific_journal-3703	261	16	other	other	ADJ
american_scientific_journal-3703	261	17	words	word	NOUN
american_scientific_journal-3703	261	18	,	,	PUNCT
american_scientific_journal-3703	261	19	that	that	SCONJ
american_scientific_journal-3703	261	20	t	t	PROPN
american_scientific_journal-3703	261	21	d	d	X
american_scientific_journal-3703	261	22	t	t	PROPN
american_scientific_journal-3703	261	23	t	t	PROPN
american_scientific_journal-3703	261	24	=	=	PROPN
american_scientific_journal-3703	261	25	o	o	X
american_scientific_journal-3703	261	26	o	o	NOUN
american_scientific_journal-3703	261	27	.	.	PUNCT
american_scientific_journal-3703	262	1	there	there	ADV
american_scientific_journal-3703	262	2	four	four	NUM
american_scientific_journal-3703	262	3	cases	case	NOUN
american_scientific_journal-3703	262	4	to	to	PART
american_scientific_journal-3703	262	5	consider	consider	VERB
american_scientific_journal-3703	262	6	for	for	ADP
american_scientific_journal-3703	262	7	t	t	NOUN
american_scientific_journal-3703	262	8	to	to	PART
american_scientific_journal-3703	262	9	.	.	PUNCT
american_scientific_journal-3703	263	1	(	(	PUNCT
american_scientific_journal-3703	263	2	)	)	PUNCT
american_scientific_journal-3703	263	3	(	(	PUNCT
american_scientific_journal-3703	263	4	)	)	PUNCT
american_scientific_journal-3703	263	5	(	(	PUNCT
american_scientific_journal-3703	263	6	)	)	PUNCT
american_scientific_journal-3703	263	7	(	(	PUNCT
american_scientific_journal-3703	263	8	)	)	PUNCT
american_scientific_journal-3703	263	9	1	1	NUM
american_scientific_journal-3703	263	10	10	10	NUM
american_scientific_journal-3703	263	11	0	0	NUM
american_scientific_journal-3703	263	12	2	2	NUM
american_scientific_journal-3703	263	13	2	2	NUM
american_scientific_journal-3703	263	14	2	2	NUM
american_scientific_journal-3703	263	15	44	44	NUM
american_scientific_journal-3703	263	16	2x	2x	NUM
american_scientific_journal-3703	263	17	t	t	NOUN
american_scientific_journal-3703	263	18	x	x	SYM
american_scientific_journal-3703	263	19	t	t	PROPN
american_scientific_journal-3703	263	20	t	t	PROPN
american_scientific_journal-3703	263	21	x	x	SYM
american_scientific_journal-3703	263	22	t	t	NOUN
american_scientific_journal-3703	263	23	x	x	PUNCT
american_scientific_journal-3703	263	24	x	x	PUNCT
american_scientific_journal-3703	263	25	x≤	x≤	PRON
american_scientific_journal-3703	263	26	≤	≤	ADJ
american_scientific_journal-3703	263	27	⇒	⇒	VERB
american_scientific_journal-3703	263	28	≤	≤	ADJ
american_scientific_journal-3703	263	29	≤	≤	ADJ
american_scientific_journal-3703	263	30	⇒	⇒	NOUN
american_scientific_journal-3703	263	31	=	=	PUNCT
american_scientific_journal-3703	264	1	=	=	PUNCT
american_scientific_journal-3703	264	2	=	=	NUM
american_scientific_journal-3703	264	3	o	o	X
american_scientific_journal-3703	264	4	(	(	PUNCT
american_scientific_journal-3703	264	5	)	)	PUNCT
american_scientific_journal-3703	264	6	(	(	PUNCT
american_scientific_journal-3703	264	7	)	)	PUNCT
american_scientific_journal-3703	264	8	(	(	PUNCT
american_scientific_journal-3703	264	9	)	)	PUNCT
american_scientific_journal-3703	264	10	(	(	PUNCT
american_scientific_journal-3703	264	11	)	)	SYM
american_scientific_journal-3703	264	12	1	1	NUM
american_scientific_journal-3703	264	13	1	1	NUM
american_scientific_journal-3703	264	14	1	1	NUM
american_scientific_journal-3703	264	15	1	1	NUM
american_scientific_journal-3703	264	16	2	2	NUM
american_scientific_journal-3703	264	17	2	2	NUM
american_scientific_journal-3703	264	18	2	2	NUM
american_scientific_journal-3703	264	19	2	2	NUM
american_scientific_journal-3703	264	20	2	2	NUM
american_scientific_journal-3703	264	21	44	44	NUM
american_scientific_journal-3703	264	22	2	2	NUM
american_scientific_journal-3703	264	23	2x	2x	NUM
american_scientific_journal-3703	264	24	t	t	NOUN
american_scientific_journal-3703	264	25	x	x	SYM
american_scientific_journal-3703	264	26	t	t	PROPN
american_scientific_journal-3703	264	27	t	t	PROPN
american_scientific_journal-3703	264	28	x	x	SYM
american_scientific_journal-3703	264	29	t	t	NOUN
american_scientific_journal-3703	264	30	x	x	PUNCT
american_scientific_journal-3703	264	31	x	x	PUNCT
american_scientific_journal-3703	264	32	x≤	x≤	PRON
american_scientific_journal-3703	264	33	≤	≤	ADJ
american_scientific_journal-3703	264	34	⇒	⇒	VERB
american_scientific_journal-3703	264	35	≤	≤	ADJ
american_scientific_journal-3703	264	36	≤	≤	ADJ
american_scientific_journal-3703	264	37	⇒	⇒	NOUN
american_scientific_journal-3703	264	38	=	=	PUNCT
american_scientific_journal-3703	265	1	=	=	PUNCT
american_scientific_journal-3703	265	2	−	−	PROPN
american_scientific_journal-3703	265	3	=	=	SYM
american_scientific_journal-3703	265	4	−o	−o	PROPN
american_scientific_journal-3703	265	5	(	(	PUNCT
american_scientific_journal-3703	265	6	)	)	PUNCT
american_scientific_journal-3703	265	7	(	(	PUNCT
american_scientific_journal-3703	265	8	)	)	PUNCT
american_scientific_journal-3703	265	9	(	(	PUNCT
american_scientific_journal-3703	265	10	)	)	PUNCT
american_scientific_journal-3703	265	11	(	(	PUNCT
american_scientific_journal-3703	265	12	)	)	PUNCT
american_scientific_journal-3703	265	13	31	31	NUM
american_scientific_journal-3703	265	14	1	1	NUM
american_scientific_journal-3703	265	15	1	1	NUM
american_scientific_journal-3703	265	16	2	2	NUM
american_scientific_journal-3703	265	17	2	2	NUM
american_scientific_journal-3703	265	18	2	2	NUM
american_scientific_journal-3703	265	19	2	2	NUM
american_scientific_journal-3703	265	20	2	2	NUM
american_scientific_journal-3703	265	21	2	2	NUM
american_scientific_journal-3703	265	22	4	4	NUM
american_scientific_journal-3703	265	23	22	22	NUM
american_scientific_journal-3703	265	24	4	4	NUM
american_scientific_journal-3703	265	25	2x	2x	NUM
american_scientific_journal-3703	265	26	t	t	NOUN
american_scientific_journal-3703	265	27	x	x	SYM
american_scientific_journal-3703	265	28	t	t	PROPN
american_scientific_journal-3703	265	29	t	t	PROPN
american_scientific_journal-3703	265	30	x	x	SYM
american_scientific_journal-3703	265	31	t	t	NOUN
american_scientific_journal-3703	265	32	x	x	PUNCT
american_scientific_journal-3703	265	33	x	x	PUNCT
american_scientific_journal-3703	265	34	x≤	x≤	PRON
american_scientific_journal-3703	265	35	≤	≤	ADJ
american_scientific_journal-3703	265	36	⇒	⇒	VERB
american_scientific_journal-3703	265	37	≤	≤	ADJ
american_scientific_journal-3703	265	38	≤	≤	ADJ
american_scientific_journal-3703	265	39	⇒	⇒	NOUN
american_scientific_journal-3703	265	40	=	=	PUNCT
american_scientific_journal-3703	265	41	−	−	PROPN
american_scientific_journal-3703	265	42	=	=	PUNCT
american_scientific_journal-3703	266	1	−	−	PROPN
american_scientific_journal-3703	266	2	−	−	PROPN
american_scientific_journal-3703	266	3	=	=	SYM
american_scientific_journal-3703	266	4	−o	−o	PROPN
american_scientific_journal-3703	266	5	(	(	PUNCT
american_scientific_journal-3703	266	6	)	)	PUNCT
american_scientific_journal-3703	266	7	(	(	PUNCT
american_scientific_journal-3703	266	8	)	)	PUNCT
american_scientific_journal-3703	266	9	(	(	PUNCT
american_scientific_journal-3703	266	10	)	)	PUNCT
american_scientific_journal-3703	266	11	(	(	PUNCT
american_scientific_journal-3703	266	12	)	)	PUNCT
american_scientific_journal-3703	266	13	3	3	NUM
american_scientific_journal-3703	266	14	11	11	NUM
american_scientific_journal-3703	266	15	0	0	NUM
american_scientific_journal-3703	266	16	2	2	NUM
american_scientific_journal-3703	266	17	2	2	NUM
american_scientific_journal-3703	266	18	2	2	NUM
american_scientific_journal-3703	266	19	2	2	NUM
american_scientific_journal-3703	266	20	2	2	NUM
american_scientific_journal-3703	266	21	4	4	NUM
american_scientific_journal-3703	266	22	44	44	NUM
american_scientific_journal-3703	266	23	2x	2x	NUM
american_scientific_journal-3703	266	24	t	t	NOUN
american_scientific_journal-3703	266	25	x	x	SYM
american_scientific_journal-3703	266	26	t	t	PROPN
american_scientific_journal-3703	266	27	t	t	PROPN
american_scientific_journal-3703	266	28	x	x	SYM
american_scientific_journal-3703	266	29	t	t	NOUN
american_scientific_journal-3703	266	30	x	x	PUNCT
american_scientific_journal-3703	266	31	x	x	PUNCT
american_scientific_journal-3703	266	32	x≤	x≤	PRON
american_scientific_journal-3703	266	33	≤	≤	ADJ
american_scientific_journal-3703	266	34	⇒	⇒	VERB
american_scientific_journal-3703	266	35	≤	≤	ADJ
american_scientific_journal-3703	266	36	≤	≤	ADJ
american_scientific_journal-3703	266	37	⇒	⇒	NOUN
american_scientific_journal-3703	266	38	=	=	PUNCT
american_scientific_journal-3703	266	39	−	−	PROPN
american_scientific_journal-3703	266	40	=	=	SYM
american_scientific_journal-3703	266	41	−	−	PROPN
american_scientific_journal-3703	266	42	=	=	SYM
american_scientific_journal-3703	266	43	−o	−o	PROPN
american_scientific_journal-3703	266	44	similarly	similarly	ADV
american_scientific_journal-3703	266	45	,	,	PUNCT
american_scientific_journal-3703	266	46	there	there	PRON
american_scientific_journal-3703	266	47	are	be	VERB
american_scientific_journal-3703	266	48	four	four	NUM
american_scientific_journal-3703	266	49	cases	case	NOUN
american_scientific_journal-3703	266	50	for	for	ADP
american_scientific_journal-3703	266	51	t	t	PROPN
american_scientific_journal-3703	266	52	do	do	AUX
american_scientific_journal-3703	266	53	:	:	PUNCT
american_scientific_journal-3703	266	54	(	(	PUNCT
american_scientific_journal-3703	266	55	)	)	PUNCT
american_scientific_journal-3703	266	56	(	(	PUNCT
american_scientific_journal-3703	266	57	)	)	PUNCT
american_scientific_journal-3703	266	58	(	(	PUNCT
american_scientific_journal-3703	266	59	)	)	PUNCT
american_scientific_journal-3703	266	60	(	(	PUNCT
american_scientific_journal-3703	266	61	)	)	PUNCT
american_scientific_journal-3703	266	62	1	1	NUM
american_scientific_journal-3703	266	63	10	10	NUM
american_scientific_journal-3703	266	64	0	0	NUM
american_scientific_journal-3703	266	65	2	2	NUM
american_scientific_journal-3703	266	66	2	2	NUM
american_scientific_journal-3703	266	67	2	2	NUM
american_scientific_journal-3703	266	68	44	44	NUM
american_scientific_journal-3703	266	69	2x	2x	NUM
american_scientific_journal-3703	266	70	d	d	X
american_scientific_journal-3703	266	71	x	x	PROPN
american_scientific_journal-3703	266	72	t	t	NOUN
american_scientific_journal-3703	266	73	d	d	X
american_scientific_journal-3703	266	74	x	x	X
american_scientific_journal-3703	266	75	t	t	NOUN
american_scientific_journal-3703	266	76	x	x	SYM
american_scientific_journal-3703	266	77	x	x	PUNCT
american_scientific_journal-3703	266	78	x≤	x≤	PRON
american_scientific_journal-3703	266	79	≤	≤	ADJ
american_scientific_journal-3703	266	80	⇒	⇒	VERB
american_scientific_journal-3703	266	81	≤	≤	ADJ
american_scientific_journal-3703	266	82	≤	≤	ADJ
american_scientific_journal-3703	266	83	⇒	⇒	NOUN
american_scientific_journal-3703	266	84	=	=	PUNCT
american_scientific_journal-3703	267	1	=	=	PUNCT
american_scientific_journal-3703	267	2	=	=	NUM
american_scientific_journal-3703	267	3	o	o	X
american_scientific_journal-3703	267	4	(	(	PUNCT
american_scientific_journal-3703	267	5	)	)	PUNCT
american_scientific_journal-3703	267	6	(	(	PUNCT
american_scientific_journal-3703	267	7	)	)	PUNCT
american_scientific_journal-3703	267	8	(	(	PUNCT
american_scientific_journal-3703	267	9	)	)	PUNCT
american_scientific_journal-3703	267	10	(	(	PUNCT
american_scientific_journal-3703	267	11	)	)	SYM
american_scientific_journal-3703	267	12	1	1	NUM
american_scientific_journal-3703	267	13	1	1	NUM
american_scientific_journal-3703	267	14	1	1	NUM
american_scientific_journal-3703	267	15	1	1	NUM
american_scientific_journal-3703	267	16	2	2	NUM
american_scientific_journal-3703	267	17	2	2	NUM
american_scientific_journal-3703	267	18	2	2	NUM
american_scientific_journal-3703	267	19	2	2	NUM
american_scientific_journal-3703	267	20	2	2	NUM
american_scientific_journal-3703	267	21	44	44	NUM
american_scientific_journal-3703	267	22	2	2	NUM
american_scientific_journal-3703	267	23	2x	2x	NUM
american_scientific_journal-3703	267	24	d	d	NOUN
american_scientific_journal-3703	267	25	x	x	SYM
american_scientific_journal-3703	267	26	t	t	NOUN
american_scientific_journal-3703	267	27	d	d	X
american_scientific_journal-3703	267	28	x	x	X
american_scientific_journal-3703	267	29	t	t	NOUN
american_scientific_journal-3703	267	30	x	x	SYM
american_scientific_journal-3703	267	31	x	x	PUNCT
american_scientific_journal-3703	267	32	x≤	x≤	PRON
american_scientific_journal-3703	267	33	≤	≤	ADJ
american_scientific_journal-3703	267	34	⇒	⇒	VERB
american_scientific_journal-3703	267	35	≤	≤	ADJ
american_scientific_journal-3703	267	36	≤	≤	ADJ
american_scientific_journal-3703	267	37	⇒	⇒	NOUN
american_scientific_journal-3703	267	38	=	=	PUNCT
american_scientific_journal-3703	268	1	=	=	PUNCT
american_scientific_journal-3703	268	2	−	−	PROPN
american_scientific_journal-3703	268	3	=	=	SYM
american_scientific_journal-3703	268	4	−o	−o	PROPN
american_scientific_journal-3703	268	5	(	(	PUNCT
american_scientific_journal-3703	268	6	)	)	PUNCT
american_scientific_journal-3703	268	7	(	(	PUNCT
american_scientific_journal-3703	268	8	)	)	PUNCT
american_scientific_journal-3703	268	9	(	(	PUNCT
american_scientific_journal-3703	268	10	)	)	PUNCT
american_scientific_journal-3703	268	11	(	(	PUNCT
american_scientific_journal-3703	268	12	)	)	PUNCT
american_scientific_journal-3703	268	13	31	31	NUM
american_scientific_journal-3703	269	1	1	1	NUM
american_scientific_journal-3703	269	2	0	0	NUM
american_scientific_journal-3703	269	3	2	2	NUM
american_scientific_journal-3703	269	4	1	1	NUM
american_scientific_journal-3703	269	5	2	2	NUM
american_scientific_journal-3703	269	6	2	2	NUM
american_scientific_journal-3703	269	7	1	1	NUM
american_scientific_journal-3703	269	8	4	4	NUM
american_scientific_journal-3703	269	9	22	22	NUM
american_scientific_journal-3703	269	10	4	4	NUM
american_scientific_journal-3703	269	11	2x	2x	NUM
american_scientific_journal-3703	269	12	d	d	NOUN
american_scientific_journal-3703	269	13	x	x	SYM
american_scientific_journal-3703	269	14	t	t	NOUN
american_scientific_journal-3703	269	15	d	d	X
american_scientific_journal-3703	269	16	x	x	X
american_scientific_journal-3703	269	17	t	t	NOUN
american_scientific_journal-3703	269	18	x	x	SYM
american_scientific_journal-3703	269	19	x	x	PUNCT
american_scientific_journal-3703	269	20	x≤	x≤	PRON
american_scientific_journal-3703	269	21	≤	≤	ADJ
american_scientific_journal-3703	269	22	⇒	⇒	VERB
american_scientific_journal-3703	269	23	≤	≤	ADJ
american_scientific_journal-3703	269	24	≤	≤	ADJ
american_scientific_journal-3703	269	25	⇒	⇒	NOUN
american_scientific_journal-3703	269	26	=	=	PUNCT
american_scientific_journal-3703	269	27	−	−	PROPN
american_scientific_journal-3703	269	28	=	=	SYM
american_scientific_journal-3703	269	29	−	−	PROPN
american_scientific_journal-3703	269	30	=	=	SYM
american_scientific_journal-3703	269	31	−o	−o	PROPN
american_scientific_journal-3703	269	32	(	(	PUNCT
american_scientific_journal-3703	269	33	)	)	PUNCT
american_scientific_journal-3703	269	34	(	(	PUNCT
american_scientific_journal-3703	269	35	)	)	PUNCT
american_scientific_journal-3703	269	36	(	(	PUNCT
american_scientific_journal-3703	269	37	)	)	PUNCT
american_scientific_journal-3703	269	38	(	(	PUNCT
american_scientific_journal-3703	269	39	)	)	SYM
american_scientific_journal-3703	269	40	3	3	NUM
american_scientific_journal-3703	269	41	11	11	NUM
american_scientific_journal-3703	269	42	1	1	NUM
american_scientific_journal-3703	269	43	2	2	NUM
american_scientific_journal-3703	269	44	1	1	NUM
american_scientific_journal-3703	269	45	2	2	NUM
american_scientific_journal-3703	269	46	2	2	NUM
american_scientific_journal-3703	269	47	2	2	NUM
american_scientific_journal-3703	269	48	1	1	NUM
american_scientific_journal-3703	269	49	4	4	NUM
american_scientific_journal-3703	269	50	44	44	NUM
american_scientific_journal-3703	269	51	2x	2x	NUM
american_scientific_journal-3703	270	1	d	d	X
american_scientific_journal-3703	270	2	x	x	SYM
american_scientific_journal-3703	270	3	t	t	NOUN
american_scientific_journal-3703	270	4	d	d	X
american_scientific_journal-3703	270	5	x	x	X
american_scientific_journal-3703	270	6	t	t	NOUN
american_scientific_journal-3703	270	7	x	x	SYM
american_scientific_journal-3703	270	8	x	x	PUNCT
american_scientific_journal-3703	270	9	x≤	x≤	PRON
american_scientific_journal-3703	270	10	≤	≤	ADJ
american_scientific_journal-3703	270	11	⇒	⇒	VERB
american_scientific_journal-3703	270	12	≤	≤	ADJ
american_scientific_journal-3703	270	13	≤	≤	ADJ
american_scientific_journal-3703	270	14	⇒	⇒	NOUN
american_scientific_journal-3703	270	15	=	=	PUNCT
american_scientific_journal-3703	270	16	−	−	PROPN
american_scientific_journal-3703	270	17	=	=	PUNCT
american_scientific_journal-3703	271	1	−	−	NOUN
american_scientific_journal-3703	271	2	−	−	PROPN
american_scientific_journal-3703	271	3	=	=	SYM
american_scientific_journal-3703	271	4	−o	−o	NOUN
american_scientific_journal-3703	271	5	we	we	PRON
american_scientific_journal-3703	271	6	have	have	VERB
american_scientific_journal-3703	271	7	to	to	PART
american_scientific_journal-3703	271	8	be	be	AUX
american_scientific_journal-3703	271	9	a	a	DET
american_scientific_journal-3703	271	10	little	little	ADJ
american_scientific_journal-3703	271	11	bit	bit	NOUN
american_scientific_journal-3703	271	12	careful	careful	ADJ
american_scientific_journal-3703	271	13	at	at	ADP
american_scientific_journal-3703	271	14	x=1/2	x=1/2	PROPN
american_scientific_journal-3703	271	15	since	since	SCONJ
american_scientific_journal-3703	271	16	d	d	PROPN
american_scientific_journal-3703	271	17	is	be	AUX
american_scientific_journal-3703	271	18	not	not	PART
american_scientific_journal-3703	271	19	continuous	continuous	ADJ
american_scientific_journal-3703	271	20	there	there	ADV
american_scientific_journal-3703	271	21	,	,	PUNCT
american_scientific_journal-3703	271	22	and	and	CCONJ
american_scientific_journal-3703	271	23	also	also	ADV
american_scientific_journal-3703	271	24	at	at	ADP
american_scientific_journal-3703	271	25	x=1	x=1	PROPN
american_scientific_journal-3703	271	26	since	since	SCONJ
american_scientific_journal-3703	271	27	we	we	PRON
american_scientific_journal-3703	271	28	have	have	AUX
american_scientific_journal-3703	271	29	not	not	PART
american_scientific_journal-3703	271	30	yet	yet	ADV
american_scientific_journal-3703	271	31	defined	define	VERB
american_scientific_journal-3703	271	32	d(1	d(1	PROPN
american_scientific_journal-3703	271	33	)	)	PUNCT
american_scientific_journal-3703	271	34	.	.	PUNCT
american_scientific_journal-3703	272	1	but	but	CCONJ
american_scientific_journal-3703	272	2	the	the	DET
american_scientific_journal-3703	272	3	reader	reader	NOUN
american_scientific_journal-3703	272	4	may	may	AUX
american_scientific_journal-3703	272	5	check	check	VERB
american_scientific_journal-3703	272	6	that	that	PRON
american_scientific_journal-3703	272	7	(	(	PUNCT
american_scientific_journal-3703	272	8	)	)	PUNCT
american_scientific_journal-3703	272	9	(	(	PUNCT
american_scientific_journal-3703	272	10	)	)	SYM
american_scientific_journal-3703	272	11	1	1	NUM
american_scientific_journal-3703	272	12	1	1	NUM
american_scientific_journal-3703	272	13	0,2	0,2	NUM
american_scientific_journal-3703	272	14	2	2	NUM
american_scientific_journal-3703	272	15	t	t	NOUN
american_scientific_journal-3703	272	16	d	d	NOUN
american_scientific_journal-3703	272	17	t	t	NOUN
american_scientific_journal-3703	272	18	t=	t=	PUNCT
american_scientific_journal-3703	273	1	=	=	NOUN
american_scientific_journal-3703	273	2	o	o	X
american_scientific_journal-3703	273	3	o	o	NOUN
american_scientific_journal-3703	273	4	and	and	CCONJ
american_scientific_journal-3703	273	5	that	that	PRON
american_scientific_journal-3703	273	6	(	(	PUNCT
american_scientific_journal-3703	273	7	)	)	PUNCT
american_scientific_journal-3703	273	8	(	(	PUNCT
american_scientific_journal-3703	273	9	)	)	SYM
american_scientific_journal-3703	273	10	1	1	NUM
american_scientific_journal-3703	273	11	1	1	NUM
american_scientific_journal-3703	273	12	0	0	NUM
american_scientific_journal-3703	273	13	t	t	NOUN
american_scientific_journal-3703	273	14	d	d	NOUN
american_scientific_journal-3703	273	15	t	t	NOUN
american_scientific_journal-3703	273	16	t=	t=	PUNCT
american_scientific_journal-3703	274	1	=	=	NOUN
american_scientific_journal-3703	274	2	o	o	X
american_scientific_journal-3703	274	3	o	o	NOUN
american_scientific_journal-3703	274	4	provided	provide	VERB
american_scientific_journal-3703	274	5	we	we	PRON
american_scientific_journal-3703	274	6	defined	define	VERB
american_scientific_journal-3703	274	7	(	(	PUNCT
american_scientific_journal-3703	274	8	)	)	PUNCT
american_scientific_journal-3703	274	9	1d	1d	NOUN
american_scientific_journal-3703	274	10	to	to	PART
american_scientific_journal-3703	274	11	be	be	AUX
american_scientific_journal-3703	274	12	either	either	CCONJ
american_scientific_journal-3703	274	13	0	0	NUM
american_scientific_journal-3703	274	14	or	or	CCONJ
american_scientific_journal-3703	274	15	1	1	NUM
american_scientific_journal-3703	274	16	.	.	PUNCT
american_scientific_journal-3703	275	1	it	it	PRON
american_scientific_journal-3703	275	2	is	be	AUX
american_scientific_journal-3703	275	3	also	also	ADV
american_scientific_journal-3703	275	4	straight	straight	ADV
american_scientific_journal-3703	275	5	forward	forward	ADV
american_scientific_journal-3703	275	6	to	to	PART
american_scientific_journal-3703	275	7	check	check	VERB
american_scientific_journal-3703	275	8	that	that	SCONJ
american_scientific_journal-3703	275	9	both	both	DET
american_scientific_journal-3703	275	10	t	t	NOUN
american_scientific_journal-3703	275	11	to	to	PART
american_scientific_journal-3703	275	12	and	and	CCONJ
american_scientific_journal-3703	275	13	t	t	PROPN
american_scientific_journal-3703	275	14	do	do	AUX
american_scientific_journal-3703	275	15	are	be	AUX
american_scientific_journal-3703	275	16	continuous	continuous	ADJ
american_scientific_journal-3703	275	17	on	on	ADP
american_scientific_journal-3703	275	18	[	[	PUNCT
american_scientific_journal-3703	275	19	]	]	X
american_scientific_journal-3703	275	20	0,1	0,1	NUM
american_scientific_journal-3703	275	21	.	.	PUNCT
american_scientific_journal-3703	276	1	so	so	ADV
american_scientific_journal-3703	276	2	what	what	PRON
american_scientific_journal-3703	276	3	we	we	PRON
american_scientific_journal-3703	276	4	have	have	AUX
american_scientific_journal-3703	276	5	shown	show	VERB
american_scientific_journal-3703	276	6	is	be	AUX
american_scientific_journal-3703	276	7	that	that	PRON
american_scientific_journal-3703	276	8	(	(	PUNCT
american_scientific_journal-3703	276	9	)	)	PUNCT
american_scientific_journal-3703	276	10	(	(	PUNCT
american_scientific_journal-3703	276	11	)	)	PUNCT
american_scientific_journal-3703	276	12	14	14	NUM
american_scientific_journal-3703	276	13	if	if	SCONJ
american_scientific_journal-3703	276	14	0	0	NUM
american_scientific_journal-3703	276	15	4	4	NUM
american_scientific_journal-3703	276	16	1	1	NUM
american_scientific_journal-3703	276	17	12	12	NUM
american_scientific_journal-3703	276	18	4	4	NUM
american_scientific_journal-3703	276	19	if	if	SCONJ
american_scientific_journal-3703	276	20	4	4	NUM
american_scientific_journal-3703	276	21	2	2	NUM
american_scientific_journal-3703	276	22	314	314	NUM
american_scientific_journal-3703	276	23	2	2	NUM
american_scientific_journal-3703	276	24	if	if	SCONJ
american_scientific_journal-3703	276	25	2	2	NUM
american_scientific_journal-3703	276	26	4	4	NUM
american_scientific_journal-3703	276	27	34	34	NUM
american_scientific_journal-3703	276	28	4	4	NUM
american_scientific_journal-3703	276	29	if	if	SCONJ
american_scientific_journal-3703	276	30	14	14	NUM
american_scientific_journal-3703	276	31	x	x	SYM
american_scientific_journal-3703	276	32	x	x	SYM
american_scientific_journal-3703	276	33	x	x	PUNCT
american_scientific_journal-3703	277	1	x	x	SYM
american_scientific_journal-3703	277	2	t	t	NOUN
american_scientific_journal-3703	277	3	d	d	X
american_scientific_journal-3703	277	4	x	x	SYM
american_scientific_journal-3703	277	5	t	t	NOUN
american_scientific_journal-3703	277	6	t	t	NOUN
american_scientific_journal-3703	277	7	x	x	PUNCT
american_scientific_journal-3703	277	8	x	x	PUNCT
american_scientific_journal-3703	277	9	x	x	PUNCT
american_scientific_journal-3703	277	10	x	x	SYM
american_scientific_journal-3703	277	11	x	x	SYM
american_scientific_journal-3703	277	12			VERB
american_scientific_journal-3703	277	13	≤	≤	ADJ
american_scientific_journal-3703	277	14	≤	≤	NUM
american_scientific_journal-3703	277	15			ADJ
american_scientific_journal-3703	277	16			PROPN
american_scientific_journal-3703	277	17	−	−	PROPN
american_scientific_journal-3703	277	18	≤	≤	X
american_scientific_journal-3703	277	19	≤=	≤=	PUNCT
american_scientific_journal-3703	277	20	=	=	PRON
american_scientific_journal-3703	278	1			ADP
american_scientific_journal-3703	278	2	−	−	PROPN
american_scientific_journal-3703	278	3	≤	≤	X
american_scientific_journal-3703	278	4	≤	≤	PROPN
american_scientific_journal-3703	278	5			PROPN
american_scientific_journal-3703	278	6			PROPN
american_scientific_journal-3703	278	7	−	−	PROPN
american_scientific_journal-3703	278	8	≤	≤	NUM
american_scientific_journal-3703	278	9	≤	≤	NOUN
american_scientific_journal-3703	278	10	o	o	NOUN
american_scientific_journal-3703	278	11	o	o	NOUN
american_scientific_journal-3703	279	1	and	and	CCONJ
american_scientific_journal-3703	279	2	so	so	ADV
american_scientific_journal-3703	279	3	d	d	NOUN
american_scientific_journal-3703	279	4	is	be	AUX
american_scientific_journal-3703	279	5	conjugate	conjugate	ADJ
american_scientific_journal-3703	279	6	to	to	ADP
american_scientific_journal-3703	279	7	t	t	PROPN
american_scientific_journal-3703	279	8	via	via	ADP
american_scientific_journal-3703	279	9	t	t	PROPN
american_scientific_journal-3703	279	10	for	for	ADP
american_scientific_journal-3703	279	11	the	the	DET
american_scientific_journal-3703	279	12	graph	graph	NOUN
american_scientific_journal-3703	279	13	of	of	ADP
american_scientific_journal-3703	279	14	.t	.t	PROPN
american_scientific_journal-3703	279	15	t	t	PROPN
american_scientific_journal-3703	279	16	t	t	PROPN
american_scientific_journal-3703	280	1	d	d	PUNCT
american_scientific_journal-3703	280	2	=	=	NOUN
american_scientific_journal-3703	280	3	o	o	X
american_scientific_journal-3703	280	4	o	o	X
american_scientific_journal-3703	281	1	[	[	X
american_scientific_journal-3703	281	2	9	9	NUM
american_scientific_journal-3703	281	3	]	]	SYM
american_scientific_journal-3703	281	4	4.8	4.8	NUM
american_scientific_journal-3703	281	5	proposition	proposition	NOUN
american_scientific_journal-3703	281	6	american	american	ADJ
american_scientific_journal-3703	281	7	scientific	scientific	ADJ
american_scientific_journal-3703	281	8	research	research	PROPN
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american_scientific_journal-3703	281	10	for	for	ADP
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american_scientific_journal-3703	281	12	,	,	PUNCT
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american_scientific_journal-3703	281	14	,	,	PUNCT
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american_scientific_journal-3703	281	17	(	(	PUNCT
american_scientific_journal-3703	281	18	asrjets	asrjet	NOUN
american_scientific_journal-3703	281	19	)	)	PUNCT
american_scientific_journal-3703	281	20	(	(	PUNCT
american_scientific_journal-3703	281	21	2018	2018	NUM
american_scientific_journal-3703	281	22	)	)	PUNCT
american_scientific_journal-3703	281	23	volume	volume	NOUN
american_scientific_journal-3703	281	24	43	43	NUM
american_scientific_journal-3703	281	25	,	,	PUNCT
american_scientific_journal-3703	281	26	no	no	DET
american_scientific_journal-3703	281	27	1	1	NUM
american_scientific_journal-3703	281	28	,	,	PUNCT
american_scientific_journal-3703	281	29	pp	pp	ADV
american_scientific_journal-3703	281	30	110	110	NUM
american_scientific_journal-3703	281	31	-	-	SYM
american_scientific_journal-3703	281	32	133	133	NUM
american_scientific_journal-3703	281	33	122	122	NUM
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american_scientific_journal-3703	281	35	map	map	NOUN
american_scientific_journal-3703	281	36	12	12	NUM
american_scientific_journal-3703	281	37	;	;	PUNCT
american_scientific_journal-3703	281	38	0	0	NUM
american_scientific_journal-3703	281	39	2(x	2(x	NUM
american_scientific_journal-3703	281	40	)	)	PUNCT
american_scientific_journal-3703	281	41	12	12	NUM
american_scientific_journal-3703	281	42	1	1	NUM
american_scientific_journal-3703	281	43	;	;	PUNCT
american_scientific_journal-3703	281	44	1	1	NUM
american_scientific_journal-3703	281	45	2	2	NUM
american_scientific_journal-3703	281	46	x	x	SYM
american_scientific_journal-3703	281	47	x	x	PUNCT
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american_scientific_journal-3703	281	50	x	x	SYM
american_scientific_journal-3703	281	51			VERB
american_scientific_journal-3703	281	52	≤	≤	X
american_scientific_journal-3703	281	53	<	<	X
american_scientific_journal-3703	281	54	=	=	PROPN
american_scientific_journal-3703	281	55			PRON
american_scientific_journal-3703	281	56			PROPN
american_scientific_journal-3703	281	57	−	−	PROPN
american_scientific_journal-3703	281	58	≤	≤	NOUN
american_scientific_journal-3703	281	59	<	<	X
american_scientific_journal-3703	281	60			NOUN
american_scientific_journal-3703	281	61	is	be	AUX
american_scientific_journal-3703	281	62	conjugate	conjugate	ADJ
american_scientific_journal-3703	281	63	to	to	PART
american_scientific_journal-3703	281	64	shift	shift	NOUN
american_scientific_journal-3703	281	65	map	map	NOUN
american_scientific_journal-3703	281	66	.	.	PUNCT
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american_scientific_journal-3703	282	2	.	.	PUNCT
american_scientific_journal-3703	283	1	the	the	DET
american_scientific_journal-3703	283	2	doubling	double	VERB
american_scientific_journal-3703	283	3	map	map	NOUN
american_scientific_journal-3703	283	4	is	be	AUX
american_scientific_journal-3703	283	5	defined	define	VERB
american_scientific_journal-3703	283	6	by	by	ADP
american_scientific_journal-3703	283	7	12	12	NUM
american_scientific_journal-3703	283	8	;	;	PUNCT
american_scientific_journal-3703	283	9	0	0	NUM
american_scientific_journal-3703	283	10	2(x	2(x	NUM
american_scientific_journal-3703	283	11	)	)	PUNCT
american_scientific_journal-3703	283	12	12	12	NUM
american_scientific_journal-3703	283	13	1	1	NUM
american_scientific_journal-3703	283	14	;	;	PUNCT
american_scientific_journal-3703	284	1	1	1	NUM
american_scientific_journal-3703	284	2	2	2	NUM
american_scientific_journal-3703	284	3	x	x	SYM
american_scientific_journal-3703	284	4	x	x	PUNCT
american_scientific_journal-3703	284	5	d	d	NOUN
american_scientific_journal-3703	284	6	x	x	X
american_scientific_journal-3703	284	7	x	x	SYM
american_scientific_journal-3703	284	8			VERB
american_scientific_journal-3703	284	9	≤	≤	X
american_scientific_journal-3703	284	10	<	<	X
american_scientific_journal-3703	284	11	=	=	PROPN
american_scientific_journal-3703	284	12			PRON
american_scientific_journal-3703	284	13			PROPN
american_scientific_journal-3703	284	14	−	−	PROPN
american_scientific_journal-3703	284	15	≤	≤	X
american_scientific_journal-3703	284	16	<	<	X
american_scientific_journal-3703	284	17			NOUN
american_scientific_journal-3703	284	18	let	let	VERB
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american_scientific_journal-3703	284	20	represent	represent	VERB
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american_scientific_journal-3703	284	22	[	[	PUNCT
american_scientific_journal-3703	284	23	)	)	PUNCT
american_scientific_journal-3703	284	24	0,1x∈	0,1x∈	NOUN
american_scientific_journal-3703	284	25	by	by	ADP
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american_scientific_journal-3703	284	27	binary	binary	ADJ
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american_scientific_journal-3703	284	29	:	:	PUNCT
american_scientific_journal-3703	284	30	31	31	NUM
american_scientific_journal-3703	284	31	2	2	NUM
american_scientific_journal-3703	284	32	4	4	NUM
american_scientific_journal-3703	284	33	2	2	NUM
american_scientific_journal-3703	284	34	1	1	NUM
american_scientific_journal-3703	284	35	2	2	NUM
american_scientific_journal-3703	284	36	3	3	NUM
american_scientific_journal-3703	284	37	2	2	NUM
american_scientific_journal-3703	284	38	3	3	NUM
american_scientific_journal-3703	284	39	40	40	NUM
american_scientific_journal-3703	284	40	.	.	PUNCT
american_scientific_journal-3703	284	41	...	...	PUNCT
american_scientific_journal-3703	285	1	...	...	PUNCT
american_scientific_journal-3703	286	1	2	2	NUM
american_scientific_journal-3703	286	2	2	2	NUM
american_scientific_journal-3703	286	3	2	2	NUM
american_scientific_journal-3703	286	4	2	2	NUM
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american_scientific_journal-3703	286	8	b	b	PROPN
american_scientific_journal-3703	286	9	b	b	PROPN
american_scientific_journal-3703	286	10	b=	b=	NOUN
american_scientific_journal-3703	286	11	=	=	PUNCT
american_scientific_journal-3703	287	1	+	+	PUNCT
american_scientific_journal-3703	288	1	+	+	PUNCT
american_scientific_journal-3703	288	2	+	+	X
american_scientific_journal-3703	288	3	+	+	CCONJ
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american_scientific_journal-3703	289	3	{	{	PUNCT
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american_scientific_journal-3703	289	5	0,1	0,1	NUM
american_scientific_journal-3703	289	6	.ib	.ib	PUNCT
american_scientific_journal-3703	289	7	∈	∈	PROPN
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american_scientific_journal-3703	289	9	1	1	NUM
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american_scientific_journal-3703	289	21	0	0	NUM
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american_scientific_journal-3703	289	23	,	,	PUNCT
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american_scientific_journal-3703	289	26	1	1	NUM
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american_scientific_journal-3703	289	28	.	.	PUNCT
american_scientific_journal-3703	290	1	then	then	ADV
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american_scientific_journal-3703	290	3	1	1	NUM
american_scientific_journal-3703	290	4	0b	0b	NOUN
american_scientific_journal-3703	290	5	=	=	PUNCT
american_scientific_journal-3703	290	6	,	,	PUNCT
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american_scientific_journal-3703	290	8	know	know	VERB
american_scientific_journal-3703	290	9	[	[	X
american_scientific_journal-3703	290	10	0	0	NUM
american_scientific_journal-3703	290	11	,	,	PUNCT
american_scientific_journal-3703	290	12	1/2)x∈	1/2)x∈	NUM
american_scientific_journal-3703	290	13	similarly	similarly	ADV
american_scientific_journal-3703	290	14	,	,	PUNCT
american_scientific_journal-3703	290	15	1	1	NUM
american_scientific_journal-3703	290	16	1b	1b	NUM
american_scientific_journal-3703	290	17	=	=	PUNCT
american_scientific_journal-3703	290	18	,	,	PUNCT
american_scientific_journal-3703	290	19	we	we	PRON
american_scientific_journal-3703	290	20	know	know	VERB
american_scientific_journal-3703	290	21	[	[	PUNCT
american_scientific_journal-3703	290	22	)	)	SYM
american_scientific_journal-3703	290	23	1	1	NUM
american_scientific_journal-3703	291	1	.1/	.1/	NOUN
american_scientific_journal-3703	291	2	2,x∈	2,x∈	NUM
american_scientific_journal-3703	291	3	suppose	suppose	VERB
american_scientific_journal-3703	291	4	[	[	X
american_scientific_journal-3703	291	5	0	0	NUM
american_scientific_journal-3703	291	6	,	,	PUNCT
american_scientific_journal-3703	291	7	1/2)x∈	1/2)x∈	PROPN
american_scientific_journal-3703	291	8	is	be	AUX
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american_scientific_journal-3703	291	10	.	.	PUNCT
american_scientific_journal-3703	292	1	32	32	NUM
american_scientific_journal-3703	292	2	4	4	NUM
american_scientific_journal-3703	292	3	2	2	NUM
american_scientific_journal-3703	292	4	2	2	NUM
american_scientific_journal-3703	292	5	3	3	NUM
american_scientific_journal-3703	292	6	4	4	NUM
american_scientific_journal-3703	292	7	2	2	NUM
american_scientific_journal-3703	292	8	3	3	NUM
american_scientific_journal-3703	292	9	4	4	NUM
american_scientific_journal-3703	292	10	00	00	NUM
american_scientific_journal-3703	292	11	.	.	PROPN
american_scientific_journal-3703	292	12	0	0	NUM
american_scientific_journal-3703	292	13	...	...	PUNCT
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american_scientific_journal-3703	293	1	2	2	NUM
american_scientific_journal-3703	293	2	2	2	NUM
american_scientific_journal-3703	293	3	2	2	NUM
american_scientific_journal-3703	293	4	2	2	NUM
american_scientific_journal-3703	293	5	bb	bb	NUM
american_scientific_journal-3703	293	6	bx	bx	PROPN
american_scientific_journal-3703	293	7	b	b	PROPN
american_scientific_journal-3703	293	8	b	b	PROPN
american_scientific_journal-3703	293	9	b=	b=	NOUN
american_scientific_journal-3703	293	10	=	=	PUNCT
american_scientific_journal-3703	294	1	+	+	PUNCT
american_scientific_journal-3703	295	1	+	+	PUNCT
american_scientific_journal-3703	295	2	+	+	PUNCT
american_scientific_journal-3703	295	3	+	+	X
american_scientific_journal-3703	295	4	.then	.then	X
american_scientific_journal-3703	295	5	(	(	PUNCT
american_scientific_journal-3703	295	6	)	)	PUNCT
american_scientific_journal-3703	295	7	32	32	NUM
american_scientific_journal-3703	295	8	4	4	NUM
american_scientific_journal-3703	295	9	2	2	NUM
american_scientific_journal-3703	295	10	2	2	NUM
american_scientific_journal-3703	295	11	3	3	NUM
american_scientific_journal-3703	295	12	4	4	NUM
american_scientific_journal-3703	295	13	2	2	NUM
american_scientific_journal-3703	295	14	3	3	NUM
american_scientific_journal-3703	295	15	4	4	NUM
american_scientific_journal-3703	295	16	02	02	NUM
american_scientific_journal-3703	295	17	0	0	NUM
american_scientific_journal-3703	295	18	.	.	NUM
american_scientific_journal-3703	295	19	0	0	NUM
american_scientific_journal-3703	295	20	...	...	PUNCT
american_scientific_journal-3703	295	21	...	...	PUNCT
american_scientific_journal-3703	296	1	2	2	NUM
american_scientific_journal-3703	296	2	2	2	NUM
american_scientific_journal-3703	296	3	2	2	NUM
american_scientific_journal-3703	296	4	2	2	NUM
american_scientific_journal-3703	296	5	bbbd	bbbd	NOUN
american_scientific_journal-3703	296	6	x	x	X
american_scientific_journal-3703	297	1	b	b	X
american_scientific_journal-3703	297	2	bx	bx	X
american_scientific_journal-3703	297	3	b	b	NOUN
american_scientific_journal-3703	297	4	=	=	PUNCT
american_scientific_journal-3703	297	5	=	=	PUNCT
american_scientific_journal-3703	298	1	=	=	PUNCT
american_scientific_journal-3703	299	1	+	+	PUNCT
american_scientific_journal-3703	299	2	+	+	PUNCT
american_scientific_journal-3703	299	3	+	+	CCONJ
american_scientific_journal-3703	299	4	+	+	CCONJ
american_scientific_journal-3703	299	5	consider	consider	VERB
american_scientific_journal-3703	299	6	20	20	NUM
american_scientific_journal-3703	299	7	.	.	NUM
american_scientific_journal-3703	300	1	01010110	01010110	NUM
american_scientific_journal-3703	300	2	.....	.....	PUNCT
american_scientific_journal-3703	301	1	then	then	ADV
american_scientific_journal-3703	301	2	1/	1/	NUM
american_scientific_journal-3703	301	3	4	4	NUM
american_scientific_journal-3703	301	4	1/16	1/16	NUM
american_scientific_journal-3703	301	5	1/	1/	NUM
american_scientific_journal-3703	301	6	64	64	NUM
american_scientific_journal-3703	301	7	1/128	1/128	NUM
american_scientific_journal-3703	301	8	...	...	PUNCT
american_scientific_journal-3703	302	1	x	x	X
american_scientific_journal-3703	302	2	x=	x=	PUNCT
american_scientific_journal-3703	303	1	=	=	PUNCT
american_scientific_journal-3703	304	1	+	+	PUNCT
american_scientific_journal-3703	305	1	+	+	PUNCT
american_scientific_journal-3703	305	2	+	+	CCONJ
american_scientific_journal-3703	305	3	+	+	CCONJ
american_scientific_journal-3703	305	4	and	and	CCONJ
american_scientific_journal-3703	305	5	(	(	PUNCT
american_scientific_journal-3703	305	6	)	)	PUNCT
american_scientific_journal-3703	305	7	2	2	NUM
american_scientific_journal-3703	305	8	2	2	NUM
american_scientific_journal-3703	305	9	/	/	SYM
american_scientific_journal-3703	305	10	4	4	NUM
american_scientific_journal-3703	305	11	2	2	NUM
american_scientific_journal-3703	305	12	/16	/16	SYM
american_scientific_journal-3703	305	13	2	2	NUM
american_scientific_journal-3703	305	14	/	/	SYM
american_scientific_journal-3703	305	15	64	64	NUM
american_scientific_journal-3703	305	16	2	2	NUM
american_scientific_journal-3703	305	17	/128	/128	SYM
american_scientific_journal-3703	305	18	1/	1/	NUM
american_scientific_journal-3703	305	19	2	2	NUM
american_scientific_journal-3703	305	20	1/	1/	NUM
american_scientific_journal-3703	305	21	8	8	NUM
american_scientific_journal-3703	305	22	1/	1/	NUM
american_scientific_journal-3703	305	23	32	32	NUM
american_scientific_journal-3703	305	24	1/	1/	NUM
american_scientific_journal-3703	305	25	64	64	NUM
american_scientific_journal-3703	305	26	...	...	PUNCT
american_scientific_journal-3703	306	1	d	d	X
american_scientific_journal-3703	306	2	x	x	X
american_scientific_journal-3703	306	3	x=	x=	PUNCT
american_scientific_journal-3703	307	1	=	=	PUNCT
american_scientific_journal-3703	308	1	+	+	PUNCT
american_scientific_journal-3703	309	1	+	+	PUNCT
american_scientific_journal-3703	309	2	+	+	PUNCT
american_scientific_journal-3703	309	3	=	=	X
american_scientific_journal-3703	310	1	+	+	PUNCT
american_scientific_journal-3703	310	2	+	+	PUNCT
american_scientific_journal-3703	310	3	+	+	CCONJ
american_scientific_journal-3703	310	4	+	+	NUM
american_scientific_journal-3703	310	5	1/64	1/64	NUM
american_scientific_journal-3703	310	6	...	...	PUNCT
american_scientific_journal-3703	310	7	20	20	NUM
american_scientific_journal-3703	310	8	.	.	PUNCT
american_scientific_journal-3703	310	9	1010110	1010110	NUM
american_scientific_journal-3703	310	10	....	....	PUNCT
american_scientific_journal-3703	311	1	=	=	PRON
american_scientific_journal-3703	311	2	now	now	ADV
american_scientific_journal-3703	311	3	suppose	suppose	VERB
american_scientific_journal-3703	311	4	[	[	PUNCT
american_scientific_journal-3703	311	5	)	)	PUNCT
american_scientific_journal-3703	311	6	1/	1/	NUM
american_scientific_journal-3703	311	7	2,1x∈	2,1x∈	PROPN
american_scientific_journal-3703	311	8	is	be	AUX
american_scientific_journal-3703	311	9	given	give	VERB
american_scientific_journal-3703	311	10	.	.	PUNCT
american_scientific_journal-3703	312	1	then	then	ADV
american_scientific_journal-3703	312	2	32	32	NUM
american_scientific_journal-3703	312	3	4	4	NUM
american_scientific_journal-3703	312	4	2	2	NUM
american_scientific_journal-3703	312	5	2	2	NUM
american_scientific_journal-3703	312	6	3	3	NUM
american_scientific_journal-3703	312	7	4	4	NUM
american_scientific_journal-3703	312	8	2	2	NUM
american_scientific_journal-3703	312	9	3	3	NUM
american_scientific_journal-3703	312	10	4	4	NUM
american_scientific_journal-3703	312	11	10	10	NUM
american_scientific_journal-3703	312	12	.	.	PUNCT
american_scientific_journal-3703	313	1	1	1	NUM
american_scientific_journal-3703	313	2	...	...	PUNCT
american_scientific_journal-3703	313	3	=	=	SYM
american_scientific_journal-3703	313	4	...	...	PUNCT
american_scientific_journal-3703	313	5	2	2	NUM
american_scientific_journal-3703	313	6	2	2	NUM
american_scientific_journal-3703	313	7	2	2	NUM
american_scientific_journal-3703	313	8	2	2	NUM
american_scientific_journal-3703	313	9	bb	bb	NUM
american_scientific_journal-3703	313	10	bx	bx	PROPN
american_scientific_journal-3703	313	11	b	b	PROPN
american_scientific_journal-3703	313	12	b	b	PROPN
american_scientific_journal-3703	313	13	b=	b=	NOUN
american_scientific_journal-3703	313	14	+	+	X
american_scientific_journal-3703	314	1	+	+	PUNCT
american_scientific_journal-3703	314	2	+	+	X
american_scientific_journal-3703	314	3	.	.	PUNCT
american_scientific_journal-3703	315	1	then	then	ADV
american_scientific_journal-3703	315	2	(	(	PUNCT
american_scientific_journal-3703	315	3	)	)	PUNCT
american_scientific_journal-3703	315	4	2	2	NUM
american_scientific_journal-3703	315	5	2	2	NUM
american_scientific_journal-3703	315	6	3	3	NUM
american_scientific_journal-3703	315	7	4	4	NUM
american_scientific_journal-3703	315	8	2	2	NUM
american_scientific_journal-3703	315	9	2	2	NUM
american_scientific_journal-3703	315	10	3	3	NUM
american_scientific_journal-3703	315	11	42	42	NUM
american_scientific_journal-3703	315	12	1	1	NUM
american_scientific_journal-3703	315	13	1	1	NUM
american_scientific_journal-3703	315	14	.	.	PUNCT
american_scientific_journal-3703	315	15	...	...	PUNCT
american_scientific_journal-3703	316	1	-1=0	-1=0	PROPN
american_scientific_journal-3703	316	2	.	.	PUNCT
american_scientific_journal-3703	316	3	...	...	PUNCT
american_scientific_journal-3703	317	1	d	d	X
american_scientific_journal-3703	317	2	x	x	PUNCT
american_scientific_journal-3703	317	3	x	x	SYM
american_scientific_journal-3703	317	4	b	b	X
american_scientific_journal-3703	317	5	b	b	PROPN
american_scientific_journal-3703	317	6	b	b	PROPN
american_scientific_journal-3703	317	7	b	b	PROPN
american_scientific_journal-3703	317	8	b	b	PROPN
american_scientific_journal-3703	317	9	b=	b=	NOUN
american_scientific_journal-3703	317	10	−	−	NOUN
american_scientific_journal-3703	318	1	=	=	PUNCT
american_scientific_journal-3703	318	2	hence	hence	ADV
american_scientific_journal-3703	318	3	on	on	ADP
american_scientific_journal-3703	318	4	[	[	PUNCT
american_scientific_journal-3703	318	5	)	)	SYM
american_scientific_journal-3703	318	6	0,1	0,1	NUM
american_scientific_journal-3703	318	7	,	,	PUNCT
american_scientific_journal-3703	318	8	(	(	PUNCT
american_scientific_journal-3703	318	9	)	)	PUNCT
american_scientific_journal-3703	318	10	d	d	X
american_scientific_journal-3703	318	11	x	x	X
american_scientific_journal-3703	318	12	is	be	AUX
american_scientific_journal-3703	318	13	equivalent	equivalent	ADJ
american_scientific_journal-3703	318	14	to	to	ADP
american_scientific_journal-3703	318	15	(	(	PUNCT
american_scientific_journal-3703	318	16	)	)	PUNCT
american_scientific_journal-3703	318	17	xσ	xσ	X
american_scientific_journal-3703	318	18	,	,	PUNCT
american_scientific_journal-3703	318	19	the	the	DET
american_scientific_journal-3703	318	20	shift	shift	NOUN
american_scientific_journal-3703	318	21	map	map	NOUN
american_scientific_journal-3703	318	22	on	on	ADP
american_scientific_journal-3703	318	23	two	two	NUM
american_scientific_journal-3703	318	24	symbols	symbol	NOUN
american_scientific_journal-3703	318	25	.	.	PUNCT
american_scientific_journal-3703	319	1	we	we	PRON
american_scientific_journal-3703	319	2	have	have	AUX
american_scientific_journal-3703	319	3	already	already	ADV
american_scientific_journal-3703	319	4	seen	see	VERB
american_scientific_journal-3703	319	5	that	that	SCONJ
american_scientific_journal-3703	319	6	the	the	DET
american_scientific_journal-3703	319	7	shift	shift	NOUN
american_scientific_journal-3703	319	8	map	map	NOUN
american_scientific_journal-3703	319	9	(	(	PUNCT
american_scientific_journal-3703	319	10	)	)	PUNCT
american_scientific_journal-3703	319	11	xσ	xσ	PROPN
american_scientific_journal-3703	319	12	is	be	AUX
american_scientific_journal-3703	319	13	chaotic	chaotic	ADJ
american_scientific_journal-3703	319	14	on	on	ADP
american_scientific_journal-3703	319	15	the	the	DET
american_scientific_journal-3703	319	16	entire	entire	ADJ
american_scientific_journal-3703	319	17	space	space	NOUN
american_scientific_journal-3703	319	18	of	of	ADP
american_scientific_journal-3703	319	19	sequences	sequence	NOUN
american_scientific_journal-3703	319	20	of	of	ADP
american_scientific_journal-3703	319	21	two	two	NUM
american_scientific_journal-3703	319	22	symbols	symbol	NOUN
american_scientific_journal-3703	319	23	;	;	PUNCT
american_scientific_journal-3703	319	24	hence	hence	ADV
american_scientific_journal-3703	319	25	d(x	d(x	PROPN
american_scientific_journal-3703	319	26	)	)	PUNCT
american_scientific_journal-3703	319	27	is	be	AUX
american_scientific_journal-3703	319	28	chaotic	chaotic	ADJ
american_scientific_journal-3703	319	29	on	on	ADP
american_scientific_journal-3703	319	30	the	the	DET
american_scientific_journal-3703	319	31	entire	entire	ADJ
american_scientific_journal-3703	319	32	interval	interval	NOUN
american_scientific_journal-3703	319	33	[	[	X
american_scientific_journal-3703	319	34	0	0	NUM
american_scientific_journal-3703	319	35	,	,	PUNCT
american_scientific_journal-3703	319	36	1	1	NUM
american_scientific_journal-3703	319	37	)	)	PUNCT
american_scientific_journal-3703	320	1	[	[	X
american_scientific_journal-3703	320	2	chaos	chaos	NOUN
american_scientific_journal-3703	320	3	notes	note	VERB
american_scientific_journal-3703	320	4	]	]	PUNCT
american_scientific_journal-3703	320	5	.	.	PUNCT
american_scientific_journal-3703	321	1	4.9	4.9	NUM
american_scientific_journal-3703	321	2	proposition	proposition	NOUN
american_scientific_journal-3703	321	3	let	let	VERB
american_scientific_journal-3703	321	4	(	(	PUNCT
american_scientific_journal-3703	321	5	)	)	PUNCT
american_scientific_journal-3703	321	6	fn	fn	NOUN
american_scientific_journal-3703	321	7	x	x	VERB
american_scientific_journal-3703	321	8	be	be	AUX
american_scientific_journal-3703	321	9	newton	newton	PROPN
american_scientific_journal-3703	321	10	iteration	iteration	NOUN
american_scientific_journal-3703	321	11	function	function	NOUN
american_scientific_journal-3703	321	12	associated	associate	VERB
american_scientific_journal-3703	321	13	to	to	ADP
american_scientific_journal-3703	321	14	.1	.1	NUM
american_scientific_journal-3703	321	15	)	)	PUNCT
american_scientific_journal-3703	321	16	(	(	PUNCT
american_scientific_journal-3703	321	17	2	2	NUM
american_scientific_journal-3703	321	18	+	+	NOUN
american_scientific_journal-3703	321	19	=	=	NOUN
american_scientific_journal-3703	321	20	xxf	xxf	NOUN
american_scientific_journal-3703	321	21	then	then	ADV
american_scientific_journal-3703	321	22	)	)	PUNCT
american_scientific_journal-3703	321	23	(	(	PUNCT
american_scientific_journal-3703	321	24	xn	xn	PROPN
american_scientific_journal-3703	321	25	f	f	PROPN
american_scientific_journal-3703	321	26	is	be	AUX
american_scientific_journal-3703	321	27	conjugate	conjugate	ADJ
american_scientific_journal-3703	321	28	to	to	ADP
american_scientific_journal-3703	321	29	)	)	PUNCT
american_scientific_journal-3703	322	1	.(xd	.(xd	NOUN
american_scientific_journal-3703	322	2	proof	proof	NOUN
american_scientific_journal-3703	322	3	.	.	PUNCT
american_scientific_journal-3703	323	1	let	let	VERB
american_scientific_journal-3703	323	2			NOUN
american_scientific_journal-3703	323	3			VERB
american_scientific_journal-3703	323	4			PROPN
american_scientific_journal-3703	323	5	<	<	X
american_scientific_journal-3703	323	6	≤−	≤−	ADP
american_scientific_journal-3703	323	7	<	<	X
american_scientific_journal-3703	323	8	≤	≤	X
american_scientific_journal-3703	323	9	=	=	PUNCT
american_scientific_journal-3703	323	10	12/112	12/112	NUM
american_scientific_journal-3703	323	11	2/102	2/102	NUM
american_scientific_journal-3703	323	12	)	)	PUNCT
american_scientific_journal-3703	324	1	(	(	PUNCT
american_scientific_journal-3703	324	2	xx	xx	NUM
american_scientific_journal-3703	324	3	xx	xx	INTJ
american_scientific_journal-3703	324	4	xd	xd	INTJ
american_scientific_journal-3703	324	5	be	be	AUX
american_scientific_journal-3703	324	6	chaotic	chaotic	ADJ
american_scientific_journal-3703	324	7	on	on	ADP
american_scientific_journal-3703	324	8	[	[	X
american_scientific_journal-3703	324	9	0,1	0,1	NUM
american_scientific_journal-3703	324	10	)	)	PUNCT
american_scientific_journal-3703	324	11	,	,	PUNCT
american_scientific_journal-3703	324	12	and	and	CCONJ
american_scientific_journal-3703	324	13	let	let	VERB
american_scientific_journal-3703	324	14			NOUN
american_scientific_journal-3703	324	15			PUNCT
american_scientific_journal-3703	325	1			PROPN
american_scientific_journal-3703	325	2			NOUN
american_scientific_journal-3703	325	3			NOUN
american_scientific_journal-3703	325	4			NOUN
american_scientific_journal-3703	325	5	−=	−=	VERB
american_scientific_journal-3703	325	6	+	+	PUNCT
american_scientific_journal-3703	325	7	−=	−=	NOUN
american_scientific_journal-3703	325	8	x	x	NOUN
american_scientific_journal-3703	325	9	x	x	X
american_scientific_journal-3703	325	10	x	x	X
american_scientific_journal-3703	325	11	xxxn	xxxn	VERB
american_scientific_journal-3703	325	12	f	f	NOUN
american_scientific_journal-3703	325	13	1	1	NUM
american_scientific_journal-3703	325	14	2	2	NUM
american_scientific_journal-3703	325	15	1	1	NUM
american_scientific_journal-3703	325	16	2	2	NUM
american_scientific_journal-3703	325	17	1	1	NUM
american_scientific_journal-3703	325	18	)	)	PUNCT
american_scientific_journal-3703	325	19	(	(	PUNCT
american_scientific_journal-3703	325	20	2	2	NUM
american_scientific_journal-3703	325	21	be	be	AUX
american_scientific_journal-3703	325	22	defined	define	VERB
american_scientific_journal-3703	325	23	on	on	ADP
american_scientific_journal-3703	325	24	¡	¡	NOUN
american_scientific_journal-3703	325	25	define	define	VERB
american_scientific_journal-3703	325	26	the	the	DET
american_scientific_journal-3703	325	27	conjugacy	conjugacy	ADJ
american_scientific_journal-3703	325	28	function	function	NOUN
american_scientific_journal-3703	325	29	:	:	PUNCT
american_scientific_journal-3703	326	1	[	[	X
american_scientific_journal-3703	326	2	0,1)h	0,1)h	NUM
american_scientific_journal-3703	326	3	→	→	SYM
american_scientific_journal-3703	326	4	¡	¡	NOUN
american_scientific_journal-3703	326	5	by	by	ADP
american_scientific_journal-3703	326	6	)	)	PUNCT
american_scientific_journal-3703	326	7	.cot	.cot	PROPN
american_scientific_journal-3703	326	8	(	(	PUNCT
american_scientific_journal-3703	326	9	)	)	PUNCT
american_scientific_journal-3703	326	10	(	(	PUNCT
american_scientific_journal-3703	326	11	xxh	xxh	SYM
american_scientific_journal-3703	326	12	π=	π=	PROPN
american_scientific_journal-3703	326	13	then	then	ADV
american_scientific_journal-3703	326	14	we	we	PRON
american_scientific_journal-3703	326	15	have	have	VERB
american_scientific_journal-3703	326	16	(	(	PUNCT
american_scientific_journal-3703	326	17	)	)	PUNCT
american_scientific_journal-3703	326	18	(	(	PUNCT
american_scientific_journal-3703	326	19	)	)	PUNCT
american_scientific_journal-3703	326	20	(	(	PUNCT
american_scientific_journal-3703	326	21	)	)	PUNCT
american_scientific_journal-3703	326	22	(	(	PUNCT
american_scientific_journal-3703	326	23	)	)	PUNCT
american_scientific_journal-3703	326	24	2	2	NUM
american_scientific_journal-3703	326	25	2cos	2co	NOUN
american_scientific_journal-3703	326	26	(	(	PUNCT
american_scientific_journal-3703	326	27	)	)	PUNCT
american_scientific_journal-3703	326	28	sin	sin	NOUN
american_scientific_journal-3703	326	29	(	(	PUNCT
american_scientific_journal-3703	326	30	)	)	PUNCT
american_scientific_journal-3703	326	31	cot	cot	NOUN
american_scientific_journal-3703	326	32	cot	cot	NOUN
american_scientific_journal-3703	326	33	2	2	NUM
american_scientific_journal-3703	326	34	2sin	2sin	NUM
american_scientific_journal-3703	326	35	(	(	PUNCT
american_scientific_journal-3703	326	36	)	)	PUNCT
american_scientific_journal-3703	326	37	cos	cos	PROPN
american_scientific_journal-3703	326	38	(	(	PUNCT
american_scientific_journal-3703	326	39	)	)	PUNCT
american_scientific_journal-3703	326	40	x	x	PROPN
american_scientific_journal-3703	326	41	xh	xh	PROPN
american_scientific_journal-3703	327	1	d	d	NOUN
american_scientific_journal-3703	327	2	x	x	X
american_scientific_journal-3703	327	3	d	d	NOUN
american_scientific_journal-3703	327	4	x	x	X
american_scientific_journal-3703	327	5	x	x	PUNCT
american_scientific_journal-3703	327	6	x	x	PUNCT
american_scientific_journal-3703	327	7	x	x	SYM
american_scientific_journal-3703	327	8	π	π	NOUN
american_scientific_journal-3703	327	9	ππ	ππ	ADP
american_scientific_journal-3703	327	10	π	π	PROPN
american_scientific_journal-3703	327	11	π	π	NOUN
american_scientific_journal-3703	327	12	π	π	X
american_scientific_journal-3703	327	13	−	−	PUNCT
american_scientific_journal-3703	327	14	=	=	SYM
american_scientific_journal-3703	327	15	⋅	⋅	PROPN
american_scientific_journal-3703	327	16	=	=	PUNCT
american_scientific_journal-3703	327	17	=	=	NOUN
american_scientific_journal-3703	327	18	o	o	X
american_scientific_journal-3703	327	19	(	(	PUNCT
american_scientific_journal-3703	327	20	)	)	PUNCT
american_scientific_journal-3703	327	21	1	1	NUM
american_scientific_journal-3703	327	22	cot	cot	NOUN
american_scientific_journal-3703	327	23	(	(	PUNCT
american_scientific_journal-3703	327	24	)	)	PUNCT
american_scientific_journal-3703	327	25	tan	tan	PROPN
american_scientific_journal-3703	327	26	(	(	PUNCT
american_scientific_journal-3703	327	27	)	)	PUNCT
american_scientific_journal-3703	327	28	2	2	NUM
american_scientific_journal-3703	327	29	x	x	SYM
american_scientific_journal-3703	327	30	xπ	xπ	ADP
american_scientific_journal-3703	327	31	π=	π=	NUM
american_scientific_journal-3703	327	32	−	−	NOUN
american_scientific_journal-3703	327	33	)	)	PUNCT
american_scientific_journal-3703	327	34	(	(	PUNCT
american_scientific_journal-3703	327	35	xhn	xhn	PROPN
american_scientific_journal-3703	327	36	f	f	PROPN
american_scientific_journal-3703	327	37	o=	o=	PROPN
american_scientific_journal-3703	327	38	.	.	PUNCT
american_scientific_journal-3703	328	1	therefore	therefore	ADV
american_scientific_journal-3703	328	2	,	,	PUNCT
american_scientific_journal-3703	328	3	(	(	PUNCT
american_scientific_journal-3703	328	4	)	)	PUNCT
american_scientific_journal-3703	328	5	fn	fn	NOUN
american_scientific_journal-3703	328	6	x	x	VERB
american_scientific_journal-3703	328	7	is	be	AUX
american_scientific_journal-3703	328	8	conjugate	conjugate	ADJ
american_scientific_journal-3703	328	9	to	to	ADP
american_scientific_journal-3703	328	10	(	(	PUNCT
american_scientific_journal-3703	328	11	)	)	PUNCT
american_scientific_journal-3703	328	12	.d	.d	NOUN
american_scientific_journal-3703	328	13	x	x	NOUN
american_scientific_journal-3703	328	14	that	that	ADV
american_scientific_journal-3703	328	15	is	is	ADV
american_scientific_journal-3703	328	16	,	,	PUNCT
american_scientific_journal-3703	328	17	we	we	PRON
american_scientific_journal-3703	328	18	have	have	VERB
american_scientific_journal-3703	328	19	the	the	DET
american_scientific_journal-3703	328	20	following	following	ADJ
american_scientific_journal-3703	328	21	commutative	commutative	ADJ
american_scientific_journal-3703	328	22	diagram	diagram	NOUN
american_scientific_journal-3703	328	23	:	:	PUNCT
american_scientific_journal-3703	328	24	american	american	PROPN
american_scientific_journal-3703	328	25	scientific	scientific	ADJ
american_scientific_journal-3703	328	26	research	research	PROPN
american_scientific_journal-3703	328	27	journal	journal	NOUN
american_scientific_journal-3703	328	28	for	for	ADP
american_scientific_journal-3703	328	29	engineering	engineering	NOUN
american_scientific_journal-3703	328	30	,	,	PUNCT
american_scientific_journal-3703	328	31	technology	technology	NOUN
american_scientific_journal-3703	328	32	,	,	PUNCT
american_scientific_journal-3703	328	33	and	and	CCONJ
american_scientific_journal-3703	328	34	sciences	science	NOUN
american_scientific_journal-3703	328	35	(	(	PUNCT
american_scientific_journal-3703	328	36	asrjets	asrjet	NOUN
american_scientific_journal-3703	328	37	)	)	PUNCT
american_scientific_journal-3703	328	38	(	(	PUNCT
american_scientific_journal-3703	328	39	2018	2018	NUM
american_scientific_journal-3703	328	40	)	)	PUNCT
american_scientific_journal-3703	328	41	volume	volume	NOUN
american_scientific_journal-3703	328	42	43	43	NUM
american_scientific_journal-3703	328	43	,	,	PUNCT
american_scientific_journal-3703	328	44	no	no	DET
american_scientific_journal-3703	328	45	1	1	NUM
american_scientific_journal-3703	328	46	,	,	PUNCT
american_scientific_journal-3703	328	47	pp	pp	ADV
american_scientific_journal-3703	328	48	110	110	NUM
american_scientific_journal-3703	328	49	-	-	SYM
american_scientific_journal-3703	328	50	133	133	NUM
american_scientific_journal-3703	328	51	123	123	NUM
american_scientific_journal-3703	328	52	[	[	NOUN
american_scientific_journal-3703	328	53	0,1	0,1	NUM
american_scientific_journal-3703	328	54	)	)	PUNCT
american_scientific_journal-3703	329	1	[	[	X
american_scientific_journal-3703	329	2	0,1	0,1	NUM
american_scientific_journal-3703	329	3	)	)	PUNCT
american_scientific_journal-3703	329	4	f	f	NOUN
american_scientific_journal-3703	330	1	d	d	PROPN
american_scientific_journal-3703	330	2	n	n	PROPN
american_scientific_journal-3703	330	3	h	h	NOUN
american_scientific_journal-3703	330	4	h	h	NOUN
american_scientific_journal-3703	330	5	→	→	PROPN
american_scientific_journal-3703	330	6	↓	↓	PROPN
american_scientific_journal-3703	330	7	↓	↓	NOUN
american_scientific_journal-3703	330	8	→	→	NUM
american_scientific_journal-3703	330	9	¡	¡	PROPN
american_scientific_journal-3703	330	10	¡	¡	PROPN
american_scientific_journal-3703	330	11	thus	thus	ADV
american_scientific_journal-3703	330	12	the	the	DET
american_scientific_journal-3703	330	13	proof	proof	NOUN
american_scientific_journal-3703	330	14	is	be	AUX
american_scientific_journal-3703	330	15	complete	complete	ADJ
american_scientific_journal-3703	330	16	[	[	X
american_scientific_journal-3703	330	17	9	9	NUM
american_scientific_journal-3703	330	18	]	]	PUNCT
american_scientific_journal-3703	330	19	.	.	PUNCT
american_scientific_journal-3703	331	1	4.10	4.10	NUM
american_scientific_journal-3703	331	2	proposition	proposition	NOUN
american_scientific_journal-3703	331	3	the	the	DET
american_scientific_journal-3703	331	4	doubling	double	VERB
american_scientific_journal-3703	331	5	function	function	NOUN
american_scientific_journal-3703	331	6	d	d	NOUN
american_scientific_journal-3703	331	7	is	be	AUX
american_scientific_journal-3703	331	8	chaotic	chaotic	ADJ
american_scientific_journal-3703	331	9	on	on	ADP
american_scientific_journal-3703	331	10	the	the	DET
american_scientific_journal-3703	331	11	unit	unit	NOUN
american_scientific_journal-3703	331	12	circle	circle	NOUN
american_scientific_journal-3703	331	13	.	.	PUNCT
american_scientific_journal-3703	332	1	proof	proof	NOUN
american_scientific_journal-3703	332	2	.	.	PUNCT
american_scientific_journal-3703	333	1	we	we	PRON
american_scientific_journal-3703	333	2	will	will	AUX
american_scientific_journal-3703	333	3	again	again	ADV
american_scientific_journal-3703	333	4	make	make	VERB
american_scientific_journal-3703	333	5	use	use	NOUN
american_scientific_journal-3703	333	6	of	of	ADP
american_scientific_journal-3703	333	7	a	a	DET
american_scientific_journal-3703	333	8	semi	semi	ADJ
american_scientific_journal-3703	333	9	-	-	ADJ
american_scientific_journal-3703	333	10	conjugacy	conjugacy	ADJ
american_scientific_journal-3703	333	11	.	.	PUNCT
american_scientific_journal-3703	334	1	define	define	VERB
american_scientific_journal-3703	334	2	the	the	DET
american_scientific_journal-3703	334	3	function	function	NOUN
american_scientific_journal-3703	334	4	]	]	PUNCT
american_scientific_journal-3703	334	5	2,2	2,2	NUM
american_scientific_journal-3703	334	6	[:	[:	X
american_scientific_journal-3703	334	7	1	1	NUM
american_scientific_journal-3703	334	8	−→cb	−→cb	ADV
american_scientific_journal-3703	334	9	be	be	AUX
american_scientific_journal-3703	334	10	given	give	VERB
american_scientific_journal-3703	334	11	by	by	ADP
american_scientific_journal-3703	334	12	)	)	PUNCT
american_scientific_journal-3703	334	13	.cos(2	.cos(2	NOUN
american_scientific_journal-3703	334	14	)	)	PUNCT
american_scientific_journal-3703	334	15	(	(	PUNCT
american_scientific_journal-3703	334	16	θθ	θθ	NOUN
american_scientific_journal-3703	334	17	=	=	PROPN
american_scientific_journal-3703	334	18	b	b	NOUN
american_scientific_journal-3703	334	19	since	since	ADV
american_scientific_journal-3703	334	20	)	)	PUNCT
american_scientific_journal-3703	334	21	cos(θ	cos(θ	X
american_scientific_journal-3703	334	22	is	be	AUX
american_scientific_journal-3703	334	23	the	the	DET
american_scientific_journal-3703	334	24	x	x	NOUN
american_scientific_journal-3703	334	25	-	-	NOUN
american_scientific_journal-3703	334	26	coordinate	coordinate	NOUN
american_scientific_journal-3703	334	27	of	of	ADP
american_scientific_journal-3703	334	28	the	the	DET
american_scientific_journal-3703	334	29	point	point	NOUN
american_scientific_journal-3703	334	30	θ	θ	PROPN
american_scientific_journal-3703	334	31	on	on	ADP
american_scientific_journal-3703	334	32	1c	1c	NOUN
american_scientific_journal-3703	334	33	,	,	PUNCT
american_scientific_journal-3703	334	34	the	the	DET
american_scientific_journal-3703	334	35	map	map	NOUN
american_scientific_journal-3703	334	36	b	b	NOUN
american_scientific_journal-3703	334	37	is	be	AUX
american_scientific_journal-3703	334	38	given	give	VERB
american_scientific_journal-3703	334	39	geometrically	geometrically	ADV
american_scientific_journal-3703	334	40	by	by	ADP
american_scientific_journal-3703	334	41	projecting	project	VERB
american_scientific_journal-3703	334	42	points	point	NOUN
american_scientific_journal-3703	334	43	vertically	vertically	ADV
american_scientific_journal-3703	334	44	from	from	ADP
american_scientific_journal-3703	334	45	the	the	DET
american_scientific_journal-3703	334	46	circle	circle	NOUN
american_scientific_journal-3703	334	47	o	o	NOUN
american_scientific_journal-3703	334	48	the	the	DET
american_scientific_journal-3703	334	49	x	x	NOUN
american_scientific_journal-3703	334	50	-	-	NOUN
american_scientific_journal-3703	334	51	axis	axis	ADJ
american_scientific_journal-3703	334	52	,	,	PUNCT
american_scientific_journal-3703	334	53	and	and	CCONJ
american_scientific_journal-3703	334	54	then	then	ADV
american_scientific_journal-3703	334	55	stretching	stretch	VERB
american_scientific_journal-3703	334	56	by	by	ADP
american_scientific_journal-3703	334	57	a	a	DET
american_scientific_journal-3703	334	58	factor	factor	NOUN
american_scientific_journal-3703	334	59	of	of	ADP
american_scientific_journal-3703	334	60	2	2	NUM
american_scientific_journal-3703	334	61	(	(	PUNCT
american_scientific_journal-3703	334	62	fig	fig	NOUN
american_scientific_journal-3703	334	63	.	.	PUNCT
american_scientific_journal-3703	335	1	10.5	10.5	NUM
american_scientific_journal-3703	335	2	)	)	PUNCT
american_scientific_journal-3703	335	3	…	…	PUNCT
american_scientific_journal-3703	335	4	note	note	VERB
american_scientific_journal-3703	335	5	that	that	SCONJ
american_scientific_journal-3703	335	6	b	b	PROPN
american_scientific_journal-3703	335	7	is	be	AUX
american_scientific_journal-3703	335	8	two	two	NUM
american_scientific_journal-3703	335	9	-	-	PUNCT
american_scientific_journal-3703	335	10	to	to	ADP
american_scientific_journal-3703	335	11	-	-	PUNCT
american_scientific_journal-3703	335	12	one	one	NUM
american_scientific_journal-3703	335	13	except	except	SCONJ
american_scientific_journal-3703	335	14	at	at	ADP
american_scientific_journal-3703	335	15	the	the	DET
american_scientific_journal-3703	335	16	points	point	NOUN
american_scientific_journal-3703	335	17	𝜋𝜋	𝜋𝜋	NOUN
american_scientific_journal-3703	335	18	and	and	CCONJ
american_scientific_journal-3703	335	19	0	0	NUM
american_scientific_journal-3703	335	20	on	on	ADP
american_scientific_journal-3703	335	21	1c	1c	NUM
american_scientific_journal-3703	335	22	.consider	.consider	PUNCT
american_scientific_journal-3703	335	23	the	the	DET
american_scientific_journal-3703	335	24	diagram	diagram	NOUN
american_scientific_journal-3703	335	25	1	1	NUM
american_scientific_journal-3703	335	26	1	1	NUM
american_scientific_journal-3703	335	27	?	?	PUNCT
american_scientific_journal-3703	335	28	[	[	PUNCT
american_scientific_journal-3703	335	29	2,2	2,2	NUM
american_scientific_journal-3703	335	30	]	]	X
american_scientific_journal-3703	335	31	[	[	PUNCT
american_scientific_journal-3703	335	32	2,2	2,2	NUM
american_scientific_journal-3703	335	33	]	]	X
american_scientific_journal-3703	335	34	dc	dc	PROPN
american_scientific_journal-3703	336	1	c	c	PROPN
american_scientific_journal-3703	336	2	b	b	PROPN
american_scientific_journal-3703	336	3	b	b	PROPN
american_scientific_journal-3703	336	4	→	→	PROPN
american_scientific_journal-3703	336	5	↓	↓	NOUN
american_scientific_journal-3703	336	6	↓	↓	NOUN
american_scientific_journal-3703	337	1	−	−	PROPN
american_scientific_journal-3703	337	2	→	→	PROPN
american_scientific_journal-3703	337	3	−	−	PROPN
american_scientific_journal-3703	337	4	as	as	SCONJ
american_scientific_journal-3703	337	5	before	before	SCONJ
american_scientific_journal-3703	337	6	we	we	PRON
american_scientific_journal-3703	337	7	ask	ask	VERB
american_scientific_journal-3703	337	8	which	which	DET
american_scientific_journal-3703	337	9	function	function	NOUN
american_scientific_journal-3703	337	10	completes	complete	VERB
american_scientific_journal-3703	337	11	the	the	DET
american_scientific_journal-3703	337	12	diagram	diagram	NOUN
american_scientific_journal-3703	337	13	.	.	PUNCT
american_scientific_journal-3703	338	1	we	we	PRON
american_scientific_journal-3703	338	2	have	have	AUX
american_scientific_journal-3703	338	3	,	,	PUNCT
american_scientific_journal-3703	338	4	(	(	PUNCT
american_scientific_journal-3703	338	5	)	)	PUNCT
american_scientific_journal-3703	338	6	(	(	PUNCT
american_scientific_journal-3703	338	7	)	)	PUNCT
american_scientific_journal-3703	338	8	2cosb	2cosb	NUM
american_scientific_journal-3703	338	9	d	d	NUM
american_scientific_journal-3703	338	10	θ	θ	NOUN
american_scientific_journal-3703	338	11	θ	θ	PUNCT
american_scientific_journal-3703	338	12	=	=	NOUN
american_scientific_journal-3703	338	13	o	o	NOUN
american_scientific_journal-3703	338	14	so	so	ADV
american_scientific_journal-3703	338	15	we	we	PRON
american_scientific_journal-3703	338	16	must	must	AUX
american_scientific_journal-3703	338	17	find	find	VERB
american_scientific_journal-3703	338	18	the	the	DET
american_scientific_journal-3703	338	19	function	function	NOUN
american_scientific_journal-3703	338	20	that	that	PRON
american_scientific_journal-3703	338	21	takes	take	VERB
american_scientific_journal-3703	338	22	,	,	PUNCT
american_scientific_journal-3703	338	23	(	(	PUNCT
american_scientific_journal-3703	338	24	)	)	PUNCT
american_scientific_journal-3703	338	25	θcos2	θcos2	PROPN
american_scientific_journal-3703	338	26	↦	↦	PROPN
american_scientific_journal-3703	338	27	(	(	PUNCT
american_scientific_journal-3703	338	28	)	)	PUNCT
american_scientific_journal-3703	338	29	2cos	2co	NOUN
american_scientific_journal-3703	338	30	2θ	2θ	NUM
american_scientific_journal-3703	338	31	however	however	ADV
american_scientific_journal-3703	338	32	,	,	PUNCT
american_scientific_journal-3703	338	33	we	we	PRON
american_scientific_journal-3703	338	34	may	may	AUX
american_scientific_journal-3703	338	35	write	write	VERB
american_scientific_journal-3703	338	36	,	,	PUNCT
american_scientific_journal-3703	338	37	(	(	PUNCT
american_scientific_journal-3703	338	38	)	)	PUNCT
american_scientific_journal-3703	338	39	(	(	PUNCT
american_scientific_journal-3703	338	40	)	)	SYM
american_scientific_journal-3703	338	41	2	2	NUM
american_scientific_journal-3703	338	42	2	2	NUM
american_scientific_journal-3703	338	43	22cos	22co	NOUN
american_scientific_journal-3703	338	44	2	2	NUM
american_scientific_journal-3703	338	45	2(2cos	2(2co	NOUN
american_scientific_journal-3703	338	46	(	(	PUNCT
american_scientific_journal-3703	338	47	)	)	PUNCT
american_scientific_journal-3703	338	48	1	1	NUM
american_scientific_journal-3703	338	49	)	)	PUNCT
american_scientific_journal-3703	338	50	(	(	PUNCT
american_scientific_journal-3703	338	51	2cos	2co	NOUN
american_scientific_journal-3703	338	52	(	(	PUNCT
american_scientific_journal-3703	338	53	)	)	PUNCT
american_scientific_journal-3703	338	54	)	)	PUNCT
american_scientific_journal-3703	338	55	2	2	NUM
american_scientific_journal-3703	338	56	q	q	NOUN
american_scientific_journal-3703	338	57	xθ	xθ	PROPN
american_scientific_journal-3703	338	58	θ	θ	PROPN
american_scientific_journal-3703	338	59	θ	θ	PROPN
american_scientific_journal-3703	338	60	−=	−=	NOUN
american_scientific_journal-3703	338	61	−	−	PROPN
american_scientific_journal-3703	338	62	=	=	SYM
american_scientific_journal-3703	338	63	−	−	PROPN
american_scientific_journal-3703	339	1	=	=	PUNCT
american_scientific_journal-3703	339	2	then	then	ADV
american_scientific_journal-3703	339	3	the	the	DET
american_scientific_journal-3703	339	4	required	require	VERB
american_scientific_journal-3703	339	5	diagram	diagram	NOUN
american_scientific_journal-3703	339	6	is	be	AUX
american_scientific_journal-3703	339	7	(	(	PUNCT
american_scientific_journal-3703	339	8	)	)	SYM
american_scientific_journal-3703	339	9	2	2	NUM
american_scientific_journal-3703	339	10	1	1	NUM
american_scientific_journal-3703	339	11	1	1	NUM
american_scientific_journal-3703	339	12	[	[	PUNCT
american_scientific_journal-3703	339	13	2	2	NUM
american_scientific_journal-3703	339	14	,	,	PUNCT
american_scientific_journal-3703	339	15	2	2	NUM
american_scientific_journal-3703	339	16	]	]	PUNCT
american_scientific_journal-3703	339	17	[	[	PUNCT
american_scientific_journal-3703	339	18	2,2	2,2	NUM
american_scientific_journal-3703	339	19	]	]	X
american_scientific_journal-3703	339	20	d	d	X
american_scientific_journal-3703	339	21	q	q	X
american_scientific_journal-3703	339	22	x	x	X
american_scientific_journal-3703	339	23	c	c	NOUN
american_scientific_journal-3703	339	24	c	c	PROPN
american_scientific_journal-3703	339	25	b	b	PROPN
american_scientific_journal-3703	339	26	b	b	X
american_scientific_journal-3703	339	27	−	−	PROPN
american_scientific_journal-3703	339	28	→	→	PROPN
american_scientific_journal-3703	339	29	↓	↓	NOUN
american_scientific_journal-3703	339	30	↓	↓	NOUN
american_scientific_journal-3703	339	31	−	−	PROPN
american_scientific_journal-3703	339	32	→	→	NOUN
american_scientific_journal-3703	339	33	−	−	ADP
american_scientific_journal-3703	340	1	so	so	ADV
american_scientific_journal-3703	340	2	the	the	DET
american_scientific_journal-3703	340	3	required	require	VERB
american_scientific_journal-3703	340	4	function	function	NOUN
american_scientific_journal-3703	340	5	is	be	AUX
american_scientific_journal-3703	340	6	our	our	PRON
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american_scientific_journal-3703	340	8	the	the	DET
american_scientific_journal-3703	340	9	quadratic	quadratic	ADJ
american_scientific_journal-3703	340	10	function	function	NOUN
american_scientific_journal-3703	340	11	2	2	NUM
american_scientific_journal-3703	340	12	)	)	PUNCT
american_scientific_journal-3703	340	13	(	(	PUNCT
american_scientific_journal-3703	340	14	2	2	NUM
american_scientific_journal-3703	340	15	−=	−=	NOUN
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american_scientific_journal-3703	340	17	.	.	PUNCT
american_scientific_journal-3703	341	1	thus	thus	ADV
american_scientific_journal-3703	341	2	d	d	X
american_scientific_journal-3703	341	3	and	and	CCONJ
american_scientific_journal-3703	341	4	2−q	2−q	NUM
american_scientific_journal-3703	341	5	are	be	AUX
american_scientific_journal-3703	341	6	semi	semi	ADV
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american_scientific_journal-3703	341	8	.	.	PUNCT
american_scientific_journal-3703	342	1	it	it	PRON
american_scientific_journal-3703	342	2	is	be	AUX
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american_scientific_journal-3703	342	4	difficult	difficult	ADJ
american_scientific_journal-3703	342	5	to	to	PART
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american_scientific_journal-3703	342	7	the	the	DET
american_scientific_journal-3703	342	8	arguments	argument	NOUN
american_scientific_journal-3703	342	9	given	give	VERB
american_scientific_journal-3703	342	10	above	above	ADV
american_scientific_journal-3703	342	11	to	to	ADP
american_scientific_journal-3703	342	12	the	the	DET
american_scientific_journal-3703	342	13	complete	complete	ADJ
american_scientific_journal-3703	342	14	the	the	DET
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american_scientific_journal-3703	342	16	[	[	X
american_scientific_journal-3703	342	17	10	10	NUM
american_scientific_journal-3703	342	18	]	]	PUNCT
american_scientific_journal-3703	342	19	.	.	PUNCT
american_scientific_journal-3703	343	1	5	5	X
american_scientific_journal-3703	343	2	.	.	X
american_scientific_journal-3703	343	3	results	result	NOUN
american_scientific_journal-3703	343	4	and	and	CCONJ
american_scientific_journal-3703	343	5	discussion	discussion	NOUN
american_scientific_journal-3703	343	6	:	:	PUNCT
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american_scientific_journal-3703	343	8	behavior	behavior	NOUN
american_scientific_journal-3703	343	9	of	of	ADP
american_scientific_journal-3703	343	10	doubling	doubling	NOUN
american_scientific_journal-3703	343	11	map	map	VERB
american_scientific_journal-3703	343	12	5.1	5.1	NUM
american_scientific_journal-3703	343	13	chaotic	chaotic	ADJ
american_scientific_journal-3703	343	14	behavior	behavior	NOUN
american_scientific_journal-3703	343	15	of	of	ADP
american_scientific_journal-3703	343	16	doubling	double	VERB
american_scientific_journal-3703	343	17	map	map	NOUN
american_scientific_journal-3703	343	18	considering	consider	VERB
american_scientific_journal-3703	343	19	initial	initial	ADJ
american_scientific_journal-3703	343	20	seeds	seed	NOUN
american_scientific_journal-3703	343	21	american	american	ADJ
american_scientific_journal-3703	343	22	scientific	scientific	ADJ
american_scientific_journal-3703	343	23	research	research	NOUN
american_scientific_journal-3703	343	24	journal	journal	NOUN
american_scientific_journal-3703	343	25	for	for	ADP
american_scientific_journal-3703	343	26	engineering	engineering	NOUN
american_scientific_journal-3703	343	27	,	,	PUNCT
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american_scientific_journal-3703	343	29	,	,	PUNCT
american_scientific_journal-3703	343	30	and	and	CCONJ
american_scientific_journal-3703	343	31	sciences	science	NOUN
american_scientific_journal-3703	343	32	(	(	PUNCT
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american_scientific_journal-3703	343	34	)	)	PUNCT
american_scientific_journal-3703	343	35	(	(	PUNCT
american_scientific_journal-3703	343	36	2018	2018	NUM
american_scientific_journal-3703	343	37	)	)	PUNCT
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american_scientific_journal-3703	343	40	,	,	PUNCT
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american_scientific_journal-3703	343	42	1	1	NUM
american_scientific_journal-3703	343	43	,	,	PUNCT
american_scientific_journal-3703	343	44	pp	pp	ADV
american_scientific_journal-3703	343	45	110	110	NUM
american_scientific_journal-3703	343	46	-	-	SYM
american_scientific_journal-3703	343	47	133	133	NUM
american_scientific_journal-3703	343	48	124	124	NUM
american_scientific_journal-3703	343	49	the	the	DET
american_scientific_journal-3703	343	50	doubling	double	VERB
american_scientific_journal-3703	343	51	map	map	NOUN
american_scientific_journal-3703	343	52	is	be	AUX
american_scientific_journal-3703	343	53	given	give	VERB
american_scientific_journal-3703	343	54	by	by	ADP
american_scientific_journal-3703	343	55	12	12	NUM
american_scientific_journal-3703	343	56	;	;	PUNCT
american_scientific_journal-3703	343	57	0	0	NUM
american_scientific_journal-3703	343	58	2(x	2(x	NUM
american_scientific_journal-3703	343	59	)	)	PUNCT
american_scientific_journal-3703	343	60	12	12	NUM
american_scientific_journal-3703	343	61	1	1	NUM
american_scientific_journal-3703	343	62	;	;	PUNCT
american_scientific_journal-3703	343	63	1	1	NUM
american_scientific_journal-3703	343	64	2	2	NUM
american_scientific_journal-3703	343	65	x	x	SYM
american_scientific_journal-3703	343	66	x	x	PUNCT
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american_scientific_journal-3703	343	68	x	x	X
american_scientific_journal-3703	343	69	x	x	SYM
american_scientific_journal-3703	343	70			VERB
american_scientific_journal-3703	343	71	≤	≤	X
american_scientific_journal-3703	343	72	<	<	X
american_scientific_journal-3703	343	73	=	=	PROPN
american_scientific_journal-3703	343	74			PRON
american_scientific_journal-3703	343	75			PROPN
american_scientific_journal-3703	343	76	−	−	PROPN
american_scientific_journal-3703	343	77	≤	≤	X
american_scientific_journal-3703	343	78	<	<	X
american_scientific_journal-3703	343	79			NOUN
american_scientific_journal-3703	343	80	considering	consider	VERB
american_scientific_journal-3703	343	81	the	the	DET
american_scientific_journal-3703	343	82	initial	initial	ADJ
american_scientific_journal-3703	343	83	seeds	seed	NOUN
american_scientific_journal-3703	343	84	0	0	NUM
american_scientific_journal-3703	343	85	0	0	NUM
american_scientific_journal-3703	343	86	0	0	NUM
american_scientific_journal-3703	343	87	0	0	NUM
american_scientific_journal-3703	343	88	0	0	NUM
american_scientific_journal-3703	343	89	0	0	NUM
american_scientific_journal-3703	343	90	0	0	NUM
american_scientific_journal-3703	343	91	0	0	NUM
american_scientific_journal-3703	343	92	1	1	NUM
american_scientific_journal-3703	343	93	1	1	NUM
american_scientific_journal-3703	343	94	1	1	NUM
american_scientific_journal-3703	343	95	1	1	NUM
american_scientific_journal-3703	343	96	1	1	NUM
american_scientific_journal-3703	343	97	30.3	30.3	NUM
american_scientific_journal-3703	343	98	,	,	PUNCT
american_scientific_journal-3703	343	99	0.7	0.7	NUM
american_scientific_journal-3703	343	100	,	,	PUNCT
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american_scientific_journal-3703	343	102	,	,	PUNCT
american_scientific_journal-3703	343	103	,	,	PUNCT
american_scientific_journal-3703	343	104	,	,	PUNCT
american_scientific_journal-3703	343	105	,	,	PUNCT
american_scientific_journal-3703	343	106	.	.	PUNCT
american_scientific_journal-3703	344	1	8	8	NUM
american_scientific_journal-3703	344	2	16	16	NUM
american_scientific_journal-3703	344	3	7	7	NUM
american_scientific_journal-3703	344	4	14	14	NUM
american_scientific_journal-3703	344	5	11	11	NUM
american_scientific_journal-3703	344	6	22	22	NUM
american_scientific_journal-3703	344	7	x	x	NOUN
american_scientific_journal-3703	344	8	x	x	PUNCT
american_scientific_journal-3703	344	9	x	x	PUNCT
american_scientific_journal-3703	344	10	x	x	PUNCT
american_scientific_journal-3703	344	11	x	x	PUNCT
american_scientific_journal-3703	344	12	x	x	PUNCT
american_scientific_journal-3703	344	13	x	x	NOUN
american_scientific_journal-3703	344	14	x=	x=	PUNCT
american_scientific_journal-3703	344	15	=	=	PUNCT
american_scientific_journal-3703	345	1	=	=	PUNCT
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american_scientific_journal-3703	345	3	=	=	PUNCT
american_scientific_journal-3703	345	4	=	=	PUNCT
american_scientific_journal-3703	346	1	=	=	PUNCT
american_scientific_journal-3703	346	2	=	=	PUNCT
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american_scientific_journal-3703	346	5	of	of	ADP
american_scientific_journal-3703	346	6	the	the	DET
american_scientific_journal-3703	346	7	following	follow	VERB
american_scientific_journal-3703	346	8	seeds	seed	NOUN
american_scientific_journal-3703	346	9	discuss	discuss	VERB
american_scientific_journal-3703	346	10	the	the	DET
american_scientific_journal-3703	346	11	behavior	behavior	NOUN
american_scientific_journal-3703	346	12	of	of	ADP
american_scientific_journal-3703	346	13	the	the	DET
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american_scientific_journal-3703	346	18	)	)	PUNCT
american_scientific_journal-3703	346	19	.	.	PUNCT
american_scientific_journal-3703	347	1	(	(	PUNCT
american_scientific_journal-3703	347	2	i	i	NOUN
american_scientific_journal-3703	347	3	)	)	PUNCT
american_scientific_journal-3703	347	4	0	0	NUM
american_scientific_journal-3703	348	1	0.3x	0.3x	NOUN
american_scientific_journal-3703	348	2	=	=	SYM
american_scientific_journal-3703	348	3	(	(	PUNCT
american_scientific_journal-3703	348	4	)	)	PUNCT
american_scientific_journal-3703	348	5	(	(	PUNCT
american_scientific_journal-3703	348	6	)	)	PUNCT
american_scientific_journal-3703	348	7	(	(	PUNCT
american_scientific_journal-3703	348	8	)	)	PUNCT
american_scientific_journal-3703	348	9	(	(	PUNCT
american_scientific_journal-3703	348	10	)	)	PUNCT
american_scientific_journal-3703	348	11	(	(	PUNCT
american_scientific_journal-3703	348	12	)	)	PUNCT
american_scientific_journal-3703	348	13	since	since	SCONJ
american_scientific_journal-3703	348	14	0.3	0.3	NUM
american_scientific_journal-3703	348	15	0.6	0.6	NUM
american_scientific_journal-3703	348	16	,	,	PUNCT
american_scientific_journal-3703	348	17	0.6	0.6	NUM
american_scientific_journal-3703	348	18	0.2	0.2	NUM
american_scientific_journal-3703	348	19	,	,	PUNCT
american_scientific_journal-3703	348	20	0.2	0.2	NUM
american_scientific_journal-3703	348	21	0.4	0.4	NUM
american_scientific_journal-3703	348	22	,	,	PUNCT
american_scientific_journal-3703	348	23	0.4	0.4	NUM
american_scientific_journal-3703	348	24	0.8	0.8	NUM
american_scientific_journal-3703	348	25	and	and	CCONJ
american_scientific_journal-3703	348	26	0.8	0.8	NUM
american_scientific_journal-3703	348	27	0.6d	0.6d	NUM
american_scientific_journal-3703	349	1	d	d	NOUN
american_scientific_journal-3703	349	2	d	d	PROPN
american_scientific_journal-3703	349	3	d	d	NOUN
american_scientific_journal-3703	349	4	d=	d=	NOUN
american_scientific_journal-3703	349	5	=	=	PUNCT
american_scientific_journal-3703	350	1	=	=	SYM
american_scientific_journal-3703	350	2	=	=	PUNCT
american_scientific_journal-3703	351	1	=	=	PUNCT
american_scientific_journal-3703	351	2	the	the	DET
american_scientific_journal-3703	351	3	orbit	orbit	NOUN
american_scientific_journal-3703	351	4	of	of	ADP
american_scientific_journal-3703	351	5	0.3	0.3	NUM
american_scientific_journal-3703	351	6	is	be	AUX
american_scientific_journal-3703	351	7	eventually	eventually	ADV
american_scientific_journal-3703	351	8	periodic	periodic	ADJ
american_scientific_journal-3703	351	9	with	with	ADP
american_scientific_journal-3703	351	10	period	period	NOUN
american_scientific_journal-3703	351	11	1	1	NUM
american_scientific_journal-3703	351	12	and	and	CCONJ
american_scientific_journal-3703	351	13	period	period	NOUN
american_scientific_journal-3703	351	14	4	4	NUM
american_scientific_journal-3703	351	15	.	.	PUNCT
american_scientific_journal-3703	352	1	we	we	PRON
american_scientific_journal-3703	352	2	write	write	VERB
american_scientific_journal-3703	352	3	1	1	NUM
american_scientific_journal-3703	352	4	40.3	40.3	NUM
american_scientific_journal-3703	352	5	per	per	ADP
american_scientific_journal-3703	352	6	d∈	d∈	PROPN
american_scientific_journal-3703	352	7	(	(	PUNCT
american_scientific_journal-3703	352	8	ii	ii	PROPN
american_scientific_journal-3703	352	9	)	)	PUNCT
american_scientific_journal-3703	352	10	0	0	NUM
american_scientific_journal-3703	353	1	0.7x	0.7x	NOUN
american_scientific_journal-3703	353	2	=	=	PRON
american_scientific_journal-3703	353	3	.	.	PUNCT
american_scientific_journal-3703	354	1	(	(	PUNCT
american_scientific_journal-3703	354	2	)	)	PUNCT
american_scientific_journal-3703	354	3	4since	4since	NUM
american_scientific_journal-3703	354	4	0.7	0.7	NUM
american_scientific_journal-3703	354	5	0.4,and	0.4,and	NOUN
american_scientific_journal-3703	354	6	since	since	SCONJ
american_scientific_journal-3703	354	7	0.4	0.4	NUM
american_scientific_journal-3703	354	8	perd	perd	NOUN
american_scientific_journal-3703	354	9	d=	d=	NOUN
american_scientific_journal-3703	354	10	∈	∈	PROPN
american_scientific_journal-3703	354	11	from	from	ADP
american_scientific_journal-3703	354	12	exercise	exercise	NOUN
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american_scientific_journal-3703	354	16	that	that	SCONJ
american_scientific_journal-3703	354	17	1	1	NUM
american_scientific_journal-3703	354	18	40.7	40.7	NUM
american_scientific_journal-3703	354	19	per	per	ADP
american_scientific_journal-3703	354	20	d∈	d∈	PROPN
american_scientific_journal-3703	354	21	.	.	PUNCT
american_scientific_journal-3703	355	1	(	(	PUNCT
american_scientific_journal-3703	355	2	iii	iii	NOUN
american_scientific_journal-3703	355	3	)	)	PUNCT
american_scientific_journal-3703	355	4	0	0	NUM
american_scientific_journal-3703	356	1	1	1	NUM
american_scientific_journal-3703	356	2	8	8	NUM
american_scientific_journal-3703	356	3	x	x	X
american_scientific_journal-3703	356	4	=	=	X
american_scientific_journal-3703	356	5	;	;	PUNCT
american_scientific_journal-3703	356	6	1	1	NUM
american_scientific_journal-3703	356	7	2	2	NUM
american_scientific_journal-3703	356	8	4	4	NUM
american_scientific_journal-3703	356	9	1mod1	1mod1	NUM
american_scientific_journal-3703	356	10	0	0	NUM
american_scientific_journal-3703	356	11	8	8	NUM
american_scientific_journal-3703	356	12	8	8	NUM
american_scientific_journal-3703	356	13	8	8	NUM
american_scientific_journal-3703	356	14	=	=	NOUN
american_scientific_journal-3703	356	15	a	a	PRON
american_scientific_journal-3703	356	16	a	a	PRON
american_scientific_journal-3703	356	17	a	a	DET
american_scientific_journal-3703	356	18	.but	.but	NOUN
american_scientific_journal-3703	356	19	0	0	NUM
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american_scientific_journal-3703	356	21	fixed	fix	VERB
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american_scientific_journal-3703	356	23	d	d	PROPN
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american_scientific_journal-3703	356	25	3	3	NUM
american_scientific_journal-3703	356	26	1	1	NUM
american_scientific_journal-3703	356	27	1	1	NUM
american_scientific_journal-3703	356	28	per	per	ADP
american_scientific_journal-3703	356	29	fix	fix	NOUN
american_scientific_journal-3703	356	30	.	.	PUNCT
american_scientific_journal-3703	357	1	8	8	NUM
american_scientific_journal-3703	358	1	d	d	SYM
american_scientific_journal-3703	358	2	d∈	d∈	PROPN
american_scientific_journal-3703	358	3	⊆	⊆	NUM
american_scientific_journal-3703	358	4	(	(	PUNCT
american_scientific_journal-3703	358	5	iv	iv	X
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american_scientific_journal-3703	358	7	0	0	NUM
american_scientific_journal-3703	358	8	1	1	NUM
american_scientific_journal-3703	358	9	16	16	NUM
american_scientific_journal-3703	358	10	x	x	X
american_scientific_journal-3703	358	11	=	=	X
american_scientific_journal-3703	358	12	;	;	PUNCT
american_scientific_journal-3703	358	13	1	1	NUM
american_scientific_journal-3703	358	14	2	2	NUM
american_scientific_journal-3703	358	15	4	4	NUM
american_scientific_journal-3703	358	16	8	8	NUM
american_scientific_journal-3703	358	17	0	0	NUM
american_scientific_journal-3703	358	18	.	.	PUNCT
american_scientific_journal-3703	359	1	16	16	NUM
american_scientific_journal-3703	359	2	16	16	NUM
american_scientific_journal-3703	359	3	16	16	NUM
american_scientific_journal-3703	359	4	16	16	NUM
american_scientific_journal-3703	359	5	a	a	DET
american_scientific_journal-3703	359	6	a	a	DET
american_scientific_journal-3703	359	7	a	a	PRON
american_scientific_journal-3703	359	8	a	a	PRON
american_scientific_journal-3703	359	9	therefore	therefore	ADV
american_scientific_journal-3703	359	10	,	,	PUNCT
american_scientific_journal-3703	359	11	4	4	NUM
american_scientific_journal-3703	359	12	1	1	NUM
american_scientific_journal-3703	359	13	1	1	NUM
american_scientific_journal-3703	359	14	per	per	ADP
american_scientific_journal-3703	359	15	16	16	NUM
american_scientific_journal-3703	359	16	d∈	d∈	PROPN
american_scientific_journal-3703	359	17	.	.	PUNCT
american_scientific_journal-3703	360	1	(	(	PUNCT
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american_scientific_journal-3703	360	4	0	0	NUM
american_scientific_journal-3703	361	1	1	1	NUM
american_scientific_journal-3703	361	2	7	7	NUM
american_scientific_journal-3703	361	3	x	x	X
american_scientific_journal-3703	361	4	=	=	X
american_scientific_journal-3703	361	5	;	;	PUNCT
american_scientific_journal-3703	361	6	1	1	NUM
american_scientific_journal-3703	361	7	2	2	NUM
american_scientific_journal-3703	361	8	2	2	NUM
american_scientific_journal-3703	361	9	4	4	NUM
american_scientific_journal-3703	361	10	4	4	NUM
american_scientific_journal-3703	361	11	1since	1since	NUM
american_scientific_journal-3703	361	12	,	,	PUNCT
american_scientific_journal-3703	361	13	,	,	PUNCT
american_scientific_journal-3703	361	14	and	and	CCONJ
american_scientific_journal-3703	361	15	,	,	PUNCT
american_scientific_journal-3703	361	16	7	7	NUM
american_scientific_journal-3703	361	17	7	7	NUM
american_scientific_journal-3703	361	18	7	7	NUM
american_scientific_journal-3703	361	19	7	7	NUM
american_scientific_journal-3703	361	20	7	7	NUM
american_scientific_journal-3703	361	21	7	7	NUM
american_scientific_journal-3703	361	22	d	d	NOUN
american_scientific_journal-3703	361	23	d	d	X
american_scientific_journal-3703	361	24	d	d	PROPN
american_scientific_journal-3703	361	25			PROPN
american_scientific_journal-3703	361	26			PROPN
american_scientific_journal-3703	361	27			PROPN
american_scientific_journal-3703	361	28			PROPN
american_scientific_journal-3703	361	29	=	=	X
american_scientific_journal-3703	362	1	=	=	SYM
american_scientific_journal-3703	362	2	=	=	NOUN
american_scientific_journal-3703	362	3			NOUN
american_scientific_journal-3703	362	4			NOUN
american_scientific_journal-3703	362	5			NOUN
american_scientific_journal-3703	362	6			NOUN
american_scientific_journal-3703	362	7			NOUN
american_scientific_journal-3703	362	8			VERB
american_scientific_journal-3703	362	9			NOUN
american_scientific_journal-3703	362	10			PUNCT
american_scientific_journal-3703	362	11			NOUN
american_scientific_journal-3703	362	12			PUNCT
american_scientific_journal-3703	362	13			NOUN
american_scientific_journal-3703	362	14			PUNCT
american_scientific_journal-3703	363	1	we	we	PRON
american_scientific_journal-3703	363	2	have	have	VERB
american_scientific_journal-3703	363	3	that	that	PRON
american_scientific_journal-3703	363	4	3	3	NUM
american_scientific_journal-3703	363	5	1	1	NUM
american_scientific_journal-3703	363	6	per	per	ADP
american_scientific_journal-3703	363	7	7	7	NUM
american_scientific_journal-3703	363	8	d∈	d∈	PROPN
american_scientific_journal-3703	363	9	.	.	PUNCT
american_scientific_journal-3703	364	1	(	(	PUNCT
american_scientific_journal-3703	364	2	vi	vi	NOUN
american_scientific_journal-3703	364	3	)	)	PUNCT
american_scientific_journal-3703	364	4	0	0	NUM
american_scientific_journal-3703	364	5	1	1	NUM
american_scientific_journal-3703	364	6	14	14	NUM
american_scientific_journal-3703	364	7	x	x	SYM
american_scientific_journal-3703	364	8	=	=	X
american_scientific_journal-3703	364	9	;	;	PUNCT
american_scientific_journal-3703	364	10	1	1	NUM
american_scientific_journal-3703	364	11	2	2	NUM
american_scientific_journal-3703	364	12	1since	1since	NUM
american_scientific_journal-3703	364	13	.	.	PUNCT
american_scientific_journal-3703	365	1	14	14	NUM
american_scientific_journal-3703	365	2	14	14	NUM
american_scientific_journal-3703	365	3	7	7	NUM
american_scientific_journal-3703	365	4	d	d	PROPN
american_scientific_journal-3703	365	5			NOUN
american_scientific_journal-3703	365	6			PUNCT
american_scientific_journal-3703	366	1	=	=	PUNCT
american_scientific_journal-3703	367	1	=	=	NOUN
american_scientific_journal-3703	367	2			NOUN
american_scientific_journal-3703	367	3			VERB
american_scientific_journal-3703	367	4			PRON
american_scientific_journal-3703	367	5			PUNCT
american_scientific_journal-3703	368	1	but	but	CCONJ
american_scientific_journal-3703	368	2	it	it	PRON
american_scientific_journal-3703	368	3	was	be	AUX
american_scientific_journal-3703	368	4	shown	show	VERB
american_scientific_journal-3703	368	5	in	in	ADP
american_scientific_journal-3703	368	6	(	(	PUNCT
american_scientific_journal-3703	368	7	e	e	NOUN
american_scientific_journal-3703	368	8	)	)	PUNCT
american_scientific_journal-3703	368	9	that	that	SCONJ
american_scientific_journal-3703	368	10	3	3	NUM
american_scientific_journal-3703	368	11	1	1	NUM
american_scientific_journal-3703	368	12	per	per	ADP
american_scientific_journal-3703	368	13	7	7	NUM
american_scientific_journal-3703	368	14	d∈	d∈	PROPN
american_scientific_journal-3703	368	15	.therefore	.therefore	NOUN
american_scientific_journal-3703	368	16	,	,	PUNCT
american_scientific_journal-3703	368	17	1	1	NUM
american_scientific_journal-3703	368	18	3	3	NUM
american_scientific_journal-3703	368	19	1	1	NUM
american_scientific_journal-3703	368	20	per	per	ADP
american_scientific_journal-3703	368	21	14	14	NUM
american_scientific_journal-3703	368	22	d∈	d∈	PROPN
american_scientific_journal-3703	368	23	.	.	PUNCT
american_scientific_journal-3703	369	1	(	(	PUNCT
american_scientific_journal-3703	369	2	vii	vii	PROPN
american_scientific_journal-3703	369	3	)	)	PUNCT
american_scientific_journal-3703	369	4	0	0	NUM
american_scientific_journal-3703	369	5	1	1	NUM
american_scientific_journal-3703	369	6	11	11	NUM
american_scientific_journal-3703	369	7	x	x	X
american_scientific_journal-3703	369	8	=	=	X
american_scientific_journal-3703	369	9	;	;	PUNCT
american_scientific_journal-3703	369	10	1	1	NUM
american_scientific_journal-3703	369	11	2	2	NUM
american_scientific_journal-3703	369	12	4	4	NUM
american_scientific_journal-3703	369	13	8	8	NUM
american_scientific_journal-3703	369	14	5	5	NUM
american_scientific_journal-3703	369	15	10	10	NUM
american_scientific_journal-3703	369	16	9	9	NUM
american_scientific_journal-3703	369	17	7	7	NUM
american_scientific_journal-3703	369	18	3	3	NUM
american_scientific_journal-3703	369	19	6	6	NUM
american_scientific_journal-3703	369	20	1	1	NUM
american_scientific_journal-3703	369	21	11	11	NUM
american_scientific_journal-3703	369	22	11	11	NUM
american_scientific_journal-3703	369	23	11	11	NUM
american_scientific_journal-3703	369	24	11	11	NUM
american_scientific_journal-3703	369	25	11	11	NUM
american_scientific_journal-3703	369	26	11	11	NUM
american_scientific_journal-3703	369	27	11	11	NUM
american_scientific_journal-3703	369	28	11	11	NUM
american_scientific_journal-3703	369	29	11	11	NUM
american_scientific_journal-3703	369	30	11	11	NUM
american_scientific_journal-3703	369	31	11	11	NUM
american_scientific_journal-3703	369	32	a	a	DET
american_scientific_journal-3703	369	33	a	a	DET
american_scientific_journal-3703	369	34	a	a	DET
american_scientific_journal-3703	369	35	a	a	DET
american_scientific_journal-3703	369	36	a	a	DET
american_scientific_journal-3703	369	37	a	a	DET
american_scientific_journal-3703	369	38	a	a	DET
american_scientific_journal-3703	369	39	a	a	DET
american_scientific_journal-3703	369	40	a	a	DET
american_scientific_journal-3703	369	41	a	a	NOUN
american_scientific_journal-3703	369	42	,	,	PUNCT
american_scientific_journal-3703	369	43	we	we	PRON
american_scientific_journal-3703	369	44	see	see	VERB
american_scientific_journal-3703	369	45	that	that	SCONJ
american_scientific_journal-3703	369	46	10	10	NUM
american_scientific_journal-3703	369	47	1	1	NUM
american_scientific_journal-3703	369	48	per	per	ADP
american_scientific_journal-3703	369	49	11	11	NUM
american_scientific_journal-3703	369	50	d∈	d∈	PROPN
american_scientific_journal-3703	369	51	.	.	PUNCT
american_scientific_journal-3703	370	1	(	(	PUNCT
american_scientific_journal-3703	370	2	viii	viii	NOUN
american_scientific_journal-3703	370	3	)	)	PUNCT
american_scientific_journal-3703	370	4	0	0	NUM
american_scientific_journal-3703	370	5	3	3	NUM
american_scientific_journal-3703	370	6	22	22	NUM
american_scientific_journal-3703	370	7	x	x	SYM
american_scientific_journal-3703	370	8	=	=	SYM
american_scientific_journal-3703	370	9	1	1	NUM
american_scientific_journal-3703	370	10	10	10	NUM
american_scientific_journal-3703	370	11	10	10	NUM
american_scientific_journal-3703	370	12	3	3	NUM
american_scientific_journal-3703	370	13	6	6	NUM
american_scientific_journal-3703	370	14	3	3	NUM
american_scientific_journal-3703	370	15	3;since	3;since	NOUN
american_scientific_journal-3703	370	16	,	,	PUNCT
american_scientific_journal-3703	370	17	we	we	PRON
american_scientific_journal-3703	370	18	have	have	VERB
american_scientific_journal-3703	370	19	that	that	PRON
american_scientific_journal-3703	370	20	per	per	ADP
american_scientific_journal-3703	370	21	22	22	NUM
american_scientific_journal-3703	370	22	22	22	NUM
american_scientific_journal-3703	370	23	11	11	NUM
american_scientific_journal-3703	370	24	22	22	NUM
american_scientific_journal-3703	370	25	d	d	NOUN
american_scientific_journal-3703	370	26	per	per	ADP
american_scientific_journal-3703	370	27	d	d	X
american_scientific_journal-3703	370	28	d	d	PROPN
american_scientific_journal-3703	370	29			PUNCT
american_scientific_journal-3703	371	1	=	=	PUNCT
american_scientific_journal-3703	371	2	=	=	SYM
american_scientific_journal-3703	371	3	∈	∈	PROPN
american_scientific_journal-3703	371	4	∈	∈	NOUN
american_scientific_journal-3703	371	5			VERB
american_scientific_journal-3703	371	6			PRON
american_scientific_journal-3703	371	7			PUNCT
american_scientific_journal-3703	372	1	but	but	CCONJ
american_scientific_journal-3703	372	2	we	we	PRON
american_scientific_journal-3703	372	3	can	can	AUX
american_scientific_journal-3703	372	4	see	see	VERB
american_scientific_journal-3703	372	5	that	that	PRON
american_scientific_journal-3703	372	6	for	for	ADP
american_scientific_journal-3703	372	7	initial	initial	ADJ
american_scientific_journal-3703	372	8	seed	seed	NOUN
american_scientific_journal-3703	372	9	0	0	NUM
american_scientific_journal-3703	372	10	1	1	NUM
american_scientific_journal-3703	372	11	7	7	NUM
american_scientific_journal-3703	372	12	x	x	X
american_scientific_journal-3703	372	13	=	=	PRON
american_scientific_journal-3703	372	14	,	,	PUNCT
american_scientific_journal-3703	372	15	this	this	PRON
american_scientific_journal-3703	372	16	is	be	AUX
american_scientific_journal-3703	372	17	a	a	DET
american_scientific_journal-3703	372	18	periodic	periodic	ADJ
american_scientific_journal-3703	372	19	point	point	NOUN
american_scientific_journal-3703	372	20	with	with	ADP
american_scientific_journal-3703	372	21	prime	prime	ADJ
american_scientific_journal-3703	372	22	period-3	period-3	PROPN
american_scientific_journal-3703	372	23	and	and	CCONJ
american_scientific_journal-3703	372	24	therefore	therefore	ADV
american_scientific_journal-3703	372	25	the	the	DET
american_scientific_journal-3703	372	26	doubling	double	VERB
american_scientific_journal-3703	372	27	map	map	NOUN
american_scientific_journal-3703	372	28	is	be	AUX
american_scientific_journal-3703	372	29	chaotic	chaotic	ADJ
american_scientific_journal-3703	372	30	by	by	ADP
american_scientific_journal-3703	372	31	the	the	DET
american_scientific_journal-3703	372	32	period	period	NOUN
american_scientific_journal-3703	372	33	three	three	NUM
american_scientific_journal-3703	372	34	theorem	theorem	NOUN
american_scientific_journal-3703	372	35	[	[	X
american_scientific_journal-3703	372	36	7	7	NUM
american_scientific_journal-3703	372	37	]	]	PUNCT
american_scientific_journal-3703	372	38	.	.	PUNCT
american_scientific_journal-3703	373	1	5.2	5.2	NUM
american_scientific_journal-3703	373	2	orbit	orbit	NOUN
american_scientific_journal-3703	373	3	analysis	analysis	NOUN
american_scientific_journal-3703	373	4	of	of	ADP
american_scientific_journal-3703	373	5	doubling	double	VERB
american_scientific_journal-3703	373	6	map	map	NOUN
american_scientific_journal-3703	373	7	by	by	ADP
american_scientific_journal-3703	373	8	newton	newton	PROPN
american_scientific_journal-3703	373	9	’s	’s	PART
american_scientific_journal-3703	373	10	iteration	iteration	NOUN
american_scientific_journal-3703	373	11	the	the	DET
american_scientific_journal-3703	373	12	behavior	behavior	NOUN
american_scientific_journal-3703	373	13	of	of	ADP
american_scientific_journal-3703	373	14	orbit	orbit	NOUN
american_scientific_journal-3703	373	15	of	of	ADP
american_scientific_journal-3703	373	16	newton	newton	PROPN
american_scientific_journal-3703	373	17	iteration	iteration	PROPN
american_scientific_journal-3703	373	18	function	function	NOUN
american_scientific_journal-3703	373	19	associated	associate	VERB
american_scientific_journal-3703	373	20	to	to	ADP
american_scientific_journal-3703	373	21	doubling	double	VERB
american_scientific_journal-3703	373	22	function	function	NOUN
american_scientific_journal-3703	373	23	american	american	PROPN
american_scientific_journal-3703	373	24	scientific	scientific	ADJ
american_scientific_journal-3703	373	25	research	research	NOUN
american_scientific_journal-3703	373	26	journal	journal	NOUN
american_scientific_journal-3703	373	27	for	for	ADP
american_scientific_journal-3703	373	28	engineering	engineering	NOUN
american_scientific_journal-3703	373	29	,	,	PUNCT
american_scientific_journal-3703	373	30	technology	technology	NOUN
american_scientific_journal-3703	373	31	,	,	PUNCT
american_scientific_journal-3703	373	32	and	and	CCONJ
american_scientific_journal-3703	373	33	sciences	science	NOUN
american_scientific_journal-3703	373	34	(	(	PUNCT
american_scientific_journal-3703	373	35	asrjets	asrjet	NOUN
american_scientific_journal-3703	373	36	)	)	PUNCT
american_scientific_journal-3703	373	37	(	(	PUNCT
american_scientific_journal-3703	373	38	2018	2018	NUM
american_scientific_journal-3703	373	39	)	)	PUNCT
american_scientific_journal-3703	373	40	volume	volume	NOUN
american_scientific_journal-3703	373	41	43	43	NUM
american_scientific_journal-3703	373	42	,	,	PUNCT
american_scientific_journal-3703	373	43	no	no	DET
american_scientific_journal-3703	373	44	1	1	NUM
american_scientific_journal-3703	373	45	,	,	PUNCT
american_scientific_journal-3703	373	46	pp	pp	ADV
american_scientific_journal-3703	373	47	110	110	NUM
american_scientific_journal-3703	373	48	-	-	SYM
american_scientific_journal-3703	373	49	133	133	NUM
american_scientific_journal-3703	373	50	125	125	NUM
american_scientific_journal-3703	373	51	the	the	DET
american_scientific_journal-3703	373	52	doubling	double	VERB
american_scientific_journal-3703	373	53	function	function	NOUN
american_scientific_journal-3703	373	54	2	2	NUM
american_scientific_journal-3703	373	55	0	0	SYM
american_scientific_journal-3703	373	56	1/	1/	NUM
american_scientific_journal-3703	373	57	2	2	NUM
american_scientific_journal-3703	373	58	(	(	PUNCT
american_scientific_journal-3703	373	59	)	)	PUNCT
american_scientific_journal-3703	373	60	2	2	NUM
american_scientific_journal-3703	373	61	1	1	NUM
american_scientific_journal-3703	373	62	1/	1/	NUM
american_scientific_journal-3703	373	63	2	2	NUM
american_scientific_journal-3703	373	64	1	1	NUM
american_scientific_journal-3703	373	65	x	x	SYM
american_scientific_journal-3703	373	66	x	x	PUNCT
american_scientific_journal-3703	373	67	d	d	NOUN
american_scientific_journal-3703	373	68	x	x	X
american_scientific_journal-3703	373	69	x	x	X
american_scientific_journal-3703	373	70	x	x	SYM
american_scientific_journal-3703	373	71	≤	≤	NOUN
american_scientific_journal-3703	373	72	<	<	X
american_scientific_journal-3703	373	73			NOUN
american_scientific_journal-3703	373	74	=	=	PUNCT
american_scientific_journal-3703	373	75			ADP
american_scientific_journal-3703	373	76	−	−	PROPN
american_scientific_journal-3703	373	77	≤	≤	NOUN
american_scientific_journal-3703	373	78	<	<	X
american_scientific_journal-3703	373	79			NOUN
american_scientific_journal-3703	373	80	is	be	AUX
american_scientific_journal-3703	373	81	chaotic	chaotic	ADJ
american_scientific_journal-3703	373	82	on	on	ADP
american_scientific_journal-3703	373	83	]	]	PUNCT
american_scientific_journal-3703	373	84	.1,0	.1,0	PROPN
american_scientific_journal-3703	374	1	[	[	PUNCT
american_scientific_journal-3703	374	2	obviously	obviously	ADV
american_scientific_journal-3703	374	3	,	,	PUNCT
american_scientific_journal-3703	374	4	d	d	PROPN
american_scientific_journal-3703	374	5	has	have	VERB
american_scientific_journal-3703	374	6	two	two	NUM
american_scientific_journal-3703	374	7	roots	root	NOUN
american_scientific_journal-3703	374	8	0	0	NUM
american_scientific_journal-3703	374	9	and	and	CCONJ
american_scientific_journal-3703	374	10	2/1	2/1	NUM
american_scientific_journal-3703	374	11	which	which	PRON
american_scientific_journal-3703	374	12	are	be	AUX
american_scientific_journal-3703	374	13	on	on	ADP
american_scientific_journal-3703	374	14	the	the	DET
american_scientific_journal-3703	374	15	real	real	ADJ
american_scientific_journal-3703	374	16	line	line	NOUN
american_scientific_journal-3703	374	17	.	.	PUNCT
american_scientific_journal-3703	375	1	figure	figure	NOUN
american_scientific_journal-3703	375	2	1	1	NUM
american_scientific_journal-3703	375	3	:	:	PUNCT
american_scientific_journal-3703	375	4	the	the	DET
american_scientific_journal-3703	375	5	graph	graph	NOUN
american_scientific_journal-3703	375	6	of	of	ADP
american_scientific_journal-3703	375	7	doubling	double	VERB
american_scientific_journal-3703	375	8	function	function	NOUN
american_scientific_journal-3703	375	9	figure	figure	NOUN
american_scientific_journal-3703	375	10	2	2	NUM
american_scientific_journal-3703	375	11	:	:	PUNCT
american_scientific_journal-3703	375	12	chaos	chaos	NOUN
american_scientific_journal-3703	375	13	in	in	ADP
american_scientific_journal-3703	375	14	doubling	double	VERB
american_scientific_journal-3703	375	15	function	function	NOUN
american_scientific_journal-3703	375	16	(	(	PUNCT
american_scientific_journal-3703	375	17	1	1	X
american_scientific_journal-3703	375	18	)	)	PUNCT
american_scientific_journal-3703	375	19	the	the	DET
american_scientific_journal-3703	375	20	newton	newton	PROPN
american_scientific_journal-3703	375	21	iteration	iteration	PROPN
american_scientific_journal-3703	375	22	function	function	NOUN
american_scientific_journal-3703	375	23	associated	associate	VERB
american_scientific_journal-3703	375	24	to	to	ADP
american_scientific_journal-3703	375	25	)	)	PUNCT
american_scientific_journal-3703	375	26	(	(	PUNCT
american_scientific_journal-3703	375	27	xd	xd	INTJ
american_scientific_journal-3703	375	28	is	be	AUX
american_scientific_journal-3703	375	29	(	(	PUNCT
american_scientific_journal-3703	375	30	)	)	PUNCT
american_scientific_journal-3703	376	1	.0	.0	NUM
american_scientific_journal-3703	376	2	2	2	NUM
american_scientific_journal-3703	376	3	2	2	NUM
american_scientific_journal-3703	376	4	=	=	NOUN
american_scientific_journal-3703	376	5	−=	−=	X
american_scientific_journal-3703	376	6	xxxn	xxxn	VERB
american_scientific_journal-3703	376	7	note	note	VERB
american_scientific_journal-3703	376	8	that	that	SCONJ
american_scientific_journal-3703	376	9	n	n	PRON
american_scientific_journal-3703	376	10	has	have	AUX
american_scientific_journal-3703	376	11	fixed	fix	VERB
american_scientific_journal-3703	376	12	point	point	NOUN
american_scientific_journal-3703	376	13	,	,	PUNCT
american_scientific_journal-3703	376	14	at	at	ADP
american_scientific_journal-3703	376	15	the	the	DET
american_scientific_journal-3703	376	16	root	root	NOUN
american_scientific_journal-3703	376	17	0	0	NUM
american_scientific_journal-3703	376	18	of	of	ADP
american_scientific_journal-3703	376	19	.d	.d	NOUN
american_scientific_journal-3703	376	20	we	we	PRON
american_scientific_journal-3703	376	21	compute	compute	VERB
american_scientific_journal-3703	376	22	,	,	PUNCT
american_scientific_journal-3703	376	23	2)0	2)0	NUM
american_scientific_journal-3703	376	24	(	(	PUNCT
american_scientific_journal-3703	376	25	=	=	NOUN
american_scientific_journal-3703	376	26	′d	′d	NOUN
american_scientific_journal-3703	377	1	and	and	CCONJ
american_scientific_journal-3703	377	2	we	we	PRON
american_scientific_journal-3703	377	3	see	see	VERB
american_scientific_journal-3703	377	4	that	that	PRON
american_scientific_journal-3703	377	5	.0)0	.0)0	PUNCT
american_scientific_journal-3703	378	1	(	(	PUNCT
american_scientific_journal-3703	378	2	=	=	VERB
american_scientific_journal-3703	378	3	′n	′n	VERB
american_scientific_journal-3703	378	4	thus	thus	ADV
american_scientific_journal-3703	378	5	the	the	DET
american_scientific_journal-3703	378	6	fixed	fixed	ADJ
american_scientific_journal-3703	378	7	point	point	NOUN
american_scientific_journal-3703	378	8	0	0	NUM
american_scientific_journal-3703	378	9	of	of	ADP
american_scientific_journal-3703	378	10	n	n	PROPN
american_scientific_journal-3703	378	11	is	be	AUX
american_scientific_journal-3703	378	12	attracting	attract	VERB
american_scientific_journal-3703	378	13	fixed	fix	VERB
american_scientific_journal-3703	378	14	point	point	NOUN
american_scientific_journal-3703	378	15	.	.	PUNCT
american_scientific_journal-3703	379	1	obviously	obviously	ADV
american_scientific_journal-3703	379	2	,	,	PUNCT
american_scientific_journal-3703	379	3	orbit	orbit	NOUN
american_scientific_journal-3703	379	4	of	of	ADP
american_scientific_journal-3703	379	5	any	any	DET
american_scientific_journal-3703	379	6	real	real	ADJ
american_scientific_journal-3703	379	7	point	point	NOUN
american_scientific_journal-3703	379	8	under	under	ADP
american_scientific_journal-3703	379	9	n	n	NOUN
american_scientific_journal-3703	379	10	converges	converge	NOUN
american_scientific_journal-3703	379	11	to	to	ADP
american_scientific_journal-3703	379	12	fixed	fix	VERB
american_scientific_journal-3703	379	13	point	point	NOUN
american_scientific_journal-3703	379	14	.0	.0	NUM
american_scientific_journal-3703	379	15	(	(	PUNCT
american_scientific_journal-3703	379	16	2	2	X
american_scientific_journal-3703	379	17	)	)	PUNCT
american_scientific_journal-3703	379	18	the	the	DET
american_scientific_journal-3703	379	19	newton	newton	PROPN
american_scientific_journal-3703	379	20	iteration	iteration	PROPN
american_scientific_journal-3703	379	21	function	function	NOUN
american_scientific_journal-3703	379	22	associated	associate	VERB
american_scientific_journal-3703	379	23	to	to	ADP
american_scientific_journal-3703	379	24	)	)	PUNCT
american_scientific_journal-3703	379	25	(	(	PUNCT
american_scientific_journal-3703	379	26	xd	xd	INTJ
american_scientific_journal-3703	379	27	is	be	AUX
american_scientific_journal-3703	379	28	(	(	PUNCT
american_scientific_journal-3703	379	29	)	)	PUNCT
american_scientific_journal-3703	379	30	.	.	PUNCT
american_scientific_journal-3703	380	1	2	2	NUM
american_scientific_journal-3703	380	2	1	1	NUM
american_scientific_journal-3703	380	3	2	2	NUM
american_scientific_journal-3703	380	4	12	12	NUM
american_scientific_journal-3703	380	5	=	=	SYM
american_scientific_journal-3703	380	6	−	−	PROPN
american_scientific_journal-3703	380	7	−=	−=	ADV
american_scientific_journal-3703	380	8	xxxn	xxxn	VERB
american_scientific_journal-3703	381	1	n	n	CCONJ
american_scientific_journal-3703	381	2	has	have	AUX
american_scientific_journal-3703	381	3	fixed	fix	VERB
american_scientific_journal-3703	381	4	point	point	NOUN
american_scientific_journal-3703	381	5	,	,	PUNCT
american_scientific_journal-3703	381	6	at	at	ADP
american_scientific_journal-3703	381	7	the	the	DET
american_scientific_journal-3703	381	8	root	root	NOUN
american_scientific_journal-3703	381	9	2/1	2/1	NUM
american_scientific_journal-3703	381	10	of	of	ADP
american_scientific_journal-3703	381	11	.d	.d	NOUN
american_scientific_journal-3703	381	12	we	we	PRON
american_scientific_journal-3703	381	13	compute	compute	VERB
american_scientific_journal-3703	381	14	,	,	PUNCT
american_scientific_journal-3703	381	15	2)2/1	2)2/1	PROPN
american_scientific_journal-3703	381	16	(	(	PUNCT
american_scientific_journal-3703	382	1	=	=	NOUN
american_scientific_journal-3703	382	2	′d	′d	NOUN
american_scientific_journal-3703	382	3	and	and	CCONJ
american_scientific_journal-3703	382	4	we	we	PRON
american_scientific_journal-3703	382	5	see	see	VERB
american_scientific_journal-3703	382	6	that	that	SCONJ
american_scientific_journal-3703	382	7	.0)2/1	.0)2/1	PRON
american_scientific_journal-3703	382	8	(	(	PUNCT
american_scientific_journal-3703	382	9	=	=	VERB
american_scientific_journal-3703	382	10	′n	′n	VERB
american_scientific_journal-3703	382	11	thus	thus	ADV
american_scientific_journal-3703	382	12	the	the	DET
american_scientific_journal-3703	382	13	fixed	fixed	ADJ
american_scientific_journal-3703	382	14	point	point	NOUN
american_scientific_journal-3703	382	15	2/1	2/1	NUM
american_scientific_journal-3703	382	16	of	of	ADP
american_scientific_journal-3703	382	17	n	n	PRON
american_scientific_journal-3703	382	18	is	be	AUX
american_scientific_journal-3703	382	19	attracting	attract	VERB
american_scientific_journal-3703	382	20	fixed	fix	VERB
american_scientific_journal-3703	382	21	point	point	NOUN
american_scientific_journal-3703	382	22	.	.	PUNCT
american_scientific_journal-3703	383	1	obviously	obviously	ADV
american_scientific_journal-3703	383	2	,	,	PUNCT
american_scientific_journal-3703	383	3	orbit	orbit	NOUN
american_scientific_journal-3703	383	4	of	of	ADP
american_scientific_journal-3703	383	5	any	any	DET
american_scientific_journal-3703	383	6	real	real	ADJ
american_scientific_journal-3703	383	7	point	point	NOUN
american_scientific_journal-3703	383	8	under	under	ADP
american_scientific_journal-3703	383	9	n	n	NOUN
american_scientific_journal-3703	383	10	converges	converge	NOUN
american_scientific_journal-3703	383	11	to	to	ADP
american_scientific_journal-3703	383	12	fixed	fix	VERB
american_scientific_journal-3703	383	13	point	point	NOUN
american_scientific_journal-3703	383	14	1	1	NUM
american_scientific_journal-3703	383	15	2	2	NUM
american_scientific_journal-3703	383	16	[	[	X
american_scientific_journal-3703	383	17	8	8	NUM
american_scientific_journal-3703	383	18	]	]	PUNCT
american_scientific_journal-3703	383	19	.	.	PUNCT
american_scientific_journal-3703	384	1	5.3	5.3	NUM
american_scientific_journal-3703	384	2	sensitivity	sensitivity	NOUN
american_scientific_journal-3703	384	3	to	to	ADP
american_scientific_journal-3703	384	4	numerical	numerical	ADJ
american_scientific_journal-3703	384	5	inaccuracies	inaccuracy	NOUN
american_scientific_journal-3703	384	6	of	of	ADP
american_scientific_journal-3703	384	7	doubling	doubling	NOUN
american_scientific_journal-3703	384	8	map	map	NOUN
american_scientific_journal-3703	384	9	the	the	DET
american_scientific_journal-3703	384	10	doubling	double	VERB
american_scientific_journal-3703	384	11	map	map	NOUN
american_scientific_journal-3703	384	12	(	(	PUNCT
american_scientific_journal-3703	384	13	)	)	PUNCT
american_scientific_journal-3703	384	14	2	2	NUM
american_scientific_journal-3703	384	15	;	;	PUNCT
american_scientific_journal-3703	384	16	0	0	NUM
american_scientific_journal-3703	384	17	0.5	0.5	NUM
american_scientific_journal-3703	384	18	2	2	NUM
american_scientific_journal-3703	384	19	1	1	NUM
american_scientific_journal-3703	384	20	;	;	PUNCT
american_scientific_journal-3703	384	21	0.5	0.5	NUM
american_scientific_journal-3703	384	22	x	x	SYM
american_scientific_journal-3703	384	23	1	1	NUM
american_scientific_journal-3703	384	24	x	x	SYM
american_scientific_journal-3703	384	25	x	x	SYM
american_scientific_journal-3703	384	26	d	d	NOUN
american_scientific_journal-3703	384	27	x	x	X
american_scientific_journal-3703	384	28	x	x	SYM
american_scientific_journal-3703	384	29	≤	≤	NOUN
american_scientific_journal-3703	384	30	<	<	X
american_scientific_journal-3703	384	31			NOUN
american_scientific_journal-3703	384	32	=	=	PUNCT
american_scientific_journal-3703	384	33			ADP
american_scientific_journal-3703	384	34	−	−	PROPN
american_scientific_journal-3703	384	35	≤	≤	NOUN
american_scientific_journal-3703	384	36	<	<	X
american_scientific_journal-3703	384	37			NOUN
american_scientific_journal-3703	384	38	is	be	AUX
american_scientific_journal-3703	384	39	very	very	ADV
american_scientific_journal-3703	384	40	sensitive	sensitive	ADJ
american_scientific_journal-3703	384	41	to	to	ADP
american_scientific_journal-3703	384	42	numerical	numerical	ADJ
american_scientific_journal-3703	384	43	inaccuracies	inaccuracy	NOUN
american_scientific_journal-3703	384	44	.	.	PUNCT
american_scientific_journal-3703	385	1	to	to	PART
american_scientific_journal-3703	385	2	see	see	VERB
american_scientific_journal-3703	385	3	this	this	PRON
american_scientific_journal-3703	385	4	,	,	PUNCT
american_scientific_journal-3703	385	5	we	we	PRON
american_scientific_journal-3703	385	6	calculate	calculate	VERB
american_scientific_journal-3703	385	7	100	100	NUM
american_scientific_journal-3703	385	8	values	value	NOUN
american_scientific_journal-3703	385	9	from	from	ADP
american_scientific_journal-3703	385	10	the	the	DET
american_scientific_journal-3703	385	11	map	map	NOUN
american_scientific_journal-3703	385	12	,	,	PUNCT
american_scientific_journal-3703	385	13	the	the	DET
american_scientific_journal-3703	385	14	first	first	ADJ
american_scientific_journal-3703	385	15	by	by	ADP
american_scientific_journal-3703	385	16	using	use	VERB
american_scientific_journal-3703	385	17	normal	normal	ADJ
american_scientific_journal-3703	385	18	decimal	decimal	ADJ
american_scientific_journal-3703	385	19	numbers	number	NOUN
american_scientific_journal-3703	385	20	and	and	CCONJ
american_scientific_journal-3703	385	21	then	then	ADV
american_scientific_journal-3703	385	22	by	by	ADP
american_scientific_journal-3703	385	23	using	use	VERB
american_scientific_journal-3703	385	24	high	high	ADJ
american_scientific_journal-3703	385	25	-	-	PUNCT
american_scientific_journal-3703	385	26	precision	precision	NOUN
american_scientific_journal-3703	385	27	numbers	number	NOUN
american_scientific_journal-3703	385	28	.	.	PUNCT
american_scientific_journal-3703	386	1	in	in	ADP
american_scientific_journal-3703	386	2	the	the	DET
american_scientific_journal-3703	386	3	latter	latter	ADJ
american_scientific_journal-3703	386	4	case	case	NOUN
american_scientific_journal-3703	386	5	,	,	PUNCT
american_scientific_journal-3703	386	6	we	we	PRON
american_scientific_journal-3703	386	7	start	start	VERB
american_scientific_journal-3703	386	8	with	with	ADP
american_scientific_journal-3703	386	9	numbers	number	NOUN
american_scientific_journal-3703	386	10	that	that	PRON
american_scientific_journal-3703	386	11	have	have	VERB
american_scientific_journal-3703	386	12	a	a	DET
american_scientific_journal-3703	386	13	precision	precision	NOUN
american_scientific_journal-3703	386	14	of	of	ADP
american_scientific_journal-3703	386	15	65	65	NUM
american_scientific_journal-3703	386	16	digits	digit	NOUN
american_scientific_journal-3703	386	17	:	:	PUNCT
american_scientific_journal-3703	387	1	vals1	vals1	NOUN
american_scientific_journal-3703	387	2	=	=	PUNCT
american_scientific_journal-3703	387	3	nestlist	nestlist	PROPN
american_scientific_journal-3703	387	4	�	�	PROPN
american_scientific_journal-3703	387	5	piecewise	piecewise	PROPN
american_scientific_journal-3703	387	6	�	�	PROPN
american_scientific_journal-3703	387	7	�	�	PROPN
american_scientific_journal-3703	387	8	{2#,0	{2#,0	NOUN
american_scientific_journal-3703	387	9	≤	≤	NUM
american_scientific_journal-3703	387	10	#	#	NOUN
american_scientific_journal-3703	387	11	<	<	X
american_scientific_journal-3703	387	12	1	1	NUM
american_scientific_journal-3703	387	13	2⁄	2⁄	NUM
american_scientific_journal-3703	387	14	}	}	PUNCT
american_scientific_journal-3703	387	15	,	,	PUNCT
american_scientific_journal-3703	387	16	{	{	PUNCT
american_scientific_journal-3703	387	17	2	2	NUM
american_scientific_journal-3703	387	18	#	#	NOUN
american_scientific_journal-3703	387	19	−	−	NOUN
american_scientific_journal-3703	387	20	1	1	NUM
american_scientific_journal-3703	387	21	,	,	PUNCT
american_scientific_journal-3703	387	22	1	1	NUM
american_scientific_journal-3703	387	23	2⁄	2⁄	NUM
american_scientific_journal-3703	387	24	≤	≤	NUM
american_scientific_journal-3703	387	25	#	#	NOUN
american_scientific_journal-3703	387	26	<	<	X
american_scientific_journal-3703	387	27	1}	1}	NUM
american_scientific_journal-3703	387	28	�	�	PROPN
american_scientific_journal-3703	387	29	�	�	PROPN
american_scientific_journal-3703	387	30	&,0.003,100	&,0.003,100	PROPN
american_scientific_journal-3703	387	31	�	�	PROPN
american_scientific_journal-3703	387	32	;	;	PUNCT
american_scientific_journal-3703	387	33	vals2	vals2	X
american_scientific_journal-3703	387	34	=	=	SYM
american_scientific_journal-3703	387	35	nestlist[piecewise[{{2#,0	nestlist[piecewise[{{2#,0	PROPN
american_scientific_journal-3703	387	36	≤	≤	NUM
american_scientific_journal-3703	387	37	#	#	NOUN
american_scientific_journal-3703	387	38	<	<	X
american_scientific_journal-3703	387	39	1	1	NUM
american_scientific_journal-3703	387	40	2⁄	2⁄	NUM
american_scientific_journal-3703	387	41	}	}	PUNCT
american_scientific_journal-3703	387	42	,	,	PUNCT
american_scientific_journal-3703	387	43	{	{	PUNCT
american_scientific_journal-3703	387	44	2	2	NUM
american_scientific_journal-3703	387	45	#	#	NOUN
american_scientific_journal-3703	387	46	−	−	NOUN
american_scientific_journal-3703	387	47	1	1	NUM
american_scientific_journal-3703	387	48	,	,	PUNCT
american_scientific_journal-3703	387	49	1	1	NUM
american_scientific_journal-3703	387	50	2⁄	2⁄	NUM
american_scientific_journal-3703	387	51	≤	≤	NUM
american_scientific_journal-3703	387	52	#	#	NOUN
american_scientific_journal-3703	387	53	<	<	X
american_scientific_journal-3703	387	54	1}}]&,0.0003`65,100	1}}]&,0.0003`65,100	NUM
american_scientific_journal-3703	387	55	]	]	X
american_scientific_journal-3703	387	56	;	;	PUNCT
american_scientific_journal-3703	387	57	values	value	NOUN
american_scientific_journal-3703	387	58	corresponding	correspond	VERB
american_scientific_journal-3703	387	59	to	to	ADP
american_scientific_journal-3703	387	60	vals2	vals2	PROPN
american_scientific_journal-3703	387	61	are	be	AUX
american_scientific_journal-3703	387	62	thick	thick	ADJ
american_scientific_journal-3703	387	63	.	.	PUNCT
american_scientific_journal-3703	388	1	from	from	ADP
american_scientific_journal-3703	388	2	approximately	approximately	ADV
american_scientific_journal-3703	388	3	iteration	iteration	NOUN
american_scientific_journal-3703	388	4	50	50	NUM
american_scientific_journal-3703	388	5	on	on	ADP
american_scientific_journal-3703	388	6	,	,	PUNCT
american_scientific_journal-3703	388	7	the	the	DET
american_scientific_journal-3703	388	8	values	value	NOUN
american_scientific_journal-3703	388	9	differ	differ	VERB
american_scientific_journal-3703	388	10	greatly	greatly	ADV
american_scientific_journal-3703	388	11	.	.	PUNCT
american_scientific_journal-3703	389	1	in	in	ADP
american_scientific_journal-3703	389	2	calculating	calculate	VERB
american_scientific_journal-3703	389	3	vals2	vals2	NOUN
american_scientific_journal-3703	389	4	,	,	PUNCT
american_scientific_journal-3703	389	5	we	we	PRON
american_scientific_journal-3703	389	6	started	start	VERB
american_scientific_journal-3703	389	7	with	with	ADP
american_scientific_journal-3703	389	8	numbers	number	NOUN
american_scientific_journal-3703	389	9	having	have	VERB
american_scientific_journal-3703	389	10	65	65	NUM
american_scientific_journal-3703	389	11	digits	digit	NOUN
american_scientific_journal-3703	389	12	of	of	ADP
american_scientific_journal-3703	389	13	precision	precision	NOUN
american_scientific_journal-3703	389	14	.	.	PUNCT
american_scientific_journal-3703	390	1	during	during	ADP
american_scientific_journal-3703	390	2	the	the	DET
american_scientific_journal-3703	390	3	calculation	calculation	NOUN
american_scientific_journal-3703	390	4	,	,	PUNCT
american_scientific_journal-3703	390	5	many	many	ADJ
american_scientific_journal-3703	390	6	digits	digit	NOUN
american_scientific_journal-3703	390	7	were	be	AUX
american_scientific_journal-3703	390	8	lost	lose	VERB
american_scientific_journal-3703	390	9	so	so	SCONJ
american_scientific_journal-3703	390	10	that	that	SCONJ
american_scientific_journal-3703	390	11	the	the	DET
american_scientific_journal-3703	390	12	last	last	ADJ
american_scientific_journal-3703	390	13	value	value	NOUN
american_scientific_journal-3703	390	14	0.6128only	0.6128only	ADV
american_scientific_journal-3703	390	15	has	have	VERB
american_scientific_journal-3703	390	16	a	a	DET
american_scientific_journal-3703	390	17	precision	precision	NOUN
american_scientific_journal-3703	390	18	of	of	ADP
american_scientific_journal-3703	390	19	approximately	approximately	ADV
american_scientific_journal-3703	390	20	38.20719793550678.thus	38.20719793550678.thus	NUM
american_scientific_journal-3703	390	21	we	we	PRON
american_scientific_journal-3703	390	22	know	know	VERB
american_scientific_journal-3703	390	23	that	that	SCONJ
american_scientific_journal-3703	390	24	all	all	DET
american_scientific_journal-3703	390	25	the	the	DET
american_scientific_journal-3703	390	26	digits	digit	NOUN
american_scientific_journal-3703	390	27	of	of	ADP
american_scientific_journal-3703	390	28	vals2	vals2	NOUN
american_scientific_journal-3703	390	29	are	be	AUX
american_scientific_journal-3703	390	30	correct	correct	ADJ
american_scientific_journal-3703	390	31	.	.	PUNCT
american_scientific_journal-3703	391	1	this	this	PRON
american_scientific_journal-3703	391	2	means	mean	VERB
american_scientific_journal-3703	391	3	that	that	SCONJ
american_scientific_journal-3703	391	4	the	the	DET
american_scientific_journal-3703	391	5	values	value	NOUN
american_scientific_journal-3703	391	6	in	in	ADP
american_scientific_journal-3703	391	7	vals1are	vals1are	VERB
american_scientific_journal-3703	391	8	incorrect	incorrect	ADJ
american_scientific_journal-3703	391	9	from	from	ADP
american_scientific_journal-3703	391	10	approximately	approximately	ADV
american_scientific_journal-3703	391	11	0.2	0.2	NUM
american_scientific_journal-3703	391	12	0.4	0.4	NUM
american_scientific_journal-3703	391	13	0.6	0.6	NUM
american_scientific_journal-3703	391	14	0.8	0.8	NUM
american_scientific_journal-3703	391	15	1.0	1.0	NUM
american_scientific_journal-3703	391	16	0.2	0.2	NUM
american_scientific_journal-3703	391	17	0.4	0.4	NUM
american_scientific_journal-3703	391	18	0.6	0.6	NUM
american_scientific_journal-3703	391	19	0.8	0.8	NUM
american_scientific_journal-3703	391	20	1.0	1.0	NUM
american_scientific_journal-3703	391	21	0.2	0.2	NUM
american_scientific_journal-3703	391	22	0.4	0.4	NUM
american_scientific_journal-3703	391	23	0.6	0.6	NUM
american_scientific_journal-3703	391	24	0.8	0.8	NUM
american_scientific_journal-3703	391	25	1.0	1.0	NUM
american_scientific_journal-3703	391	26	0.2	0.2	NUM
american_scientific_journal-3703	391	27	0.4	0.4	NUM
american_scientific_journal-3703	391	28	0.6	0.6	NUM
american_scientific_journal-3703	391	29	0.8	0.8	NUM
american_scientific_journal-3703	391	30	1.0	1.0	NUM
american_scientific_journal-3703	391	31	american	american	ADJ
american_scientific_journal-3703	391	32	scientific	scientific	ADJ
american_scientific_journal-3703	391	33	research	research	NOUN
american_scientific_journal-3703	391	34	journal	journal	NOUN
american_scientific_journal-3703	391	35	for	for	ADP
american_scientific_journal-3703	391	36	engineering	engineering	NOUN
american_scientific_journal-3703	391	37	,	,	PUNCT
american_scientific_journal-3703	391	38	technology	technology	NOUN
american_scientific_journal-3703	391	39	,	,	PUNCT
american_scientific_journal-3703	391	40	and	and	CCONJ
american_scientific_journal-3703	391	41	sciences	science	NOUN
american_scientific_journal-3703	391	42	(	(	PUNCT
american_scientific_journal-3703	391	43	asrjets	asrjet	NOUN
american_scientific_journal-3703	391	44	)	)	PUNCT
american_scientific_journal-3703	391	45	(	(	PUNCT
american_scientific_journal-3703	391	46	2018	2018	NUM
american_scientific_journal-3703	391	47	)	)	PUNCT
american_scientific_journal-3703	391	48	volume	volume	NOUN
american_scientific_journal-3703	391	49	43	43	NUM
american_scientific_journal-3703	391	50	,	,	PUNCT
american_scientific_journal-3703	391	51	no	no	DET
american_scientific_journal-3703	391	52	1	1	NUM
american_scientific_journal-3703	391	53	,	,	PUNCT
american_scientific_journal-3703	391	54	pp	pp	ADV
american_scientific_journal-3703	391	55	110	110	NUM
american_scientific_journal-3703	391	56	-	-	SYM
american_scientific_journal-3703	391	57	133	133	NUM
american_scientific_journal-3703	391	58	126	126	NUM
american_scientific_journal-3703	391	59	iteration	iteration	NOUN
american_scientific_journal-3703	391	60	50	50	NUM
american_scientific_journal-3703	391	61	on	on	ADP
american_scientific_journal-3703	391	62	.	.	PUNCT
american_scientific_journal-3703	392	1	this	this	PRON
american_scientific_journal-3703	392	2	demonstrates	demonstrate	VERB
american_scientific_journal-3703	392	3	the	the	DET
american_scientific_journal-3703	392	4	sensitivity	sensitivity	NOUN
american_scientific_journal-3703	392	5	to	to	ADP
american_scientific_journal-3703	392	6	numerical	numerical	ADJ
american_scientific_journal-3703	392	7	inaccuracies	inaccuracy	NOUN
american_scientific_journal-3703	392	8	of	of	ADP
american_scientific_journal-3703	392	9	the	the	DET
american_scientific_journal-3703	392	10	doubling	double	VERB
american_scientific_journal-3703	392	11	map	map	NOUN
american_scientific_journal-3703	392	12	.	.	PUNCT
american_scientific_journal-3703	393	1	thus	thus	ADV
american_scientific_journal-3703	393	2	,	,	PUNCT
american_scientific_journal-3703	393	3	if	if	SCONJ
american_scientific_journal-3703	393	4	we	we	PRON
american_scientific_journal-3703	393	5	calculate	calculate	VERB
american_scientific_journal-3703	393	6	long	long	ADJ
american_scientific_journal-3703	393	7	sequences	sequence	NOUN
american_scientific_journal-3703	393	8	from	from	ADP
american_scientific_journal-3703	393	9	the	the	DET
american_scientific_journal-3703	393	10	doubling	double	VERB
american_scientific_journal-3703	393	11	map	map	NOUN
american_scientific_journal-3703	393	12	,	,	PUNCT
american_scientific_journal-3703	393	13	it	it	PRON
american_scientific_journal-3703	393	14	is	be	AUX
american_scientific_journal-3703	393	15	important	important	ADJ
american_scientific_journal-3703	393	16	to	to	PART
american_scientific_journal-3703	393	17	use	use	VERB
american_scientific_journal-3703	393	18	a	a	DET
american_scientific_journal-3703	393	19	high	high	ADJ
american_scientific_journal-3703	393	20	enough	enough	ADJ
american_scientific_journal-3703	393	21	precision	precision	NOUN
american_scientific_journal-3703	393	22	during	during	ADP
american_scientific_journal-3703	393	23	the	the	DET
american_scientific_journal-3703	393	24	calculation	calculation	NOUN
american_scientific_journal-3703	393	25	.	.	PUNCT
american_scientific_journal-3703	394	1	from	from	ADP
american_scientific_journal-3703	394	2	the	the	DET
american_scientific_journal-3703	394	3	plot	plot	NOUN
american_scientific_journal-3703	394	4	of	of	ADP
american_scientific_journal-3703	394	5	vals2	vals2	PROPN
american_scientific_journal-3703	394	6	,	,	PUNCT
american_scientific_journal-3703	394	7	we	we	PRON
american_scientific_journal-3703	394	8	see	see	VERB
american_scientific_journal-3703	394	9	that	that	SCONJ
american_scientific_journal-3703	394	10	the	the	DET
american_scientific_journal-3703	394	11	series	series	NOUN
american_scientific_journal-3703	394	12	behaves	behave	VERB
american_scientific_journal-3703	394	13	quite	quite	ADV
american_scientific_journal-3703	394	14	chaotically	chaotically	ADV
american_scientific_journal-3703	394	15	.	.	PUNCT
american_scientific_journal-3703	395	1	it	it	PRON
american_scientific_journal-3703	395	2	is	be	AUX
american_scientific_journal-3703	395	3	known	know	VERB
american_scientific_journal-3703	395	4	that	that	SCONJ
american_scientific_journal-3703	395	5	chaotic	chaotic	ADJ
american_scientific_journal-3703	395	6	models	model	NOUN
american_scientific_journal-3703	395	7	are	be	AUX
american_scientific_journal-3703	395	8	very	very	ADV
american_scientific_journal-3703	395	9	sensitive	sensitive	ADJ
american_scientific_journal-3703	395	10	to	to	ADP
american_scientific_journal-3703	395	11	numerical	numerical	ADJ
american_scientific_journal-3703	395	12	inaccuracies	inaccuracy	NOUN
american_scientific_journal-3703	395	13	.	.	PUNCT
american_scientific_journal-3703	396	1	figure	figure	VERB
american_scientific_journal-3703	396	2	3	3	NUM
american_scientific_journal-3703	396	3	:	:	PUNCT
american_scientific_journal-3703	396	4	the	the	DET
american_scientific_journal-3703	396	5	initial	initial	ADJ
american_scientific_journal-3703	396	6	x=1/7	x=1/7	NOUN
american_scientific_journal-3703	396	7	and	and	CCONJ
american_scientific_journal-3703	396	8	0.1/7	0.1/7	NUM
american_scientific_journal-3703	396	9	`	`	PUNCT
american_scientific_journal-3703	396	10	65	65	NUM
american_scientific_journal-3703	396	11	,	,	PUNCT
american_scientific_journal-3703	396	12	n=100	n=100	NOUN
american_scientific_journal-3703	396	13	figure	figure	VERB
american_scientific_journal-3703	396	14	4	4	NUM
american_scientific_journal-3703	396	15	:	:	PUNCT
american_scientific_journal-3703	396	16	the	the	DET
american_scientific_journal-3703	396	17	initial	initial	ADJ
american_scientific_journal-3703	396	18	x=1/3	x=1/3	PROPN
american_scientific_journal-3703	396	19	and	and	CCONJ
american_scientific_journal-3703	396	20	0.1/5`65	0.1/5`65	PROPN
american_scientific_journal-3703	396	21	,	,	PUNCT
american_scientific_journal-3703	396	22	n=100	n=100	X
american_scientific_journal-3703	396	23	figure	figure	VERB
american_scientific_journal-3703	396	24	5	5	NUM
american_scientific_journal-3703	396	25	:	:	PUNCT
american_scientific_journal-3703	396	26	the	the	DET
american_scientific_journal-3703	396	27	initial	initial	ADJ
american_scientific_journal-3703	396	28	x=0.003	x=0.003	PROPN
american_scientific_journal-3703	396	29	and	and	CCONJ
american_scientific_journal-3703	396	30	0.0003`65	0.0003`65	NUM
american_scientific_journal-3703	396	31	,	,	PUNCT
american_scientific_journal-3703	396	32	n=100	n=100	NUM
american_scientific_journal-3703	396	33	we	we	PRON
american_scientific_journal-3703	396	34	see	see	VERB
american_scientific_journal-3703	396	35	that	that	DET
american_scientific_journal-3703	396	36	figure	figure	NOUN
american_scientific_journal-3703	396	37	3	3	NUM
american_scientific_journal-3703	396	38	and	and	CCONJ
american_scientific_journal-3703	396	39	figure	figure	VERB
american_scientific_journal-3703	396	40	4	4	NUM
american_scientific_journal-3703	396	41	are	be	AUX
american_scientific_journal-3703	396	42	regular	regular	ADJ
american_scientific_journal-3703	396	43	which	which	PRON
american_scientific_journal-3703	396	44	means	mean	VERB
american_scientific_journal-3703	396	45	that	that	SCONJ
american_scientific_journal-3703	396	46	numerical	numerical	ADJ
american_scientific_journal-3703	396	47	accuracy	accuracy	NOUN
american_scientific_journal-3703	396	48	.	.	PUNCT
american_scientific_journal-3703	397	1	but	but	CCONJ
american_scientific_journal-3703	397	2	the	the	DET
american_scientific_journal-3703	397	3	figure	figure	NOUN
american_scientific_journal-3703	397	4	5	5	NUM
american_scientific_journal-3703	397	5	shows	show	VERB
american_scientific_journal-3703	397	6	that	that	SCONJ
american_scientific_journal-3703	397	7	the	the	DET
american_scientific_journal-3703	397	8	behavior	behavior	NOUN
american_scientific_journal-3703	397	9	is	be	AUX
american_scientific_journal-3703	397	10	irregular	irregular	ADJ
american_scientific_journal-3703	397	11	which	which	PRON
american_scientific_journal-3703	397	12	means	mean	VERB
american_scientific_journal-3703	397	13	numerical	numerical	ADJ
american_scientific_journal-3703	397	14	inaccuracies	inaccuracy	NOUN
american_scientific_journal-3703	397	15	.	.	PUNCT
american_scientific_journal-3703	398	1	in	in	ADP
american_scientific_journal-3703	398	2	other	other	ADJ
american_scientific_journal-3703	398	3	words	word	NOUN
american_scientific_journal-3703	398	4	,	,	PUNCT
american_scientific_journal-3703	398	5	it	it	PRON
american_scientific_journal-3703	398	6	is	be	AUX
american_scientific_journal-3703	398	7	called	call	VERB
american_scientific_journal-3703	398	8	chaotic	chaotic	ADJ
american_scientific_journal-3703	398	9	behavior	behavior	NOUN
american_scientific_journal-3703	398	10	of	of	ADP
american_scientific_journal-3703	398	11	doubling	double	VERB
american_scientific_journal-3703	398	12	map	map	NOUN
american_scientific_journal-3703	398	13	[	[	X
american_scientific_journal-3703	398	14	5	5	NUM
american_scientific_journal-3703	398	15	]	]	PUNCT
american_scientific_journal-3703	398	16	.	.	PUNCT
american_scientific_journal-3703	399	1	5.4	5.4	NUM
american_scientific_journal-3703	399	2	sensitivity	sensitivity	NOUN
american_scientific_journal-3703	399	3	analysis	analysis	NOUN
american_scientific_journal-3703	399	4	to	to	ADP
american_scientific_journal-3703	399	5	initial	initial	ADJ
american_scientific_journal-3703	399	6	value	value	NOUN
american_scientific_journal-3703	399	7	of	of	ADP
american_scientific_journal-3703	399	8	doubling	double	VERB
american_scientific_journal-3703	399	9	map	map	NOUN
american_scientific_journal-3703	399	10	chaotic	chaotic	ADJ
american_scientific_journal-3703	399	11	models	model	NOUN
american_scientific_journal-3703	399	12	are	be	AUX
american_scientific_journal-3703	399	13	also	also	ADV
american_scientific_journal-3703	399	14	very	very	ADV
american_scientific_journal-3703	399	15	sensitive	sensitive	ADJ
american_scientific_journal-3703	399	16	to	to	ADP
american_scientific_journal-3703	399	17	the	the	DET
american_scientific_journal-3703	399	18	initial	initial	ADJ
american_scientific_journal-3703	399	19	value	value	NOUN
american_scientific_journal-3703	399	20	.	.	PUNCT
american_scientific_journal-3703	400	1	to	to	PART
american_scientific_journal-3703	400	2	show	show	VERB
american_scientific_journal-3703	400	3	this	this	PRON
american_scientific_journal-3703	400	4	,	,	PUNCT
american_scientific_journal-3703	400	5	compute	compute	NOUN
american_scientific_journal-3703	400	6	,	,	PUNCT
american_scientific_journal-3703	400	7	50	50	NUM
american_scientific_journal-3703	400	8	iterations	iteration	NOUN
american_scientific_journal-3703	400	9	using	use	VERB
american_scientific_journal-3703	400	10	starting	start	VERB
american_scientific_journal-3703	400	11	points	point	NOUN
american_scientific_journal-3703	400	12	0.02	0.02	NUM
american_scientific_journal-3703	400	13	+	+	CCONJ
american_scientific_journal-3703	401	1	10−𝑖𝑖	10−𝑖𝑖	NUM
american_scientific_journal-3703	401	2	,	,	PUNCT
american_scientific_journal-3703	401	3	i	i	NOUN
american_scientific_journal-3703	401	4	=	=	NOUN
american_scientific_journal-3703	401	5	1	1	NUM
american_scientific_journal-3703	401	6	,	,	PUNCT
american_scientific_journal-3703	401	7	…	…	PUNCT
american_scientific_journal-3703	401	8	,	,	PUNCT
american_scientific_journal-3703	401	9	25	25	NUM
american_scientific_journal-3703	401	10	.	.	PUNCT
american_scientific_journal-3703	402	1	then	then	ADV
american_scientific_journal-3703	402	2	plot	plot	VERB
american_scientific_journal-3703	402	3	the	the	DET
american_scientific_journal-3703	402	4	20th	20th	ADJ
american_scientific_journal-3703	402	5	value	value	NOUN
american_scientific_journal-3703	402	6	of	of	ADP
american_scientific_journal-3703	402	7	each	each	PRON
american_scientific_journal-3703	402	8	of	of	ADP
american_scientific_journal-3703	402	9	the	the	DET
american_scientific_journal-3703	402	10	25	25	NUM
american_scientific_journal-3703	402	11	series	series	NOUN
american_scientific_journal-3703	402	12	.	.	PUNCT
american_scientific_journal-3703	403	1	also	also	ADV
american_scientific_journal-3703	403	2	plot	plot	VERB
american_scientific_journal-3703	403	3	the	the	DET
american_scientific_journal-3703	403	4	50th	50th	ADJ
american_scientific_journal-3703	403	5	value	value	NOUN
american_scientific_journal-3703	403	6	of	of	ADP
american_scientific_journal-3703	403	7	each	each	PRON
american_scientific_journal-3703	403	8	of	of	ADP
american_scientific_journal-3703	403	9	the	the	DET
american_scientific_journal-3703	403	10	25	25	NUM
american_scientific_journal-3703	403	11	series	series	NOUN
american_scientific_journal-3703	403	12	:	:	PUNCT
american_scientific_journal-3703	403	13	20	20	NUM
american_scientific_journal-3703	403	14	40	40	NUM
american_scientific_journal-3703	403	15	60	60	NUM
american_scientific_journal-3703	403	16	80	80	NUM
american_scientific_journal-3703	403	17	100	100	NUM
american_scientific_journal-3703	403	18	0.1	0.1	NUM
american_scientific_journal-3703	403	19	0.2	0.2	NUM
american_scientific_journal-3703	403	20	0.3	0.3	NUM
american_scientific_journal-3703	403	21	0.4	0.4	NUM
american_scientific_journal-3703	403	22	0.5	0.5	NUM
american_scientific_journal-3703	403	23	0.6	0.6	NUM
american_scientific_journal-3703	403	24	20	20	NUM
american_scientific_journal-3703	403	25	40	40	NUM
american_scientific_journal-3703	403	26	60	60	NUM
american_scientific_journal-3703	403	27	80	80	NUM
american_scientific_journal-3703	403	28	100	100	NUM
american_scientific_journal-3703	403	29	0.2	0.2	NUM
american_scientific_journal-3703	403	30	0.4	0.4	NUM
american_scientific_journal-3703	403	31	0.6	0.6	NUM
american_scientific_journal-3703	403	32	0.8	0.8	NUM
american_scientific_journal-3703	403	33	20	20	NUM
american_scientific_journal-3703	403	34	40	40	NUM
american_scientific_journal-3703	403	35	60	60	NUM
american_scientific_journal-3703	403	36	80	80	NUM
american_scientific_journal-3703	403	37	100	100	NUM
american_scientific_journal-3703	403	38	0.2	0.2	NUM
american_scientific_journal-3703	403	39	0.4	0.4	NUM
american_scientific_journal-3703	403	40	0.6	0.6	NUM
american_scientific_journal-3703	403	41	0.8	0.8	NUM
american_scientific_journal-3703	403	42	1.0	1.0	NUM
american_scientific_journal-3703	403	43	american	american	ADJ
american_scientific_journal-3703	403	44	scientific	scientific	ADJ
american_scientific_journal-3703	403	45	research	research	NOUN
american_scientific_journal-3703	403	46	journal	journal	NOUN
american_scientific_journal-3703	403	47	for	for	ADP
american_scientific_journal-3703	403	48	engineering	engineering	NOUN
american_scientific_journal-3703	403	49	,	,	PUNCT
american_scientific_journal-3703	403	50	technology	technology	NOUN
american_scientific_journal-3703	403	51	,	,	PUNCT
american_scientific_journal-3703	403	52	and	and	CCONJ
american_scientific_journal-3703	403	53	sciences	science	NOUN
american_scientific_journal-3703	403	54	(	(	PUNCT
american_scientific_journal-3703	403	55	asrjets	asrjet	NOUN
american_scientific_journal-3703	403	56	)	)	PUNCT
american_scientific_journal-3703	403	57	(	(	PUNCT
american_scientific_journal-3703	403	58	2018	2018	NUM
american_scientific_journal-3703	403	59	)	)	PUNCT
american_scientific_journal-3703	403	60	volume	volume	NOUN
american_scientific_journal-3703	403	61	43	43	NUM
american_scientific_journal-3703	403	62	,	,	PUNCT
american_scientific_journal-3703	403	63	no	no	DET
american_scientific_journal-3703	403	64	1	1	NUM
american_scientific_journal-3703	403	65	,	,	PUNCT
american_scientific_journal-3703	403	66	pp	pp	ADV
american_scientific_journal-3703	403	67	110	110	NUM
american_scientific_journal-3703	403	68	-	-	SYM
american_scientific_journal-3703	403	69	133	133	NUM
american_scientific_journal-3703	403	70	127	127	NUM
american_scientific_journal-3703	403	71	figure	figure	NOUN
american_scientific_journal-3703	403	72	6	6	NUM
american_scientific_journal-3703	403	73	:	:	PUNCT
american_scientific_journal-3703	403	74	the	the	DET
american_scientific_journal-3703	403	75	initial	initial	ADJ
american_scientific_journal-3703	403	76	x=0.02	x=0.02	PROPN
american_scientific_journal-3703	403	77	,	,	PUNCT
american_scientific_journal-3703	403	78	n=50	n=50	ADJ
american_scientific_journal-3703	403	79	figure	figure	NOUN
american_scientific_journal-3703	403	80	7	7	NUM
american_scientific_journal-3703	403	81	:	:	PUNCT
american_scientific_journal-3703	403	82	the	the	DET
american_scientific_journal-3703	403	83	initial	initial	ADJ
american_scientific_journal-3703	403	84	x=0.02`50	x=0.02`50	ADJ
american_scientific_journal-3703	403	85	,	,	PUNCT
american_scientific_journal-3703	403	86	n=50	n=50	ADJ
american_scientific_journal-3703	403	87	figure	figure	NOUN
american_scientific_journal-3703	403	88	8	8	NUM
american_scientific_journal-3703	403	89	:	:	PUNCT
american_scientific_journal-3703	403	90	the	the	DET
american_scientific_journal-3703	403	91	initial	initial	ADJ
american_scientific_journal-3703	403	92	x=0.02	x=0.02	PROPN
american_scientific_journal-3703	403	93	,	,	PUNCT
american_scientific_journal-3703	403	94	n=50	n=50	ADJ
american_scientific_journal-3703	403	95	figure	figure	NOUN
american_scientific_journal-3703	403	96	9	9	NUM
american_scientific_journal-3703	403	97	:	:	PUNCT
american_scientific_journal-3703	403	98	the	the	DET
american_scientific_journal-3703	403	99	initial	initial	ADJ
american_scientific_journal-3703	403	100	x=0.02`50	x=0.02`50	PROPN
american_scientific_journal-3703	403	101	,	,	PUNCT
american_scientific_journal-3703	403	102	n=50	n=50	ADJ
american_scientific_journal-3703	403	103	from	from	ADP
american_scientific_journal-3703	403	104	the	the	DET
american_scientific_journal-3703	403	105	first	first	ADJ
american_scientific_journal-3703	403	106	plot	plot	NOUN
american_scientific_journal-3703	403	107	figure	figure	NOUN
american_scientific_journal-3703	403	108	6	6	NUM
american_scientific_journal-3703	403	109	&	&	CCONJ
american_scientific_journal-3703	403	110	7	7	NUM
american_scientific_journal-3703	403	111	,	,	PUNCT
american_scientific_journal-3703	403	112	we	we	PRON
american_scientific_journal-3703	403	113	see	see	VERB
american_scientific_journal-3703	403	114	that	that	SCONJ
american_scientific_journal-3703	403	115	even	even	ADV
american_scientific_journal-3703	403	116	if	if	SCONJ
american_scientific_journal-3703	403	117	the	the	DET
american_scientific_journal-3703	403	118	starting	starting	NOUN
american_scientific_journal-3703	403	119	point	point	NOUN
american_scientific_journal-3703	403	120	differs	differ	VERB
american_scientific_journal-3703	403	121	from	from	ADP
american_scientific_journal-3703	403	122	0.02	0.02	NUM
american_scientific_journal-3703	403	123	by	by	ADP
american_scientific_journal-3703	403	124	710−	710−	NUM
american_scientific_journal-3703	403	125	or	or	CCONJ
american_scientific_journal-3703	403	126	more	more	ADJ
american_scientific_journal-3703	403	127	(	(	PUNCT
american_scientific_journal-3703	403	128	see	see	VERB
american_scientific_journal-3703	403	129	the	the	DET
american_scientific_journal-3703	403	130	first	first	ADJ
american_scientific_journal-3703	403	131	seven	seven	NUM
american_scientific_journal-3703	403	132	points	point	NOUN
american_scientific_journal-3703	403	133	in	in	ADP
american_scientific_journal-3703	403	134	the	the	DET
american_scientific_journal-3703	403	135	plot	plot	NOUN
american_scientific_journal-3703	403	136	)	)	PUNCT
american_scientific_journal-3703	403	137	,	,	PUNCT
american_scientific_journal-3703	403	138	the	the	DET
american_scientific_journal-3703	403	139	value	value	NOUN
american_scientific_journal-3703	403	140	of	of	ADP
american_scientific_journal-3703	403	141	𝐷𝐷20	𝐷𝐷20	PROPN
american_scientific_journal-3703	403	142	significantly	significantly	ADV
american_scientific_journal-3703	403	143	differs	differ	VERB
american_scientific_journal-3703	403	144	from	from	ADP
american_scientific_journal-3703	403	145	the	the	DET
american_scientific_journal-3703	403	146	value	value	NOUN
american_scientific_journal-3703	403	147	that	that	PRON
american_scientific_journal-3703	403	148	results	result	VERB
american_scientific_journal-3703	403	149	when	when	SCONJ
american_scientific_journal-3703	403	150	starting	start	VERB
american_scientific_journal-3703	403	151	from	from	ADP
american_scientific_journal-3703	403	152	0.02	0.02	NUM
american_scientific_journal-3703	403	153	.	.	PUNCT
american_scientific_journal-3703	404	1	from	from	ADP
american_scientific_journal-3703	404	2	the	the	DET
american_scientific_journal-3703	404	3	second	second	ADJ
american_scientific_journal-3703	404	4	plot	plot	NOUN
american_scientific_journal-3703	404	5	figure	figure	NOUN
american_scientific_journal-3703	404	6	8	8	NUM
american_scientific_journal-3703	404	7	&	&	CCONJ
american_scientific_journal-3703	404	8	9	9	NUM
american_scientific_journal-3703	404	9	,	,	PUNCT
american_scientific_journal-3703	404	10	we	we	PRON
american_scientific_journal-3703	404	11	see	see	VERB
american_scientific_journal-3703	404	12	that	that	SCONJ
american_scientific_journal-3703	404	13	if	if	SCONJ
american_scientific_journal-3703	404	14	the	the	DET
american_scientific_journal-3703	404	15	starting	starting	NOUN
american_scientific_journal-3703	404	16	point	point	NOUN
american_scientific_journal-3703	404	17	differs	differ	VERB
american_scientific_journal-3703	404	18	from	from	ADP
american_scientific_journal-3703	404	19	0.02	0.02	NUM
american_scientific_journal-3703	404	20	by	by	ADP
american_scientific_journal-3703	404	21	1610−	1610−	NUM
american_scientific_journal-3703	404	22	or	or	CCONJ
american_scientific_journal-3703	404	23	more	more	ADJ
american_scientific_journal-3703	404	24	,	,	PUNCT
american_scientific_journal-3703	404	25	the	the	DET
american_scientific_journal-3703	404	26	value	value	NOUN
american_scientific_journal-3703	404	27	of	of	ADP
american_scientific_journal-3703	404	28	𝐷𝐷50	𝐷𝐷50	PROPN
american_scientific_journal-3703	404	29	differs	differ	VERB
american_scientific_journal-3703	404	30	significantly	significantly	ADV
american_scientific_journal-3703	404	31	from	from	ADP
american_scientific_journal-3703	404	32	the	the	DET
american_scientific_journal-3703	404	33	value	value	NOUN
american_scientific_journal-3703	404	34	that	that	PRON
american_scientific_journal-3703	404	35	result	result	VERB
american_scientific_journal-3703	404	36	when	when	SCONJ
american_scientific_journal-3703	404	37	starting	start	VERB
american_scientific_journal-3703	404	38	from	from	ADP
american_scientific_journal-3703	404	39	0.02	0.02	NUM
american_scientific_journal-3703	405	1	[	[	X
american_scientific_journal-3703	405	2	5	5	NUM
american_scientific_journal-3703	405	3	]	]	PUNCT
american_scientific_journal-3703	405	4	.	.	PUNCT
american_scientific_journal-3703	406	1	5.5	5.5	NUM
american_scientific_journal-3703	406	2	trajectories	trajectory	NOUN
american_scientific_journal-3703	406	3	of	of	ADP
american_scientific_journal-3703	406	4	doubling	double	VERB
american_scientific_journal-3703	406	5	map	map	NOUN
american_scientific_journal-3703	406	6	we	we	PRON
american_scientific_journal-3703	406	7	first	first	ADV
american_scientific_journal-3703	406	8	calculate	calculate	VERB
american_scientific_journal-3703	406	9	a	a	DET
american_scientific_journal-3703	406	10	solution	solution	NOUN
american_scientific_journal-3703	406	11	set	set	VERB
american_scientific_journal-3703	406	12	by	by	ADP
american_scientific_journal-3703	406	13	starting	start	VERB
american_scientific_journal-3703	406	14	from	from	ADP
american_scientific_journal-3703	406	15	various	various	ADJ
american_scientific_journal-3703	406	16	points	point	NOUN
american_scientific_journal-3703	406	17	and	and	CCONJ
american_scientific_journal-3703	406	18	iterating	iterate	VERB
american_scientific_journal-3703	406	19	the	the	DET
american_scientific_journal-3703	406	20	equation	equation	NOUN
american_scientific_journal-3703	406	21	ntimes	ntime	NOUN
american_scientific_journal-3703	406	22	.	.	PUNCT
american_scientific_journal-3703	407	1	the	the	DET
american_scientific_journal-3703	407	2	starting	starting	NOUN
american_scientific_journal-3703	407	3	points	point	NOUN
american_scientific_journal-3703	407	4	are	be	AUX
american_scientific_journal-3703	407	5	chosen	choose	VERB
american_scientific_journal-3703	407	6	between	between	ADP
american_scientific_journal-3703	407	7	x01and	x01and	PROPN
american_scientific_journal-3703	407	8	x02	x02	PROPN
american_scientific_journal-3703	407	9	in	in	ADP
american_scientific_journal-3703	407	10	steps	step	NOUN
american_scientific_journal-3703	407	11	of	of	ADP
american_scientific_journal-3703	407	12	dx0	dx0	NOUN
american_scientific_journal-3703	407	13	.	.	PUNCT
american_scientific_journal-3703	408	1	we	we	PRON
american_scientific_journal-3703	408	2	get	get	VERB
american_scientific_journal-3703	408	3	the	the	DET
american_scientific_journal-3703	408	4	following	follow	VERB
american_scientific_journal-3703	408	5	trajectories	trajectory	NOUN
american_scientific_journal-3703	408	6	:	:	PUNCT
american_scientific_journal-3703	408	7	figure	figure	VERB
american_scientific_journal-3703	408	8	10	10	NUM
american_scientific_journal-3703	408	9	:	:	PUNCT
american_scientific_journal-3703	408	10	trajectory	trajectory	NOUN
american_scientific_journal-3703	408	11	for	for	ADP
american_scientific_journal-3703	408	12	x01	x01	PROPN
american_scientific_journal-3703	408	13	=	=	SYM
american_scientific_journal-3703	408	14	0.0001	0.0001	NUM
american_scientific_journal-3703	408	15	,	,	PUNCT
american_scientific_journal-3703	408	16	x02=0.11	x02=0.11	PROPN
american_scientific_journal-3703	408	17	,	,	PUNCT
american_scientific_journal-3703	408	18	step	step	NOUN
american_scientific_journal-3703	408	19	size	size	NOUN
american_scientific_journal-3703	408	20	dx0=0.01	dx0=0.01	PROPN
american_scientific_journal-3703	408	21	,	,	PUNCT
american_scientific_journal-3703	408	22	n=20	n=20	PROPN
american_scientific_journal-3703	408	23	.	.	PROPN
american_scientific_journal-3703	409	1	5	5	NUM
american_scientific_journal-3703	409	2	10	10	NUM
american_scientific_journal-3703	409	3	15	15	NUM
american_scientific_journal-3703	409	4	20	20	NUM
american_scientific_journal-3703	409	5	25	25	NUM
american_scientific_journal-3703	409	6	0.2	0.2	NUM
american_scientific_journal-3703	409	7	0.4	0.4	NUM
american_scientific_journal-3703	409	8	0.6	0.6	NUM
american_scientific_journal-3703	409	9	0.8	0.8	NUM
american_scientific_journal-3703	409	10	1.0	1.0	NUM
american_scientific_journal-3703	409	11	20th	20th	ADJ
american_scientific_journal-3703	409	12	value	value	NOUN
american_scientific_journal-3703	409	13	5	5	NUM
american_scientific_journal-3703	409	14	10	10	NUM
american_scientific_journal-3703	409	15	15	15	NUM
american_scientific_journal-3703	409	16	20	20	NUM
american_scientific_journal-3703	409	17	25	25	NUM
american_scientific_journal-3703	409	18	0.2	0.2	NUM
american_scientific_journal-3703	409	19	0.4	0.4	NUM
american_scientific_journal-3703	409	20	0.6	0.6	NUM
american_scientific_journal-3703	409	21	0.8	0.8	NUM
american_scientific_journal-3703	409	22	1.0	1.0	NUM
american_scientific_journal-3703	409	23	20th	20th	ADJ
american_scientific_journal-3703	409	24	value	value	NOUN
american_scientific_journal-3703	409	25	5	5	NUM
american_scientific_journal-3703	409	26	10	10	NUM
american_scientific_journal-3703	409	27	15	15	NUM
american_scientific_journal-3703	409	28	20	20	NUM
american_scientific_journal-3703	409	29	25	25	NUM
american_scientific_journal-3703	409	30	0.2	0.2	NUM
american_scientific_journal-3703	409	31	0.4	0.4	NUM
american_scientific_journal-3703	409	32	0.6	0.6	NUM
american_scientific_journal-3703	409	33	0.8	0.8	NUM
american_scientific_journal-3703	409	34	1.0	1.0	NUM
american_scientific_journal-3703	409	35	50th	50th	ADJ
american_scientific_journal-3703	409	36	value	value	NOUN
american_scientific_journal-3703	409	37	5	5	NUM
american_scientific_journal-3703	409	38	10	10	NUM
american_scientific_journal-3703	409	39	15	15	NUM
american_scientific_journal-3703	409	40	20	20	NUM
american_scientific_journal-3703	409	41	25	25	NUM
american_scientific_journal-3703	409	42	0.2	0.2	NUM
american_scientific_journal-3703	409	43	0.4	0.4	NUM
american_scientific_journal-3703	409	44	0.6	0.6	NUM
american_scientific_journal-3703	409	45	0.8	0.8	NUM
american_scientific_journal-3703	409	46	1.0	1.0	NUM
american_scientific_journal-3703	409	47	50th	50th	ADJ
american_scientific_journal-3703	409	48	value	value	NOUN
american_scientific_journal-3703	409	49	5	5	NUM
american_scientific_journal-3703	409	50	10	10	NUM
american_scientific_journal-3703	409	51	15	15	NUM
american_scientific_journal-3703	409	52	20	20	NUM
american_scientific_journal-3703	409	53	0.2	0.2	NUM
american_scientific_journal-3703	409	54	0.4	0.4	NUM
american_scientific_journal-3703	409	55	0.6	0.6	NUM
american_scientific_journal-3703	409	56	0.8	0.8	NUM
american_scientific_journal-3703	409	57	1.0	1.0	NUM
american_scientific_journal-3703	409	58	american	american	ADJ
american_scientific_journal-3703	409	59	scientific	scientific	ADJ
american_scientific_journal-3703	409	60	research	research	NOUN
american_scientific_journal-3703	409	61	journal	journal	NOUN
american_scientific_journal-3703	409	62	for	for	ADP
american_scientific_journal-3703	409	63	engineering	engineering	NOUN
american_scientific_journal-3703	409	64	,	,	PUNCT
american_scientific_journal-3703	409	65	technology	technology	NOUN
american_scientific_journal-3703	409	66	,	,	PUNCT
american_scientific_journal-3703	409	67	and	and	CCONJ
american_scientific_journal-3703	409	68	sciences	science	NOUN
american_scientific_journal-3703	409	69	(	(	PUNCT
american_scientific_journal-3703	409	70	asrjets	asrjet	NOUN
american_scientific_journal-3703	409	71	)	)	PUNCT
american_scientific_journal-3703	409	72	(	(	PUNCT
american_scientific_journal-3703	409	73	2018	2018	NUM
american_scientific_journal-3703	409	74	)	)	PUNCT
american_scientific_journal-3703	409	75	volume	volume	NOUN
american_scientific_journal-3703	409	76	43	43	NUM
american_scientific_journal-3703	409	77	,	,	PUNCT
american_scientific_journal-3703	409	78	no	no	DET
american_scientific_journal-3703	409	79	1	1	NUM
american_scientific_journal-3703	409	80	,	,	PUNCT
american_scientific_journal-3703	409	81	pp	pp	ADV
american_scientific_journal-3703	409	82	110	110	NUM
american_scientific_journal-3703	409	83	-	-	SYM
american_scientific_journal-3703	409	84	133	133	NUM
american_scientific_journal-3703	409	85	128	128	NUM
american_scientific_journal-3703	409	86	figure	figure	NOUN
american_scientific_journal-3703	409	87	11	11	NUM
american_scientific_journal-3703	409	88	:	:	PUNCT
american_scientific_journal-3703	409	89	trajectory	trajectory	NOUN
american_scientific_journal-3703	409	90	for	for	ADP
american_scientific_journal-3703	409	91	x01	x01	PROPN
american_scientific_journal-3703	409	92	=	=	SYM
american_scientific_journal-3703	409	93	0.0001	0.0001	NUM
american_scientific_journal-3703	409	94	,	,	PUNCT
american_scientific_journal-3703	409	95	x02=0.11	x02=0.11	PROPN
american_scientific_journal-3703	409	96	,	,	PUNCT
american_scientific_journal-3703	409	97	step	step	NOUN
american_scientific_journal-3703	409	98	size	size	NOUN
american_scientific_journal-3703	409	99	dx0=0.01	dx0=0.01	PROPN
american_scientific_journal-3703	409	100	,	,	PUNCT
american_scientific_journal-3703	409	101	n=30	n=30	PROPN
american_scientific_journal-3703	409	102	.	.	PUNCT
american_scientific_journal-3703	410	1	figure	figure	NOUN
american_scientific_journal-3703	410	2	12	12	NUM
american_scientific_journal-3703	410	3	:	:	PUNCT
american_scientific_journal-3703	410	4	trajectory	trajectory	NOUN
american_scientific_journal-3703	410	5	for	for	ADP
american_scientific_journal-3703	410	6	x01	x01	PROPN
american_scientific_journal-3703	410	7	=	=	SYM
american_scientific_journal-3703	410	8	0.0001	0.0001	NUM
american_scientific_journal-3703	410	9	,	,	PUNCT
american_scientific_journal-3703	410	10	x02=0.11	x02=0.11	PROPN
american_scientific_journal-3703	410	11	,	,	PUNCT
american_scientific_journal-3703	410	12	step	step	NOUN
american_scientific_journal-3703	410	13	size	size	NOUN
american_scientific_journal-3703	410	14	dx0=0.001	dx0=0.001	PROPN
american_scientific_journal-3703	410	15	,	,	PUNCT
american_scientific_journal-3703	410	16	n=10	n=10	PRON
american_scientific_journal-3703	410	17	.	.	PUNCT
american_scientific_journal-3703	411	1	we	we	PRON
american_scientific_journal-3703	411	2	observe	observe	VERB
american_scientific_journal-3703	411	3	that	that	SCONJ
american_scientific_journal-3703	411	4	if	if	SCONJ
american_scientific_journal-3703	411	5	we	we	PRON
american_scientific_journal-3703	411	6	take	take	VERB
american_scientific_journal-3703	411	7	the	the	DET
american_scientific_journal-3703	411	8	starting	starting	NOUN
american_scientific_journal-3703	411	9	values	value	NOUN
american_scientific_journal-3703	411	10	x01	x01	PROPN
american_scientific_journal-3703	411	11	and	and	CCONJ
american_scientific_journal-3703	411	12	x02	x02	PROPN
american_scientific_journal-3703	411	13	are	be	AUX
american_scientific_journal-3703	411	14	same	same	ADJ
american_scientific_journal-3703	411	15	even	even	ADV
american_scientific_journal-3703	411	16	step	step	NOUN
american_scientific_journal-3703	411	17	size	size	NOUN
american_scientific_journal-3703	411	18	also	also	ADV
american_scientific_journal-3703	411	19	same	same	ADJ
american_scientific_journal-3703	411	20	(	(	PUNCT
american_scientific_journal-3703	411	21	10	10	NUM
american_scientific_journal-3703	411	22	and	and	CCONJ
american_scientific_journal-3703	411	23	11	11	NUM
american_scientific_journal-3703	411	24	figure	figure	NOUN
american_scientific_journal-3703	411	25	)	)	PUNCT
american_scientific_journal-3703	411	26	then	then	ADV
american_scientific_journal-3703	411	27	the	the	DET
american_scientific_journal-3703	411	28	trajectories	trajectory	NOUN
american_scientific_journal-3703	411	29	turns	turn	VERB
american_scientific_journal-3703	411	30	to	to	ADP
american_scientific_journal-3703	411	31	chaotic	chaotic	ADJ
american_scientific_journal-3703	411	32	with	with	ADP
american_scientific_journal-3703	411	33	the	the	DET
american_scientific_journal-3703	411	34	increasing	increase	VERB
american_scientific_journal-3703	411	35	the	the	DET
american_scientific_journal-3703	411	36	number	number	NOUN
american_scientific_journal-3703	411	37	of	of	ADP
american_scientific_journal-3703	411	38	iteration	iteration	NOUN
american_scientific_journal-3703	411	39	.	.	PUNCT
american_scientific_journal-3703	412	1	if	if	SCONJ
american_scientific_journal-3703	412	2	the	the	DET
american_scientific_journal-3703	412	3	step	step	NOUN
american_scientific_journal-3703	412	4	size	size	NOUN
american_scientific_journal-3703	412	5	is	be	AUX
american_scientific_journal-3703	412	6	very	very	ADV
american_scientific_journal-3703	412	7	small	small	ADJ
american_scientific_journal-3703	412	8	,	,	PUNCT
american_scientific_journal-3703	412	9	the	the	DET
american_scientific_journal-3703	412	10	trajectories	trajectory	NOUN
american_scientific_journal-3703	412	11	also	also	ADV
american_scientific_journal-3703	412	12	chaotic	chaotic	ADJ
american_scientific_journal-3703	412	13	in	in	ADP
american_scientific_journal-3703	412	14	the	the	DET
american_scientific_journal-3703	412	15	figure	figure	NOUN
american_scientific_journal-3703	412	16	12	12	NUM
american_scientific_journal-3703	412	17	,	,	PUNCT
american_scientific_journal-3703	412	18	[	[	X
american_scientific_journal-3703	412	19	5	5	NUM
american_scientific_journal-3703	412	20	]	]	PUNCT
american_scientific_journal-3703	412	21	.	.	PUNCT
american_scientific_journal-3703	413	1	5.6	5.6	NUM
american_scientific_journal-3703	413	2	orbit	orbit	NOUN
american_scientific_journal-3703	413	3	analysis	analysis	NOUN
american_scientific_journal-3703	413	4	of	of	ADP
american_scientific_journal-3703	413	5	doubling	double	VERB
american_scientific_journal-3703	413	6	map	map	NOUN
american_scientific_journal-3703	413	7	graphically	graphically	ADV
american_scientific_journal-3703	413	8	the	the	DET
american_scientific_journal-3703	413	9	doubling	double	VERB
american_scientific_journal-3703	413	10	map	map	NOUN
american_scientific_journal-3703	413	11	is	be	AUX
american_scientific_journal-3703	413	12	defined	define	VERB
american_scientific_journal-3703	413	13	by	by	ADP
american_scientific_journal-3703	413	14	1	1	NUM
american_scientific_journal-3703	413	15	12	12	NUM
american_scientific_journal-3703	413	16	for	for	ADP
american_scientific_journal-3703	413	17	0	0	NUM
american_scientific_journal-3703	413	18	2	2	NUM
american_scientific_journal-3703	413	19	(	(	PUNCT
american_scientific_journal-3703	413	20	)	)	PUNCT
american_scientific_journal-3703	413	21	12	12	NUM
american_scientific_journal-3703	413	22	-1	-1	NOUN
american_scientific_journal-3703	413	23	for	for	ADP
american_scientific_journal-3703	413	24	1	1	NUM
american_scientific_journal-3703	413	25	2	2	NUM
american_scientific_journal-3703	413	26	n	n	CCONJ
american_scientific_journal-3703	413	27	n	n	CCONJ
american_scientific_journal-3703	413	28	n	n	CCONJ
american_scientific_journal-3703	413	29	n	n	CCONJ
american_scientific_journal-3703	413	30	n	n	CCONJ
american_scientific_journal-3703	413	31	n	n	NOUN
american_scientific_journal-3703	413	32	x	x	NOUN
american_scientific_journal-3703	413	33	x	x	PUNCT
american_scientific_journal-3703	413	34	x	x	PUNCT
american_scientific_journal-3703	413	35	d	d	NOUN
american_scientific_journal-3703	413	36	x	x	X
american_scientific_journal-3703	413	37	x	x	PUNCT
american_scientific_journal-3703	413	38	x	x	X
american_scientific_journal-3703	414	1	+	+	PUNCT
american_scientific_journal-3703	414	2			VERB
american_scientific_journal-3703	414	3	≤	≤	NOUN
american_scientific_journal-3703	414	4	<	<	X
american_scientific_journal-3703	414	5	=	=	NOUN
american_scientific_journal-3703	414	6	=	=	PUNCT
american_scientific_journal-3703	414	7			PRON
american_scientific_journal-3703	414	8			ADJ
american_scientific_journal-3703	414	9	≤	≤	NOUN
american_scientific_journal-3703	414	10	<	<	X
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american_scientific_journal-3703	417	51	5	5	NUM
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american_scientific_journal-3703	418	62	8	8	NUM
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american_scientific_journal-3703	420	3	11	11	NUM
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american_scientific_journal-3703	420	6	11	11	NUM
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american_scientific_journal-3703	420	11	11	11	NUM
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american_scientific_journal-3703	420	14	11	11	NUM
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american_scientific_journal-3703	420	17	9	9	NUM
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american_scientific_journal-3703	420	20	7	7	NUM
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american_scientific_journal-3703	421	24	iv	iv	NUM
american_scientific_journal-3703	421	25	x	x	SYM
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american_scientific_journal-3703	421	30			VERB
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american_scientific_journal-3703	422	2	29	29	NUM
american_scientific_journal-3703	422	3	29	29	NUM
american_scientific_journal-3703	422	4	29	29	NUM
american_scientific_journal-3703	422	5	29	29	NUM
american_scientific_journal-3703	422	6	29	29	NUM
american_scientific_journal-3703	422	7	29	29	NUM
american_scientific_journal-3703	422	8	29	29	NUM
american_scientific_journal-3703	422	9	29	29	NUM
american_scientific_journal-3703	422	10	29	29	NUM
american_scientific_journal-3703	422	11	29	29	NUM
american_scientific_journal-3703	422	12	23	23	NUM
american_scientific_journal-3703	422	13	23	23	NUM
american_scientific_journal-3703	422	14	46	46	NUM
american_scientific_journal-3703	422	15	33	33	NUM
american_scientific_journal-3703	422	16	7	7	NUM
american_scientific_journal-3703	422	17	14	14	NUM
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american_scientific_journal-3703	422	19	56	56	NUM
american_scientific_journal-3703	422	20	53	53	NUM
american_scientific_journal-3703	422	21	47	47	NUM
american_scientific_journal-3703	422	22	35	35	NUM
american_scientific_journal-3703	422	23	11	11	NUM
american_scientific_journal-3703	422	24	22	22	NUM
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american_scientific_journal-3703	423	2	59	59	NUM
american_scientific_journal-3703	423	3	59	59	NUM
american_scientific_journal-3703	423	4	59	59	NUM
american_scientific_journal-3703	423	5	59	59	NUM
american_scientific_journal-3703	423	6	59	59	NUM
american_scientific_journal-3703	423	7	59	59	NUM
american_scientific_journal-3703	423	8	59	59	NUM
american_scientific_journal-3703	423	9	59	59	NUM
american_scientific_journal-3703	423	10	59	59	NUM
american_scientific_journal-3703	423	11	59	59	NUM
american_scientific_journal-3703	423	12	59	59	NUM
american_scientific_journal-3703	423	13	59	59	NUM
american_scientific_journal-3703	423	14	59	59	NUM
american_scientific_journal-3703	423	15	37	37	NUM
american_scientific_journal-3703	423	16	37	37	NUM
american_scientific_journal-3703	423	17	5	5	NUM
american_scientific_journal-3703	423	18	10	10	NUM
american_scientific_journal-3703	423	19	20	20	NUM
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american_scientific_journal-3703	423	29	69	69	NUM
american_scientific_journal-3703	423	30	69	69	NUM
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american_scientific_journal-3703	423	40			PROPN
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american_scientific_journal-3703	423	43			VERB
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american_scientific_journal-3703	423	45			ADP
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american_scientific_journal-3703	423	49	=	=	SYM
american_scientific_journal-3703	423	50	11	11	NUM
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american_scientific_journal-3703	425	49	0.8	0.8	NUM
american_scientific_journal-3703	425	50	1.0	1.0	NUM
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american_scientific_journal-3703	425	54	0.8	0.8	NUM
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american_scientific_journal-3703	425	60	1.0	1.0	NUM
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american_scientific_journal-3703	425	64	0.8	0.8	NUM
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american_scientific_journal-3703	425	79	0.8	0.8	NUM
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american_scientific_journal-3703	425	91	0.2	0.2	NUM
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american_scientific_journal-3703	425	99	0.8	0.8	NUM
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american_scientific_journal-3703	425	109	0.8	0.8	NUM
american_scientific_journal-3703	425	110	1.0	1.0	NUM
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american_scientific_journal-3703	425	112	0.4	0.4	NUM
american_scientific_journal-3703	425	113	0.6	0.6	NUM
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american_scientific_journal-3703	425	115	1.0	1.0	NUM
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american_scientific_journal-3703	425	124	,	,	PUNCT
american_scientific_journal-3703	425	125	and	and	CCONJ
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american_scientific_journal-3703	425	131	2018	2018	NUM
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american_scientific_journal-3703	425	134	43	43	NUM
american_scientific_journal-3703	425	135	,	,	PUNCT
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american_scientific_journal-3703	425	137	1	1	NUM
american_scientific_journal-3703	425	138	,	,	PUNCT
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american_scientific_journal-3703	425	141	-	-	SYM
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american_scientific_journal-3703	425	143	130	130	NUM
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american_scientific_journal-3703	425	145	three	three	NUM
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american_scientific_journal-3703	425	147	,	,	PUNCT
american_scientific_journal-3703	425	148	(	(	PUNCT
american_scientific_journal-3703	425	149	iv	iv	X
american_scientific_journal-3703	425	150	)	)	PUNCT
american_scientific_journal-3703	425	151	there	there	PRON
american_scientific_journal-3703	425	152	is	be	VERB
american_scientific_journal-3703	425	153	a	a	DET
american_scientific_journal-3703	425	154	period	period	NOUN
american_scientific_journal-3703	425	155	five	five	NUM
american_scientific_journal-3703	425	156	sequence	sequence	NOUN
american_scientific_journal-3703	425	157	,	,	PUNCT
american_scientific_journal-3703	425	158	(	(	PUNCT
american_scientific_journal-3703	425	159	v	v	NOUN
american_scientific_journal-3703	425	160	)	)	PUNCT
american_scientific_journal-3703	425	161	there	there	PRON
american_scientific_journal-3703	425	162	is	be	VERB
american_scientific_journal-3703	425	163	period	period	NOUN
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american_scientific_journal-3703	425	165	and	and	CCONJ
american_scientific_journal-3703	425	166	in	in	ADP
american_scientific_journal-3703	425	167	case	case	NOUN
american_scientific_journal-3703	425	168	(	(	PUNCT
american_scientific_journal-3703	425	169	vi	vi	NOUN
american_scientific_journal-3703	425	170	)	)	PUNCT
american_scientific_journal-3703	425	171	,	,	PUNCT
american_scientific_journal-3703	425	172	(	(	PUNCT
american_scientific_journal-3703	425	173	vii	vii	PROPN
american_scientific_journal-3703	425	174	)	)	PUNCT
american_scientific_journal-3703	425	175	,	,	PUNCT
american_scientific_journal-3703	425	176	(	(	PUNCT
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american_scientific_journal-3703	425	178	)	)	PUNCT
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american_scientific_journal-3703	425	180	contained	contain	VERB
american_scientific_journal-3703	425	181	some	some	DET
american_scientific_journal-3703	425	182	list	list	NOUN
american_scientific_journal-3703	425	183	of	of	ADP
american_scientific_journal-3703	425	184	iteration	iteration	NOUN
american_scientific_journal-3703	425	185	,	,	PUNCT
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american_scientific_journal-3703	425	187	other	other	ADJ
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american_scientific_journal-3703	425	189	need	need	VERB
american_scientific_journal-3703	425	190	to	to	PART
american_scientific_journal-3703	425	191	be	be	AUX
american_scientific_journal-3703	425	192	used	use	VERB
american_scientific_journal-3703	425	193	to	to	PART
american_scientific_journal-3703	425	194	established	establish	VERB
american_scientific_journal-3703	425	195	the	the	DET
american_scientific_journal-3703	425	196	long	long	ADJ
american_scientific_journal-3703	425	197	term	term	NOUN
american_scientific_journal-3703	425	198	behaviour	behaviour	NOUN
american_scientific_journal-3703	425	199	of	of	ADP
american_scientific_journal-3703	425	200	the	the	DET
american_scientific_journal-3703	425	201	sequences	sequence	NOUN
american_scientific_journal-3703	426	1	[	[	X
american_scientific_journal-3703	426	2	2	2	NUM
american_scientific_journal-3703	426	3	]	]	PUNCT
american_scientific_journal-3703	426	4	.	.	PUNCT
american_scientific_journal-3703	427	1	5.7	5.7	NUM
american_scientific_journal-3703	427	2	staircase	staircase	NOUN
american_scientific_journal-3703	427	3	diagram	diagram	NOUN
american_scientific_journal-3703	427	4	again	again	ADV
american_scientific_journal-3703	427	5	if	if	SCONJ
american_scientific_journal-3703	427	6	we	we	PRON
american_scientific_journal-3703	427	7	iterate	iterate	VERB
american_scientific_journal-3703	427	8	the	the	DET
american_scientific_journal-3703	427	9	doubling	double	VERB
american_scientific_journal-3703	427	10	map	map	NOUN
american_scientific_journal-3703	427	11	taking	take	VERB
american_scientific_journal-3703	427	12	nearby	nearby	ADJ
american_scientific_journal-3703	427	13	initial	initial	ADJ
american_scientific_journal-3703	427	14	seeds	seed	NOUN
american_scientific_journal-3703	427	15	from	from	ADP
american_scientific_journal-3703	427	16	[	[	PUNCT
american_scientific_journal-3703	427	17	)	)	PUNCT
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american_scientific_journal-3703	427	20	,	,	PUNCT
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american_scientific_journal-3703	427	22	can	can	AUX
american_scientific_journal-3703	427	23	get	get	VERB
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american_scientific_journal-3703	427	25	following	follow	VERB
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american_scientific_journal-3703	427	27	:	:	PUNCT
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american_scientific_journal-3703	427	34	(	(	PUNCT
american_scientific_journal-3703	427	35	)	)	PUNCT
american_scientific_journal-3703	427	36	(	(	PUNCT
american_scientific_journal-3703	427	37	)	)	PUNCT
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american_scientific_journal-3703	427	40	(	(	PUNCT
american_scientific_journal-3703	427	41	)	)	PUNCT
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american_scientific_journal-3703	427	43	)	)	PUNCT
american_scientific_journal-3703	427	44	1	1	NUM
american_scientific_journal-3703	427	45	0	0	NUM
american_scientific_journal-3703	427	46	2	2	NUM
american_scientific_journal-3703	427	47	0	0	NUM
american_scientific_journal-3703	427	48	1	1	NUM
american_scientific_journal-3703	427	49	0	0	NUM
american_scientific_journal-3703	427	50	2	2	NUM
american_scientific_journal-3703	427	51	0	0	NUM
american_scientific_journal-3703	427	52	1	1	NUM
american_scientific_journal-3703	427	53	0	0	NUM
american_scientific_journal-3703	427	54	2	2	NUM
american_scientific_journal-3703	427	55	0	0	NUM
american_scientific_journal-3703	427	56	1	1	NUM
american_scientific_journal-3703	427	57	0	0	NUM
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american_scientific_journal-3703	427	59	0	0	NUM
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american_scientific_journal-3703	436	5	n=	n=	ADJ
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american_scientific_journal-3703	436	7	26	26	NUM
american_scientific_journal-3703	436	8	:	:	PUNCT
american_scientific_journal-3703	436	9	for	for	ADP
american_scientific_journal-3703	436	10	(	(	PUNCT
american_scientific_journal-3703	436	11	)	)	PUNCT
american_scientific_journal-3703	436	12	2	2	NUM
american_scientific_journal-3703	436	13	0	0	NUM
american_scientific_journal-3703	437	1	[	[	X
american_scientific_journal-3703	437	2	1/	1/	NUM
american_scientific_journal-3703	437	3	goldenratio,302]d	goldenratio,302]d	PROPN
american_scientific_journal-3703	437	4	x	x	PUNCT
american_scientific_journal-3703	437	5	n=	n=	ADJ
american_scientific_journal-3703	437	6	16difference	16difference	NUM
american_scientific_journal-3703	437	7	:	:	PUNCT
american_scientific_journal-3703	437	8	1.110223024625156	1.110223024625156	NUM
american_scientific_journal-3703	437	9	10−×	10−×	NOUN
american_scientific_journal-3703	437	10	each	each	PRON
american_scientific_journal-3703	437	11	of	of	ADP
american_scientific_journal-3703	437	12	the	the	DET
american_scientific_journal-3703	437	13	diagrams	diagram	NOUN
american_scientific_journal-3703	437	14	(	(	PUNCT
american_scientific_journal-3703	437	15	figure13	figure13	PROPN
american_scientific_journal-3703	437	16	-	-	PUNCT
american_scientific_journal-3703	437	17	26	26	NUM
american_scientific_journal-3703	437	18	)	)	PUNCT
american_scientific_journal-3703	437	19	can	can	AUX
american_scientific_journal-3703	437	20	be	be	AUX
american_scientific_journal-3703	437	21	reproduced	reproduce	VERB
american_scientific_journal-3703	437	22	by	by	ADP
american_scientific_journal-3703	437	23	using	use	VERB
american_scientific_journal-3703	437	24	mathematica	mathematica	PROPN
american_scientific_journal-3703	437	25	.	.	PUNCT
american_scientific_journal-3703	438	1	figure	figure	NOUN
american_scientific_journal-3703	438	2	show	show	VERB
american_scientific_journal-3703	438	3	that	that	SCONJ
american_scientific_journal-3703	438	4	the	the	DET
american_scientific_journal-3703	438	5	doubling	double	VERB
american_scientific_journal-3703	438	6	map	map	NOUN
american_scientific_journal-3703	438	7	displays	display	VERB
american_scientific_journal-3703	438	8	sensitivity	sensitivity	NOUN
american_scientific_journal-3703	438	9	to	to	ADP
american_scientific_journal-3703	438	10	initial	initial	ADJ
american_scientific_journal-3703	438	11	conditions	condition	NOUN
american_scientific_journal-3703	438	12	and	and	CCONJ
american_scientific_journal-3703	438	13	can	can	AUX
american_scientific_journal-3703	438	14	be	be	AUX
american_scientific_journal-3703	438	15	described	describe	VERB
american_scientific_journal-3703	438	16	as	as	ADP
american_scientific_journal-3703	438	17	being	be	AUX
american_scientific_journal-3703	438	18	chaotic	chaotic	ADJ
american_scientific_journal-3703	438	19	.	.	PUNCT
american_scientific_journal-3703	439	1	the	the	DET
american_scientific_journal-3703	439	2	iterative	iterative	NOUN
american_scientific_journal-3703	439	3	path	path	NOUN
american_scientific_journal-3703	439	4	plotted	plot	VERB
american_scientific_journal-3703	439	5	in	in	ADP
american_scientific_journal-3703	439	6	figure	figure	NOUN
american_scientific_journal-3703	439	7	23	23	NUM
american_scientific_journal-3703	439	8	,	,	PUNCT
american_scientific_journal-3703	439	9	24	24	NUM
american_scientific_journal-3703	439	10	,	,	PUNCT
american_scientific_journal-3703	439	11	26	26	NUM
american_scientific_journal-3703	439	12	appears	appear	VERB
american_scientific_journal-3703	439	13	to	to	PART
american_scientific_journal-3703	439	14	wander	wander	VERB
american_scientific_journal-3703	439	15	randomly	randomly	ADV
american_scientific_journal-3703	439	16	.	.	PUNCT
american_scientific_journal-3703	440	1	it	it	PRON
american_scientific_journal-3703	440	2	clearly	clearly	ADV
american_scientific_journal-3703	440	3	shows	show	VERB
american_scientific_journal-3703	440	4	the	the	DET
american_scientific_journal-3703	440	5	sensitivity	sensitivity	NOUN
american_scientific_journal-3703	440	6	to	to	ADP
american_scientific_journal-3703	440	7	initial	initial	ADJ
american_scientific_journal-3703	440	8	conditions	condition	NOUN
american_scientific_journal-3703	440	9	.	.	PUNCT
american_scientific_journal-3703	441	1	it	it	PRON
american_scientific_journal-3703	441	2	is	be	AUX
american_scientific_journal-3703	441	3	clear	clear	ADJ
american_scientific_journal-3703	441	4	from	from	ADP
american_scientific_journal-3703	441	5	the	the	DET
american_scientific_journal-3703	441	6	diagrams	diagram	NOUN
american_scientific_journal-3703	441	7	is	be	AUX
american_scientific_journal-3703	441	8	that	that	SCONJ
american_scientific_journal-3703	441	9	the	the	DET
american_scientific_journal-3703	441	10	three	three	NUM
american_scientific_journal-3703	441	11	basic	basic	ADJ
american_scientific_journal-3703	441	12	properties	property	NOUN
american_scientific_journal-3703	441	13	of	of	ADP
american_scientific_journal-3703	441	14	chaos	chaos	NOUN
american_scientific_journal-3703	441	15	and	and	CCONJ
american_scientific_journal-3703	441	16	they	they	PRON
american_scientific_journal-3703	441	17	are	be	AUX
american_scientific_journal-3703	441	18	mixing	mix	VERB
american_scientific_journal-3703	441	19	,	,	PUNCT
american_scientific_journal-3703	441	20	periodicity	periodicity	NOUN
american_scientific_journal-3703	441	21	,	,	PUNCT
american_scientific_journal-3703	441	22	sensitivity	sensitivity	NOUN
american_scientific_journal-3703	441	23	to	to	ADP
american_scientific_journal-3703	441	24	initial	initial	ADJ
american_scientific_journal-3703	441	25	conditions	condition	NOUN
american_scientific_journal-3703	441	26	,	,	PUNCT
american_scientific_journal-3703	441	27	and	and	CCONJ
american_scientific_journal-3703	441	28	they	they	PRON
american_scientific_journal-3703	441	29	are	be	AUX
american_scientific_journal-3703	441	30	all	all	PRON
american_scientific_journal-3703	441	31	exhibited	exhibit	VERB
american_scientific_journal-3703	441	32	for	for	ADP
american_scientific_journal-3703	441	33	certain	certain	ADJ
american_scientific_journal-3703	441	34	values	value	NOUN
american_scientific_journal-3703	441	35	.	.	PUNCT
american_scientific_journal-3703	442	1	indeed	indeed	ADV
american_scientific_journal-3703	442	2	,	,	PUNCT
american_scientific_journal-3703	442	3	a	a	DET
american_scientific_journal-3703	442	4	now	now	ADV
american_scientific_journal-3703	442	5	famous	famous	ADJ
american_scientific_journal-3703	442	6	result	result	NOUN
american_scientific_journal-3703	442	7	due	due	ADP
american_scientific_journal-3703	442	8	to	to	ADP
american_scientific_journal-3703	442	9	li	li	PROPN
american_scientific_journal-3703	442	10	and	and	CCONJ
american_scientific_journal-3703	442	11	[	[	X
american_scientific_journal-3703	442	12	3	3	NUM
american_scientific_journal-3703	442	13	]	]	PUNCT
american_scientific_journal-3703	442	14	states	state	VERB
american_scientific_journal-3703	442	15	that	that	SCONJ
american_scientific_journal-3703	442	16	if	if	SCONJ
american_scientific_journal-3703	442	17	a	a	DET
american_scientific_journal-3703	442	18	system	system	NOUN
american_scientific_journal-3703	442	19	displays	display	VERB
american_scientific_journal-3703	442	20	period	period	NOUN
american_scientific_journal-3703	442	21	-	-	PUNCT
american_scientific_journal-3703	442	22	three	three	NUM
american_scientific_journal-3703	442	23	behaviour	behaviour	NOUN
american_scientific_journal-3703	442	24	,	,	PUNCT
american_scientific_journal-3703	442	25	then	then	ADV
american_scientific_journal-3703	442	26	the	the	DET
american_scientific_journal-3703	442	27	system	system	NOUN
american_scientific_journal-3703	442	28	can	can	AUX
american_scientific_journal-3703	442	29	display	display	VERB
american_scientific_journal-3703	442	30	periodic	periodic	ADJ
american_scientific_journal-3703	442	31	behaviour	behaviour	NOUN
american_scientific_journal-3703	442	32	of	of	ADP
american_scientific_journal-3703	442	33	any	any	DET
american_scientific_journal-3703	442	34	period	period	NOUN
american_scientific_journal-3703	442	35	.	.	PUNCT
american_scientific_journal-3703	443	1	li	li	PROPN
american_scientific_journal-3703	443	2	and	and	CCONJ
american_scientific_journal-3703	443	3	yorke	yorke	PROPN
american_scientific_journal-3703	443	4	then	then	ADV
american_scientific_journal-3703	443	5	go	go	VERB
american_scientific_journal-3703	443	6	on	on	ADP
american_scientific_journal-3703	443	7	to	to	PART
american_scientific_journal-3703	443	8	prove	prove	VERB
american_scientific_journal-3703	443	9	that	that	SCONJ
american_scientific_journal-3703	443	10	the	the	DET
american_scientific_journal-3703	443	11	system	system	NOUN
american_scientific_journal-3703	443	12	can	can	AUX
american_scientific_journal-3703	443	13	display	display	VERB
american_scientific_journal-3703	443	14	chaotic	chaotic	ADJ
american_scientific_journal-3703	443	15	phenomena	phenomenon	NOUN
american_scientific_journal-3703	443	16	[	[	X
american_scientific_journal-3703	443	17	2	2	NUM
american_scientific_journal-3703	443	18	]	]	PUNCT
american_scientific_journal-3703	443	19	.	.	PUNCT
american_scientific_journal-3703	444	1	6	6	X
american_scientific_journal-3703	444	2	.	.	X
american_scientific_journal-3703	444	3	conclusion	conclusion	NOUN
american_scientific_journal-3703	444	4	chaotic	chaotic	ADJ
american_scientific_journal-3703	444	5	behavior	behavior	NOUN
american_scientific_journal-3703	444	6	of	of	ADP
american_scientific_journal-3703	444	7	one	one	NUM
american_scientific_journal-3703	444	8	dimensional	dimensional	ADJ
american_scientific_journal-3703	444	9	doubling	doubling	NOUN
american_scientific_journal-3703	444	10	map	map	NOUN
american_scientific_journal-3703	444	11	introduces	introduce	VERB
american_scientific_journal-3703	444	12	an	an	DET
american_scientific_journal-3703	444	13	interesting	interesting	ADJ
american_scientific_journal-3703	444	14	and	and	CCONJ
american_scientific_journal-3703	444	15	exciting	exciting	ADJ
american_scientific_journal-3703	444	16	part	part	NOUN
american_scientific_journal-3703	444	17	of	of	ADP
american_scientific_journal-3703	444	18	dynamical	dynamical	ADJ
american_scientific_journal-3703	444	19	systems	system	NOUN
american_scientific_journal-3703	444	20	.	.	PUNCT
american_scientific_journal-3703	445	1	in	in	ADP
american_scientific_journal-3703	445	2	this	this	DET
american_scientific_journal-3703	445	3	paper	paper	NOUN
american_scientific_journal-3703	445	4	,	,	PUNCT
american_scientific_journal-3703	445	5	we	we	PRON
american_scientific_journal-3703	445	6	have	have	AUX
american_scientific_journal-3703	445	7	introduced	introduce	VERB
american_scientific_journal-3703	445	8	one	one	NUM
american_scientific_journal-3703	445	9	dimensional	dimensional	ADJ
american_scientific_journal-3703	445	10	doubling	doubling	NOUN
american_scientific_journal-3703	445	11	map	map	NOUN
american_scientific_journal-3703	445	12	which	which	PRON
american_scientific_journal-3703	445	13	is	be	AUX
american_scientific_journal-3703	445	14	shown	show	VERB
american_scientific_journal-3703	445	15	as	as	ADP
american_scientific_journal-3703	445	16	chaotic	chaotic	ADJ
american_scientific_journal-3703	445	17	map	map	NOUN
american_scientific_journal-3703	445	18	in	in	ADP
american_scientific_journal-3703	445	19	several	several	ADJ
american_scientific_journal-3703	445	20	senses	sense	NOUN
american_scientific_journal-3703	445	21	by	by	ADP
american_scientific_journal-3703	445	22	some	some	DET
american_scientific_journal-3703	445	23	pioneers	pioneer	NOUN
american_scientific_journal-3703	445	24	.	.	PUNCT
american_scientific_journal-3703	446	1	we	we	PRON
american_scientific_journal-3703	446	2	are	be	AUX
american_scientific_journal-3703	446	3	trying	try	VERB
american_scientific_journal-3703	446	4	to	to	PART
american_scientific_journal-3703	446	5	find	find	VERB
american_scientific_journal-3703	446	6	the	the	DET
american_scientific_journal-3703	446	7	dynamical	dynamical	ADJ
american_scientific_journal-3703	446	8	behaviors	behavior	NOUN
american_scientific_journal-3703	446	9	of	of	ADP
american_scientific_journal-3703	446	10	others	other	NOUN
american_scientific_journal-3703	446	11	one	one	NUM
american_scientific_journal-3703	446	12	dimensional	dimensional	ADJ
american_scientific_journal-3703	446	13	maps	map	NOUN
american_scientific_journal-3703	446	14	with	with	ADP
american_scientific_journal-3703	446	15	applications	application	NOUN
american_scientific_journal-3703	446	16	and	and	CCONJ
american_scientific_journal-3703	446	17	establish	establish	VERB
american_scientific_journal-3703	446	18	some	some	DET
american_scientific_journal-3703	446	19	mathematical	mathematical	ADJ
american_scientific_journal-3703	446	20	formulas	formula	NOUN
american_scientific_journal-3703	446	21	concerning	concern	VERB
american_scientific_journal-3703	446	22	chaotic	chaotic	ADJ
american_scientific_journal-3703	446	23	dynamical	dynamical	ADJ
american_scientific_journal-3703	446	24	systems	system	NOUN
american_scientific_journal-3703	446	25	.	.	PUNCT
american_scientific_journal-3703	447	1	acknowledgement	acknowledgement	NOUN
american_scientific_journal-3703	447	2	it	it	PRON
american_scientific_journal-3703	447	3	is	be	AUX
american_scientific_journal-3703	447	4	starting	start	VERB
american_scientific_journal-3703	447	5	with	with	ADP
american_scientific_journal-3703	447	6	thanking	thank	VERB
american_scientific_journal-3703	447	7	the	the	DET
american_scientific_journal-3703	447	8	almighty	almighty	ADJ
american_scientific_journal-3703	447	9	allah	allah	PROPN
american_scientific_journal-3703	447	10	.	.	PUNCT
american_scientific_journal-3703	448	1	not	not	PART
american_scientific_journal-3703	448	2	only	only	ADV
american_scientific_journal-3703	448	3	this	this	DET
american_scientific_journal-3703	448	4	paper	paper	NOUN
american_scientific_journal-3703	448	5	but	but	CCONJ
american_scientific_journal-3703	448	6	also	also	ADV
american_scientific_journal-3703	448	7	my	my	PRON
american_scientific_journal-3703	448	8	whole	whole	ADJ
american_scientific_journal-3703	448	9	life	life	NOUN
american_scientific_journal-3703	448	10	is	be	AUX
american_scientific_journal-3703	448	11	blessed	bless	VERB
american_scientific_journal-3703	448	12	by	by	ADP
american_scientific_journal-3703	448	13	the	the	DET
american_scientific_journal-3703	448	14	grace	grace	NOUN
american_scientific_journal-3703	448	15	of	of	ADP
american_scientific_journal-3703	448	16	him	he	PRON
american_scientific_journal-3703	448	17	.	.	PUNCT
american_scientific_journal-3703	449	1	i	i	PRON
american_scientific_journal-3703	449	2	acknowledge	acknowledge	VERB
american_scientific_journal-3703	449	3	with	with	ADP
american_scientific_journal-3703	449	4	a	a	DET
american_scientific_journal-3703	449	5	humble	humble	ADJ
american_scientific_journal-3703	449	6	respect	respect	NOUN
american_scientific_journal-3703	449	7	to	to	ADP
american_scientific_journal-3703	449	8	my	my	PRON
american_scientific_journal-3703	449	9	supervisor	supervisor	NOUN
american_scientific_journal-3703	449	10	professor	professor	PROPN
american_scientific_journal-3703	449	11	dr	dr	PROPN
american_scientific_journal-3703	449	12	.	.	PROPN
american_scientific_journal-3703	449	13	payer	payer	PROPN
american_scientific_journal-3703	449	14	ahmed	ahmed	PROPN
american_scientific_journal-3703	449	15	,	,	PUNCT
american_scientific_journal-3703	449	16	department	department	NOUN
american_scientific_journal-3703	449	17	of	of	ADP
american_scientific_journal-3703	449	18	mathematics	mathematic	NOUN
american_scientific_journal-3703	449	19	,	,	PUNCT
american_scientific_journal-3703	449	20	faculty	faculty	NOUN
american_scientific_journal-3703	449	21	of	of	ADP
american_scientific_journal-3703	449	22	science	science	NOUN
american_scientific_journal-3703	449	23	,	,	PUNCT
american_scientific_journal-3703	449	24	jagannath	jagannath	PROPN
american_scientific_journal-3703	449	25	university	university	PROPN
american_scientific_journal-3703	449	26	,	,	PUNCT
american_scientific_journal-3703	449	27	dhaka	dhaka	PROPN
american_scientific_journal-3703	449	28	and	and	CCONJ
american_scientific_journal-3703	449	29	professor	professor	PROPN
american_scientific_journal-3703	449	30	dr	dr	PROPN
american_scientific_journal-3703	449	31	.	.	PROPN
american_scientific_journal-3703	449	32	md	md	PROPN
american_scientific_journal-3703	449	33	.	.	PROPN
american_scientific_journal-3703	450	1	rezaul	rezaul	PROPN
american_scientific_journal-3703	450	2	karim	karim	PROPN
american_scientific_journal-3703	450	3	,	,	PUNCT
american_scientific_journal-3703	450	4	chairman	chairman	NOUN
american_scientific_journal-3703	450	5	,	,	PUNCT
american_scientific_journal-3703	450	6	department	department	NOUN
american_scientific_journal-3703	450	7	of	of	ADP
american_scientific_journal-3703	450	8	mathematics	mathematics	PROPN
american_scientific_journal-3703	450	9	,	,	PUNCT
american_scientific_journal-3703	450	10	jagannath	jagannath	PROPN
american_scientific_journal-3703	450	11	university	university	PROPN
american_scientific_journal-3703	450	12	,	,	PUNCT
american_scientific_journal-3703	450	13	dhaka	dhaka	NOUN
american_scientific_journal-3703	450	14	for	for	ADP
american_scientific_journal-3703	450	15	delivering	deliver	VERB
american_scientific_journal-3703	450	16	right	right	ADJ
american_scientific_journal-3703	450	17	directions	direction	NOUN
american_scientific_journal-3703	450	18	to	to	PART
american_scientific_journal-3703	450	19	complete	complete	VERB
american_scientific_journal-3703	450	20	this	this	DET
american_scientific_journal-3703	450	21	research	research	NOUN
american_scientific_journal-3703	450	22	work	work	NOUN
american_scientific_journal-3703	450	23	properly	properly	ADV
american_scientific_journal-3703	450	24	.	.	PUNCT
american_scientific_journal-3703	451	1	i	i	PRON
american_scientific_journal-3703	451	2	am	be	AUX
american_scientific_journal-3703	451	3	also	also	ADV
american_scientific_journal-3703	451	4	gratitude	gratitude	ADJ
american_scientific_journal-3703	451	5	to	to	ADP
american_scientific_journal-3703	451	6	my	my	PRON
american_scientific_journal-3703	451	7	teacher	teacher	NOUN
american_scientific_journal-3703	451	8	a.b.s	a.b.s	ADV
american_scientific_journal-3703	451	9	.	.	PUNCT
american_scientific_journal-3703	452	1	manik	manik	PROPN
american_scientific_journal-3703	452	2	munsi	munsi	PROPN
american_scientific_journal-3703	452	3	,	,	PUNCT
american_scientific_journal-3703	452	4	lecturer	lecturer	NOUN
american_scientific_journal-3703	452	5	,	,	PUNCT
american_scientific_journal-3703	452	6	department	department	NOUN
american_scientific_journal-3703	452	7	of	of	ADP
american_scientific_journal-3703	452	8	mathematics	mathematics	PROPN
american_scientific_journal-3703	452	9	,	,	PUNCT
american_scientific_journal-3703	452	10	jagannath	jagannath	PROPN
american_scientific_journal-3703	452	11	university	university	PROPN
american_scientific_journal-3703	452	12	,	,	PUNCT
american_scientific_journal-3703	452	13	dhaka	dhaka	PROPN
american_scientific_journal-3703	452	14	for	for	ADP
american_scientific_journal-3703	452	15	his	his	PRON
american_scientific_journal-3703	452	16	constructive	constructive	ADJ
american_scientific_journal-3703	452	17	guides	guide	NOUN
american_scientific_journal-3703	452	18	during	during	ADP
american_scientific_journal-3703	452	19	my	my	PRON
american_scientific_journal-3703	452	20	research	research	NOUN
american_scientific_journal-3703	452	21	works	work	NOUN
american_scientific_journal-3703	452	22	.	.	PUNCT
american_scientific_journal-3703	453	1	7	7	X
american_scientific_journal-3703	453	2	.	.	X
american_scientific_journal-3703	453	3	constraints	constraint	NOUN
american_scientific_journal-3703	453	4	/	/	SYM
american_scientific_journal-3703	453	5	limitations	limitation	NOUN
american_scientific_journal-3703	453	6	of	of	ADP
american_scientific_journal-3703	453	7	the	the	DET
american_scientific_journal-3703	453	8	study	study	NOUN
american_scientific_journal-3703	453	9	there	there	PRON
american_scientific_journal-3703	453	10	are	be	VERB
american_scientific_journal-3703	453	11	some	some	DET
american_scientific_journal-3703	453	12	limitations	limitation	NOUN
american_scientific_journal-3703	453	13	we	we	PRON
american_scientific_journal-3703	453	14	see	see	VERB
american_scientific_journal-3703	453	15	in	in	ADP
american_scientific_journal-3703	453	16	our	our	PRON
american_scientific_journal-3703	453	17	article	article	NOUN
american_scientific_journal-3703	453	18	.	.	PUNCT
american_scientific_journal-3703	454	1	first	first	ADV
american_scientific_journal-3703	454	2	of	of	ADP
american_scientific_journal-3703	454	3	all	all	PRON
american_scientific_journal-3703	454	4	we	we	PRON
american_scientific_journal-3703	454	5	have	have	VERB
american_scientific_journal-3703	454	6	to	to	PART
american_scientific_journal-3703	454	7	face	face	VERB
american_scientific_journal-3703	454	8	software	software	NOUN
american_scientific_journal-3703	454	9	problem	problem	NOUN
american_scientific_journal-3703	454	10	while	while	SCONJ
american_scientific_journal-3703	454	11	preparing	prepare	VERB
american_scientific_journal-3703	454	12	0.2	0.2	NUM
american_scientific_journal-3703	454	13	0.4	0.4	NUM
american_scientific_journal-3703	454	14	0.6	0.6	NUM
american_scientific_journal-3703	454	15	0.8	0.8	NUM
american_scientific_journal-3703	454	16	1.0	1.0	NUM
american_scientific_journal-3703	454	17	0.2	0.2	NUM
american_scientific_journal-3703	454	18	0.4	0.4	NUM
american_scientific_journal-3703	454	19	0.6	0.6	NUM
american_scientific_journal-3703	454	20	0.8	0.8	NUM
american_scientific_journal-3703	454	21	1.0	1.0	NUM
american_scientific_journal-3703	454	22	0.2	0.2	NUM
american_scientific_journal-3703	454	23	0.4	0.4	NUM
american_scientific_journal-3703	454	24	0.6	0.6	NUM
american_scientific_journal-3703	454	25	0.8	0.8	NUM
american_scientific_journal-3703	454	26	1.0	1.0	NUM
american_scientific_journal-3703	454	27	0.2	0.2	NUM
american_scientific_journal-3703	454	28	0.4	0.4	NUM
american_scientific_journal-3703	454	29	0.6	0.6	NUM
american_scientific_journal-3703	454	30	0.8	0.8	NUM
american_scientific_journal-3703	454	31	1.0	1.0	NUM
american_scientific_journal-3703	454	32	american	american	ADJ
american_scientific_journal-3703	454	33	scientific	scientific	ADJ
american_scientific_journal-3703	454	34	research	research	NOUN
american_scientific_journal-3703	454	35	journal	journal	NOUN
american_scientific_journal-3703	454	36	for	for	ADP
american_scientific_journal-3703	454	37	engineering	engineering	NOUN
american_scientific_journal-3703	454	38	,	,	PUNCT
american_scientific_journal-3703	454	39	technology	technology	NOUN
american_scientific_journal-3703	454	40	,	,	PUNCT
american_scientific_journal-3703	454	41	and	and	CCONJ
american_scientific_journal-3703	454	42	sciences	science	NOUN
american_scientific_journal-3703	454	43	(	(	PUNCT
american_scientific_journal-3703	454	44	asrjets	asrjet	NOUN
american_scientific_journal-3703	454	45	)	)	PUNCT
american_scientific_journal-3703	454	46	(	(	PUNCT
american_scientific_journal-3703	454	47	2018	2018	NUM
american_scientific_journal-3703	454	48	)	)	PUNCT
american_scientific_journal-3703	454	49	volume	volume	NOUN
american_scientific_journal-3703	454	50	43	43	NUM
american_scientific_journal-3703	454	51	,	,	PUNCT
american_scientific_journal-3703	454	52	no	no	DET
american_scientific_journal-3703	454	53	1	1	NUM
american_scientific_journal-3703	454	54	,	,	PUNCT
american_scientific_journal-3703	454	55	pp	pp	ADV
american_scientific_journal-3703	454	56	110	110	NUM
american_scientific_journal-3703	454	57	-	-	SYM
american_scientific_journal-3703	454	58	133	133	NUM
american_scientific_journal-3703	454	59	132	132	NUM
american_scientific_journal-3703	454	60	orbit	orbit	NOUN
american_scientific_journal-3703	454	61	analysis	analysis	NOUN
american_scientific_journal-3703	454	62	and	and	CCONJ
american_scientific_journal-3703	454	63	analyzing	analyze	VERB
american_scientific_journal-3703	454	64	staircase	staircase	NOUN
american_scientific_journal-3703	454	65	diagram	diagram	NOUN
american_scientific_journal-3703	454	66	of	of	ADP
american_scientific_journal-3703	454	67	the	the	DET
american_scientific_journal-3703	454	68	doubling	double	VERB
american_scientific_journal-3703	454	69	map	map	NOUN
american_scientific_journal-3703	454	70	.	.	PUNCT
american_scientific_journal-3703	455	1	first	first	ADV
american_scientific_journal-3703	455	2	we	we	PRON
american_scientific_journal-3703	455	3	tried	try	VERB
american_scientific_journal-3703	455	4	to	to	PART
american_scientific_journal-3703	455	5	see	see	VERB
american_scientific_journal-3703	455	6	the	the	DET
american_scientific_journal-3703	455	7	said	said	ADJ
american_scientific_journal-3703	455	8	analysis	analysis	NOUN
american_scientific_journal-3703	455	9	using	use	VERB
american_scientific_journal-3703	455	10	mathematica	mathematica	PROPN
american_scientific_journal-3703	455	11	5.0	5.0	NUM
american_scientific_journal-3703	455	12	version	version	NOUN
american_scientific_journal-3703	456	1	but	but	CCONJ
american_scientific_journal-3703	456	2	it	it	PRON
american_scientific_journal-3703	456	3	did	do	AUX
american_scientific_journal-3703	456	4	not	not	PART
american_scientific_journal-3703	456	5	working	work	VERB
american_scientific_journal-3703	456	6	showing	show	VERB
american_scientific_journal-3703	456	7	graph	graph	NOUN
american_scientific_journal-3703	456	8	.	.	PUNCT
american_scientific_journal-3703	457	1	after	after	ADP
american_scientific_journal-3703	457	2	that	that	PRON
american_scientific_journal-3703	457	3	we	we	PRON
american_scientific_journal-3703	457	4	took	take	VERB
american_scientific_journal-3703	457	5	an	an	DET
american_scientific_journal-3703	457	6	attempt	attempt	NOUN
american_scientific_journal-3703	457	7	to	to	PART
american_scientific_journal-3703	457	8	use	use	VERB
american_scientific_journal-3703	457	9	mathematica	mathematica	PROPN
american_scientific_journal-3703	457	10	11.0	11.0	NUM
american_scientific_journal-3703	457	11	version	version	NOUN
american_scientific_journal-3703	457	12	.	.	PUNCT
american_scientific_journal-3703	458	1	then	then	ADV
american_scientific_journal-3703	458	2	we	we	PRON
american_scientific_journal-3703	458	3	have	have	AUX
american_scientific_journal-3703	458	4	seen	see	VERB
american_scientific_journal-3703	458	5	that	that	SCONJ
american_scientific_journal-3703	458	6	it	it	PRON
american_scientific_journal-3703	458	7	worked	work	VERB
american_scientific_journal-3703	458	8	very	very	ADV
american_scientific_journal-3703	458	9	smoothly	smoothly	ADV
american_scientific_journal-3703	458	10	and	and	CCONJ
american_scientific_journal-3703	458	11	got	get	VERB
american_scientific_journal-3703	458	12	our	our	PRON
american_scientific_journal-3703	458	13	expected	expect	VERB
american_scientific_journal-3703	458	14	result	result	NOUN
american_scientific_journal-3703	458	15	.	.	PUNCT
american_scientific_journal-3703	459	1	therefore	therefore	ADV
american_scientific_journal-3703	459	2	software	software	NOUN
american_scientific_journal-3703	459	3	version	version	NOUN
american_scientific_journal-3703	459	4	problem	problem	NOUN
american_scientific_journal-3703	459	5	can	can	AUX
american_scientific_journal-3703	459	6	be	be	AUX
american_scientific_journal-3703	459	7	treated	treat	VERB
american_scientific_journal-3703	459	8	as	as	ADP
american_scientific_journal-3703	459	9	our	our	PRON
american_scientific_journal-3703	459	10	major	major	ADJ
american_scientific_journal-3703	459	11	limitation	limitation	NOUN
american_scientific_journal-3703	459	12	of	of	ADP
american_scientific_journal-3703	459	13	our	our	PRON
american_scientific_journal-3703	459	14	paper	paper	NOUN
american_scientific_journal-3703	459	15	.	.	PUNCT
american_scientific_journal-3703	460	1	the	the	DET
american_scientific_journal-3703	460	2	2nd	2nd	ADJ
american_scientific_journal-3703	460	3	limitation	limitation	NOUN
american_scientific_journal-3703	460	4	is	be	AUX
american_scientific_journal-3703	460	5	that	that	SCONJ
american_scientific_journal-3703	460	6	as	as	SCONJ
american_scientific_journal-3703	460	7	the	the	DET
american_scientific_journal-3703	460	8	doubling	double	VERB
american_scientific_journal-3703	460	9	map	map	NOUN
american_scientific_journal-3703	460	10	does	do	AUX
american_scientific_journal-3703	460	11	not	not	PART
american_scientific_journal-3703	460	12	come	come	VERB
american_scientific_journal-3703	460	13	any	any	DET
american_scientific_journal-3703	460	14	parameter	parameter	NOUN
american_scientific_journal-3703	460	15	so	so	SCONJ
american_scientific_journal-3703	460	16	we	we	PRON
american_scientific_journal-3703	460	17	did	do	AUX
american_scientific_journal-3703	460	18	not	not	PART
american_scientific_journal-3703	460	19	have	have	AUX
american_scientific_journal-3703	460	20	desired	desire	VERB
american_scientific_journal-3703	460	21	chaotic	chaotic	ADJ
american_scientific_journal-3703	460	22	sound	sound	NOUN
american_scientific_journal-3703	460	23	like	like	ADP
american_scientific_journal-3703	460	24	others	other	NOUN
american_scientific_journal-3703	460	25	chaotic	chaotic	ADJ
american_scientific_journal-3703	460	26	maps	map	NOUN
american_scientific_journal-3703	460	27	such	such	ADJ
american_scientific_journal-3703	460	28	as	as	ADP
american_scientific_journal-3703	460	29	logistic	logistic	ADJ
american_scientific_journal-3703	460	30	map	map	NOUN
american_scientific_journal-3703	460	31	and	and	CCONJ
american_scientific_journal-3703	460	32	tent	tent	NOUN
american_scientific_journal-3703	460	33	map	map	NOUN
american_scientific_journal-3703	460	34	.	.	PUNCT
american_scientific_journal-3703	461	1	of	of	ADP
american_scientific_journal-3703	461	2	course	course	NOUN
american_scientific_journal-3703	461	3	high	high	ADJ
american_scientific_journal-3703	461	4	speed	speed	NOUN
american_scientific_journal-3703	461	5	super	super	ADJ
american_scientific_journal-3703	461	6	computer	computer	NOUN
american_scientific_journal-3703	461	7	is	be	AUX
american_scientific_journal-3703	461	8	very	very	ADV
american_scientific_journal-3703	461	9	much	much	ADV
american_scientific_journal-3703	461	10	needed	need	VERB
american_scientific_journal-3703	461	11	to	to	PART
american_scientific_journal-3703	461	12	run	run	VERB
american_scientific_journal-3703	461	13	the	the	DET
american_scientific_journal-3703	461	14	doubling	double	VERB
american_scientific_journal-3703	461	15	map	map	NOUN
american_scientific_journal-3703	461	16	related	relate	VERB
american_scientific_journal-3703	461	17	program	program	NOUN
american_scientific_journal-3703	461	18	to	to	PART
american_scientific_journal-3703	461	19	run	run	VERB
american_scientific_journal-3703	461	20	quickly	quickly	ADV
american_scientific_journal-3703	461	21	.	.	PUNCT
american_scientific_journal-3703	462	1	8	8	X
american_scientific_journal-3703	462	2	.	.	PUNCT
american_scientific_journal-3703	462	3	recommendations	recommendation	NOUN
american_scientific_journal-3703	462	4	we	we	PRON
american_scientific_journal-3703	462	5	would	would	AUX
american_scientific_journal-3703	462	6	like	like	VERB
american_scientific_journal-3703	462	7	to	to	PART
american_scientific_journal-3703	462	8	notice	notice	VERB
american_scientific_journal-3703	462	9	here	here	ADV
american_scientific_journal-3703	462	10	that	that	SCONJ
american_scientific_journal-3703	462	11	mathematica	mathematica	PROPN
american_scientific_journal-3703	462	12	11.0	11.0	NUM
american_scientific_journal-3703	462	13	version	version	NOUN
american_scientific_journal-3703	462	14	and	and	CCONJ
american_scientific_journal-3703	462	15	some	some	DET
american_scientific_journal-3703	462	16	other	other	ADJ
american_scientific_journal-3703	462	17	upgraded	upgrade	VERB
american_scientific_journal-3703	462	18	versions	version	NOUN
american_scientific_journal-3703	462	19	are	be	AUX
american_scientific_journal-3703	462	20	recommended	recommend	VERB
american_scientific_journal-3703	462	21	to	to	PART
american_scientific_journal-3703	462	22	use	use	VERB
american_scientific_journal-3703	462	23	while	while	SCONJ
american_scientific_journal-3703	462	24	performing	perform	VERB
american_scientific_journal-3703	462	25	graphical	graphical	ADJ
american_scientific_journal-3703	462	26	analysis	analysis	NOUN
american_scientific_journal-3703	462	27	,	,	PUNCT
american_scientific_journal-3703	462	28	orbit	orbit	NOUN
american_scientific_journal-3703	462	29	analysis	analysis	NOUN
american_scientific_journal-3703	462	30	,	,	PUNCT
american_scientific_journal-3703	462	31	staircase	staircase	NOUN
american_scientific_journal-3703	462	32	diagram	diagram	NOUN
american_scientific_journal-3703	462	33	etc	etc	X
american_scientific_journal-3703	462	34	.	.	X
american_scientific_journal-3703	462	35	to	to	PART
american_scientific_journal-3703	462	36	run	run	VERB
american_scientific_journal-3703	462	37	the	the	DET
american_scientific_journal-3703	462	38	program	program	NOUN
american_scientific_journal-3703	462	39	more	more	ADV
american_scientific_journal-3703	462	40	smoothly	smoothly	ADV
american_scientific_journal-3703	462	41	and	and	CCONJ
american_scientific_journal-3703	462	42	to	to	PART
american_scientific_journal-3703	462	43	find	find	VERB
american_scientific_journal-3703	462	44	actual	actual	ADJ
american_scientific_journal-3703	462	45	chaotic	chaotic	ADJ
american_scientific_journal-3703	462	46	sound	sound	NOUN
american_scientific_journal-3703	462	47	a	a	DET
american_scientific_journal-3703	462	48	powerful	powerful	ADJ
american_scientific_journal-3703	462	49	high	high	ADJ
american_scientific_journal-3703	462	50	speed	speed	NOUN
american_scientific_journal-3703	462	51	super	super	ADJ
american_scientific_journal-3703	462	52	computer	computer	NOUN
american_scientific_journal-3703	462	53	are	be	AUX
american_scientific_journal-3703	462	54	recommended	recommend	VERB
american_scientific_journal-3703	462	55	for	for	ADP
american_scientific_journal-3703	462	56	such	such	DET
american_scientific_journal-3703	462	57	a	a	DET
american_scientific_journal-3703	462	58	research	research	NOUN
american_scientific_journal-3703	462	59	so	so	SCONJ
american_scientific_journal-3703	462	60	that	that	SCONJ
american_scientific_journal-3703	462	61	the	the	DET
american_scientific_journal-3703	462	62	ambitious	ambitious	ADJ
american_scientific_journal-3703	462	63	researchers	researcher	NOUN
american_scientific_journal-3703	462	64	can	can	AUX
american_scientific_journal-3703	462	65	get	get	VERB
american_scientific_journal-3703	462	66	their	their	PRON
american_scientific_journal-3703	462	67	expected	expect	VERB
american_scientific_journal-3703	462	68	results	result	NOUN
american_scientific_journal-3703	462	69	.	.	PUNCT
american_scientific_journal-3703	463	1	references	reference	NOUN
american_scientific_journal-3703	463	2	[	[	X
american_scientific_journal-3703	463	3	1	1	NUM
american_scientific_journal-3703	463	4	]	]	PUNCT
american_scientific_journal-3703	463	5	c.	c.	PROPN
american_scientific_journal-3703	463	6	robinson	robinson	PROPN
american_scientific_journal-3703	463	7	,	,	PUNCT
american_scientific_journal-3703	463	8	dynamical	dynamical	ADJ
american_scientific_journal-3703	463	9	systems	system	NOUN
american_scientific_journal-3703	463	10	,	,	PUNCT
american_scientific_journal-3703	463	11	stability	stability	NOUN
american_scientific_journal-3703	463	12	,	,	PUNCT
american_scientific_journal-3703	463	13	symbolic	symbolic	ADJ
american_scientific_journal-3703	463	14	dynamical	dynamical	ADJ
american_scientific_journal-3703	463	15	and	and	CCONJ
american_scientific_journal-3703	463	16	chaos	chaos	NOUN
american_scientific_journal-3703	463	17	,	,	PUNCT
american_scientific_journal-3703	463	18	crc	crc	NOUN
american_scientific_journal-3703	463	19	press	press	PROPN
american_scientific_journal-3703	463	20	,	,	PUNCT
american_scientific_journal-3703	463	21	boca	boca	PROPN
american_scientific_journal-3703	463	22	eaton	eaton	PROPN
american_scientific_journal-3703	463	23	,	,	PUNCT
american_scientific_journal-3703	463	24	1995	1995	NUM
american_scientific_journal-3703	463	25	[	[	X
american_scientific_journal-3703	463	26	2	2	NUM
american_scientific_journal-3703	463	27	]	]	X
american_scientific_journal-3703	463	28	dynamical	dynamical	ADJ
american_scientific_journal-3703	463	29	systems	system	NOUN
american_scientific_journal-3703	463	30	and	and	CCONJ
american_scientific_journal-3703	463	31	ergodic	ergodic	ADJ
american_scientific_journal-3703	463	32	theory	theory	NOUN
american_scientific_journal-3703	463	33	-	-	PUNCT
american_scientific_journal-3703	463	34	the	the	DET
american_scientific_journal-3703	463	35	doubling	doubling	NOUN
american_scientific_journal-3703	463	36	map	map	NOUN
american_scientific_journal-3703	463	37	,	,	PUNCT
american_scientific_journal-3703	463	38	corinna	corinna	PROPN
american_scientific_journal-3703	463	39	ulcigrai	ulcigrai	PROPN
american_scientific_journal-3703	463	40	,	,	PUNCT
american_scientific_journal-3703	463	41	university	university	NOUN
american_scientific_journal-3703	463	42	of	of	ADP
american_scientific_journal-3703	463	43	bristol	bristol	PROPN
american_scientific_journal-3703	463	44	.	.	PUNCT
american_scientific_journal-3703	464	1	[	[	X
american_scientific_journal-3703	464	2	3	3	X
american_scientific_journal-3703	464	3	]	]	PUNCT
american_scientific_journal-3703	464	4	evan	evan	NOUN
american_scientific_journal-3703	464	5	dummit	dummit	PROPN
american_scientific_journal-3703	464	6	,	,	PUNCT
american_scientific_journal-3703	464	7	2015	2015	NUM
american_scientific_journal-3703	464	8	,	,	PUNCT
american_scientific_journal-3703	464	9	v.	v.	ADP
american_scientific_journal-3703	464	10	1.00	1.00	NUM
american_scientific_journal-3703	464	11	,	,	PUNCT
american_scientific_journal-3703	464	12	dynamics	dynamic	NOUN
american_scientific_journal-3703	464	13	,	,	PUNCT
american_scientific_journal-3703	464	14	chaos	chaos	NOUN
american_scientific_journal-3703	464	15	,	,	PUNCT
american_scientific_journal-3703	464	16	and	and	CCONJ
american_scientific_journal-3703	464	17	fractals	fractal	NOUN
american_scientific_journal-3703	464	18	(	(	PUNCT
american_scientific_journal-3703	464	19	part	part	NOUN
american_scientific_journal-3703	464	20	3	3	NUM
american_scientific_journal-3703	464	21	):	):	PUNCT
american_scientific_journal-3703	464	22	chaotic	chaotic	ADJ
american_scientific_journal-3703	464	23	dynamics	dynamic	NOUN
american_scientific_journal-3703	464	24	.	.	PUNCT
american_scientific_journal-3703	465	1	[	[	X
american_scientific_journal-3703	465	2	4	4	X
american_scientific_journal-3703	465	3	]	]	X
american_scientific_journal-3703	465	4	evgeny	evgeny	PROPN
american_scientific_journal-3703	465	5	demidov	demidov	PROPN
american_scientific_journal-3703	465	6	,	,	PUNCT
american_scientific_journal-3703	465	7	chaotic	chaotic	ADJ
american_scientific_journal-3703	465	8	1	1	NUM
american_scientific_journal-3703	465	9	d	d	NOUN
american_scientific_journal-3703	465	10	maps	map	NOUN
american_scientific_journal-3703	465	11	.	.	PUNCT
american_scientific_journal-3703	466	1	[	[	X
american_scientific_journal-3703	466	2	5	5	X
american_scientific_journal-3703	466	3	]	]	X
american_scientific_journal-3703	466	4	heikki	heikki	PROPN
american_scientific_journal-3703	466	5	ruskeepaa	ruskeepaa	PROPN
american_scientific_journal-3703	466	6	,	,	PUNCT
american_scientific_journal-3703	466	7	mathematica	mathematica	PROPN
american_scientific_journal-3703	466	8	navigator	navigator	PROPN
american_scientific_journal-3703	466	9	,	,	PUNCT
american_scientific_journal-3703	466	10	3rd	3rd	ADJ
american_scientific_journal-3703	466	11	edition	edition	NOUN
american_scientific_journal-3703	466	12	.	.	PUNCT
american_scientific_journal-3703	467	1	[	[	X
american_scientific_journal-3703	467	2	6	6	NUM
american_scientific_journal-3703	467	3	]	]	PUNCT
american_scientific_journal-3703	467	4	j.	j.	PROPN
american_scientific_journal-3703	467	5	banks	banks	PROPN
american_scientific_journal-3703	467	6	,	,	PUNCT
american_scientific_journal-3703	467	7	j.	j.	PROPN
american_scientific_journal-3703	467	8	brooks	brooks	PROPN
american_scientific_journal-3703	467	9	,	,	PUNCT
american_scientific_journal-3703	467	10	g.	g.	PROPN
american_scientific_journal-3703	467	11	cairns	cairns	PROPN
american_scientific_journal-3703	467	12	,	,	PUNCT
american_scientific_journal-3703	467	13	g.	g.	PROPN
american_scientific_journal-3703	467	14	davis	davis	PROPN
american_scientific_journal-3703	467	15	and	and	CCONJ
american_scientific_journal-3703	467	16	p.	p.	PROPN
american_scientific_journal-3703	467	17	stacey	stacey	PROPN
american_scientific_journal-3703	467	18	,	,	PUNCT
american_scientific_journal-3703	467	19	on	on	ADP
american_scientific_journal-3703	467	20	devaney	devaney	PROPN
american_scientific_journal-3703	467	21	’s	’s	PART
american_scientific_journal-3703	467	22	definition	definition	NOUN
american_scientific_journal-3703	467	23	of	of	ADP
american_scientific_journal-3703	467	24	chaos	chaos	NOUN
american_scientific_journal-3703	467	25	,	,	PUNCT
american_scientific_journal-3703	467	26	american	american	PROPN
american_scientific_journal-3703	467	27	mathematic	mathematic	ADJ
american_scientific_journal-3703	467	28	monthly	monthly	ADJ
american_scientific_journal-3703	467	29	99	99	NUM
american_scientific_journal-3703	467	30	(	(	PUNCT
american_scientific_journal-3703	467	31	1992	1992	NUM
american_scientific_journal-3703	467	32	)	)	PUNCT
american_scientific_journal-3703	467	33	,	,	PUNCT
american_scientific_journal-3703	467	34	332	332	NUM
american_scientific_journal-3703	467	35	-	-	SYM
american_scientific_journal-3703	467	36	334	334	NUM
american_scientific_journal-3703	467	37	[	[	X
american_scientific_journal-3703	467	38	7	7	NUM
american_scientific_journal-3703	467	39	]	]	SYM
american_scientific_journal-3703	467	40	li	li	PROPN
american_scientific_journal-3703	467	41	,	,	PUNCT
american_scientific_journal-3703	467	42	t.-y	t.-y	NOUN
american_scientific_journal-3703	467	43	.	.	PUNCT
american_scientific_journal-3703	467	44	,	,	PUNCT
american_scientific_journal-3703	467	45	and	and	CCONJ
american_scientific_journal-3703	467	46	yorke	yorke	PROPN
american_scientific_journal-3703	467	47	,	,	PUNCT
american_scientific_journal-3703	467	48	j.	j.	PROPN
american_scientific_journal-3703	467	49	,	,	PUNCT
american_scientific_journal-3703	467	50	“	"	PUNCT
american_scientific_journal-3703	467	51	period	period	NOUN
american_scientific_journal-3703	467	52	three	three	NUM
american_scientific_journal-3703	467	53	implies	imply	VERB
american_scientific_journal-3703	467	54	chaos	chaos	NOUN
american_scientific_journal-3703	467	55	.	.	PUNCT
american_scientific_journal-3703	467	56	”	"	PUNCT
american_scientific_journal-3703	468	1	american	american	PROPN
american_scientific_journal-3703	468	2	mathematical	mathematical	PROPN
american_scientific_journal-3703	468	3	monthly	monthly	ADJ
american_scientific_journal-3703	468	4	82	82	NUM
american_scientific_journal-3703	468	5	(	(	PUNCT
american_scientific_journal-3703	468	6	1975	1975	NUM
american_scientific_journal-3703	468	7	)	)	PUNCT
american_scientific_journal-3703	468	8	,	,	PUNCT
american_scientific_journal-3703	468	9	985	985	NUM
american_scientific_journal-3703	468	10	-	-	SYM
american_scientific_journal-3703	468	11	992	992	NUM
american_scientific_journal-3703	468	12	.	.	PUNCT
american_scientific_journal-3703	469	1	[	[	X
american_scientific_journal-3703	469	2	8	8	NUM
american_scientific_journal-3703	469	3	]	]	PUNCT
american_scientific_journal-3703	469	4	p.	p.	PROPN
american_scientific_journal-3703	469	5	ahmed	ahmed	PROPN
american_scientific_journal-3703	469	6	,	,	PUNCT
american_scientific_journal-3703	469	7	chaotic	chaotic	ADJ
american_scientific_journal-3703	469	8	homeomorphisms	homeomorphism	NOUN
american_scientific_journal-3703	469	9	in	in	ADP
american_scientific_journal-3703	469	10	one	one	NUM
american_scientific_journal-3703	469	11	-	-	PUNCT
american_scientific_journal-3703	469	12	dimensional	dimensional	ADJ
american_scientific_journal-3703	469	13	dynamics	dynamic	NOUN
american_scientific_journal-3703	469	14	,	,	PUNCT
american_scientific_journal-3703	469	15	proc	proc	NOUN
american_scientific_journal-3703	469	16	.	.	PROPN
american_scientific_journal-3703	469	17	,	,	PUNCT
american_scientific_journal-3703	469	18	iwate	iwate	PROPN
american_scientific_journal-3703	469	19	univ	univ	PROPN
american_scientific_journal-3703	469	20	.	.	PROPN
american_scientific_journal-3703	469	21	,	,	PUNCT
american_scientific_journal-3703	469	22	japan	japan	PROPN
american_scientific_journal-3703	469	23	,	,	PUNCT
american_scientific_journal-3703	469	24	may	may	AUX
american_scientific_journal-3703	469	25	56	56	NUM
american_scientific_journal-3703	469	26	,	,	PUNCT
american_scientific_journal-3703	469	27	2001	2001	NUM
american_scientific_journal-3703	469	28	.	.	PUNCT
american_scientific_journal-3703	470	1	[	[	X
american_scientific_journal-3703	470	2	9	9	NUM
american_scientific_journal-3703	470	3	]	]	PUNCT
american_scientific_journal-3703	470	4	r.	r.	PROPN
american_scientific_journal-3703	470	5	l.	l.	PROPN
american_scientific_journal-3703	470	6	devaney	devaney	PROPN
american_scientific_journal-3703	470	7	,	,	PUNCT
american_scientific_journal-3703	470	8	a	a	DET
american_scientific_journal-3703	470	9	first	first	ADJ
american_scientific_journal-3703	470	10	course	course	NOUN
american_scientific_journal-3703	470	11	in	in	ADP
american_scientific_journal-3703	470	12	chaotic	chaotic	ADJ
american_scientific_journal-3703	470	13	dynamical	dynamical	ADJ
american_scientific_journal-3703	470	14	systems	system	NOUN
american_scientific_journal-3703	470	15	:	:	PUNCT
american_scientific_journal-3703	470	16	theory	theory	NOUN
american_scientific_journal-3703	470	17	and	and	CCONJ
american_scientific_journal-3703	470	18	experiment	experiment	NOUN
american_scientific_journal-3703	470	19	,	,	PUNCT
american_scientific_journal-3703	470	20	addisionwesley	addisionwesley	NOUN
american_scientific_journal-3703	470	21	,	,	PUNCT
american_scientific_journal-3703	470	22	new	new	ADJ
american_scientific_journal-3703	470	23	york,1992	york,1992	NOUN
american_scientific_journal-3703	470	24	.	.	PUNCT
american_scientific_journal-3703	471	1	[	[	X
american_scientific_journal-3703	471	2	10	10	NUM
american_scientific_journal-3703	471	3	]	]	X
american_scientific_journal-3703	471	4	r.	r.	PROPN
american_scientific_journal-3703	471	5	l.	l.	PROPN
american_scientific_journal-3703	471	6	devaney	devaney	PROPN
american_scientific_journal-3703	471	7	,	,	PUNCT
american_scientific_journal-3703	471	8	an	an	DET
american_scientific_journal-3703	471	9	introduction	introduction	NOUN
american_scientific_journal-3703	471	10	to	to	ADP
american_scientific_journal-3703	471	11	chaotic	chaotic	ADJ
american_scientific_journal-3703	471	12	dynamical	dynamical	ADJ
american_scientific_journal-3703	471	13	systems	system	NOUN
american_scientific_journal-3703	471	14	,	,	PUNCT
american_scientific_journal-3703	471	15	second	second	ADJ
american_scientific_journal-3703	471	16	edition	edition	NOUN
american_scientific_journal-3703	471	17	,	,	PUNCT
american_scientific_journal-3703	471	18	addision	addision	NOUN
american_scientific_journal-3703	471	19	-	-	PUNCT
american_scientific_journal-3703	471	20	wesley	wesley	PROPN
american_scientific_journal-3703	471	21	,	,	PUNCT
american_scientific_journal-3703	471	22	redwoodcity,1989	redwoodcity,1989	PROPN
american_scientific_journal-3703	471	23	.	.	PUNCT
american_scientific_journal-3703	472	1	american	american	PROPN
american_scientific_journal-3703	472	2	scientific	scientific	ADJ
american_scientific_journal-3703	472	3	research	research	PROPN
american_scientific_journal-3703	472	4	journal	journal	NOUN
american_scientific_journal-3703	472	5	for	for	ADP
american_scientific_journal-3703	472	6	engineering	engineering	NOUN
american_scientific_journal-3703	472	7	,	,	PUNCT
american_scientific_journal-3703	472	8	technology	technology	NOUN
american_scientific_journal-3703	472	9	,	,	PUNCT
american_scientific_journal-3703	472	10	and	and	CCONJ
american_scientific_journal-3703	472	11	sciences	science	NOUN
american_scientific_journal-3703	472	12	(	(	PUNCT
american_scientific_journal-3703	472	13	asrjets	asrjet	NOUN
american_scientific_journal-3703	472	14	)	)	PUNCT
american_scientific_journal-3703	472	15	(	(	PUNCT
american_scientific_journal-3703	472	16	2018	2018	NUM
american_scientific_journal-3703	472	17	)	)	PUNCT
american_scientific_journal-3703	472	18	volume	volume	NOUN
american_scientific_journal-3703	472	19	43	43	NUM
american_scientific_journal-3703	472	20	,	,	PUNCT
american_scientific_journal-3703	472	21	no	no	DET
american_scientific_journal-3703	472	22	1	1	NUM
american_scientific_journal-3703	472	23	,	,	PUNCT
american_scientific_journal-3703	472	24	pp	pp	ADV
american_scientific_journal-3703	472	25	110	110	NUM
american_scientific_journal-3703	472	26	-	-	SYM
american_scientific_journal-3703	472	27	133	133	NUM
american_scientific_journal-3703	472	28	133	133	NUM
american_scientific_journal-3703	473	1	[	[	X
american_scientific_journal-3703	473	2	11	11	NUM
american_scientific_journal-3703	473	3	]	]	PUNCT
american_scientific_journal-3703	473	4	r.	r.	PROPN
american_scientific_journal-3703	473	5	l.	l.	PROPN
american_scientific_journal-3703	473	6	devaney	devaney	PROPN
american_scientific_journal-3703	473	7	and	and	CCONJ
american_scientific_journal-3703	473	8	l.	l.	PROPN
american_scientific_journal-3703	473	9	keen	keen	PROPN
american_scientific_journal-3703	473	10	,	,	PUNCT
american_scientific_journal-3703	473	11	chaos	chaos	NOUN
american_scientific_journal-3703	473	12	and	and	CCONJ
american_scientific_journal-3703	473	13	fractals	fractal	NOUN
american_scientific_journal-3703	473	14	:	:	PUNCT
american_scientific_journal-3703	473	15	the	the	DET
american_scientific_journal-3703	473	16	mathematics	mathematic	NOUN
american_scientific_journal-3703	473	17	behind	behind	ADP
american_scientific_journal-3703	473	18	the	the	DET
american_scientific_journal-3703	473	19	computer	computer	NOUN
american_scientific_journal-3703	473	20	graphics	graphic	NOUN
american_scientific_journal-3703	473	21	,	,	PUNCT
american_scientific_journal-3703	473	22	american	american	PROPN
american_scientific_journal-3703	473	23	mathematical	mathematical	ADJ
american_scientific_journal-3703	473	24	society	society	NOUN
american_scientific_journal-3703	473	25	,	,	PUNCT
american_scientific_journal-3703	473	26	providence	providence	NOUN
american_scientific_journal-3703	473	27	,	,	PUNCT
american_scientific_journal-3703	473	28	1989	1989	NUM
american_scientific_journal-3703	474	1	.	.	PUNCT
american_scientific_journal-3703	475	1	[	[	X
american_scientific_journal-3703	475	2	12	12	NUM
american_scientific_journal-3703	475	3	]	]	X
american_scientific_journal-3703	475	4	s.	s.	PROPN
american_scientific_journal-3703	475	5	kolyada	kolyada	PROPN
american_scientific_journal-3703	475	6	and	and	CCONJ
american_scientific_journal-3703	475	7	l.	l.	PROPN
american_scientific_journal-3703	475	8	snoha	snoha	PROPN
american_scientific_journal-3703	475	9	,	,	PUNCT
american_scientific_journal-3703	475	10	some	some	DET
american_scientific_journal-3703	475	11	aspects	aspect	NOUN
american_scientific_journal-3703	475	12	of	of	ADP
american_scientific_journal-3703	475	13	topological	topological	ADJ
american_scientific_journal-3703	475	14	transitivity	transitivity	NOUN
american_scientific_journal-3703	475	15	-	-	PUNCT
american_scientific_journal-3703	475	16	a	a	DET
american_scientific_journal-3703	475	17	survey	survey	NOUN
american_scientific_journal-3703	475	18	,	,	PUNCT
american_scientific_journal-3703	475	19	1997	1997	NUM
american_scientific_journal-3703	475	20	.	.	PUNCT
american_scientific_journal-3703	476	1	[	[	X
american_scientific_journal-3703	476	2	13	13	NUM
american_scientific_journal-3703	476	3	]	]	PUNCT
american_scientific_journal-3703	476	4	s.	s.	PROPN
american_scientific_journal-3703	476	5	wiggins	wiggins	PROPN
american_scientific_journal-3703	476	6	,	,	PUNCT
american_scientific_journal-3703	476	7	chaotic	chaotic	ADJ
american_scientific_journal-3703	476	8	transport	transport	NOUN
american_scientific_journal-3703	476	9	in	in	ADP
american_scientific_journal-3703	476	10	dynamical	dynamical	ADJ
american_scientific_journal-3703	476	11	systems	system	NOUN
american_scientific_journal-3703	476	12	,	,	PUNCT
american_scientific_journal-3703	476	13	interdisciplinary	interdisciplinary	ADJ
american_scientific_journal-3703	476	14	applied	apply	VERB
american_scientific_journal-3703	476	15	mathematics	mathematic	NOUN
american_scientific_journal-3703	476	16	series	series	NOUN
american_scientific_journal-3703	476	17	,	,	PUNCT
american_scientific_journal-3703	476	18	volume	volume	NOUN
american_scientific_journal-3703	476	19	2	2	NUM
american_scientific_journal-3703	476	20	,	,	PUNCT
american_scientific_journal-3703	476	21	spring	spring	NOUN
american_scientific_journal-3703	476	22	-	-	PUNCT
american_scientific_journal-3703	476	23	verlag	verlag	PROPN
american_scientific_journal-3703	476	24	,	,	PUNCT
american_scientific_journal-3703	476	25	berlin	berlin	PROPN
american_scientific_journal-3703	476	26	,	,	PUNCT
american_scientific_journal-3703	476	27	1992	1992	NUM
american_scientific_journal-3703	476	28	.	.	PUNCT
american_scientific_journal-3703	477	1	[	[	X
american_scientific_journal-3703	477	2	14	14	NUM
american_scientific_journal-3703	477	3	]	]	X
american_scientific_journal-3703	477	4	wolf	wolf	NOUN
american_scientific_journal-3703	477	5	,	,	PUNCT
american_scientific_journal-3703	477	6	a.	a.	NOUN
american_scientific_journal-3703	477	7	“	"	PUNCT
american_scientific_journal-3703	477	8	quantifying	quantify	VERB
american_scientific_journal-3703	477	9	chaos	chaos	NOUN
american_scientific_journal-3703	477	10	with	with	ADP
american_scientific_journal-3703	477	11	lyapunov	lyapunov	ADJ
american_scientific_journal-3703	477	12	exponents	exponent	NOUN
american_scientific_journal-3703	477	13	,	,	PUNCT
american_scientific_journal-3703	477	14	”	"	PUNCT
american_scientific_journal-3703	477	15	in	in	ADP
american_scientific_journal-3703	477	16	chaos	chaos	NOUN
american_scientific_journal-3703	477	17	,	,	PUNCT
american_scientific_journal-3703	477	18	edited	edit	VERB
american_scientific_journal-3703	477	19	by	by	ADP
american_scientific_journal-3703	477	20	a.	a.	PROPN
american_scientific_journal-3703	477	21	v.	v.	PROPN
american_scientific_journal-3703	477	22	holden	holden	PROPN
american_scientific_journal-3703	477	23	,	,	PUNCT
american_scientific_journal-3703	477	24	princeton	princeton	PROPN
american_scientific_journal-3703	477	25	university	university	PROPN
american_scientific_journal-3703	477	26	press	press	NOUN
american_scientific_journal-3703	477	27	,	,	PUNCT
american_scientific_journal-3703	477	28	1986	1986	NUM
american_scientific_journal-3703	477	29	.	.	PUNCT
american_scientific_journal-3703	478	1	3.2	3.2	NUM
american_scientific_journal-3703	478	2	several	several	ADJ
american_scientific_journal-3703	478	3	definitions	definition	NOUN
american_scientific_journal-3703	478	4	of	of	ADP
american_scientific_journal-3703	478	5	chaos	chaos	NOUN
american_scientific_journal-3703	478	6	4.3	4.3	NUM
american_scientific_journal-3703	478	7	proposition	proposition	NOUN
american_scientific_journal-3703	478	8	the	the	DET
american_scientific_journal-3703	478	9	doubling	double	VERB
american_scientific_journal-3703	478	10	map	map	NOUN
american_scientific_journal-3703	478	11	is	be	AUX
american_scientific_journal-3703	478	12	chaotic	chaotic	ADJ
american_scientific_journal-3703	478	13	on	on	ADP
american_scientific_journal-3703	478	14	in	in	ADP
american_scientific_journal-3703	478	15	the	the	DET
american_scientific_journal-3703	478	16	sense	sense	NOUN
american_scientific_journal-3703	478	17	of	of	ADP
american_scientific_journal-3703	478	18	lyapunov	lyapunov	PROPN
american_scientific_journal-3703	478	19	exponent	exponent	NOUN
american_scientific_journal-3703	478	20	.	.	PUNCT
american_scientific_journal-3703	479	1	4.5	4.5	NUM
american_scientific_journal-3703	479	2	proposition	proposition	NOUN
american_scientific_journal-3703	479	3	doubling	doubling	NOUN
american_scientific_journal-3703	479	4	map	map	NOUN
american_scientific_journal-3703	479	5	is	be	AUX
american_scientific_journal-3703	479	6	chaotic	chaotic	ADJ
american_scientific_journal-3703	479	7	in	in	ADP
american_scientific_journal-3703	479	8	the	the	DET
american_scientific_journal-3703	479	9	sense	sense	NOUN
american_scientific_journal-3703	479	10	of	of	ADP
american_scientific_journal-3703	479	11	wiggin	wiggin	PROPN
american_scientific_journal-3703	479	12	.	.	PUNCT
american_scientific_journal-3703	480	1	4.6	4.6	NUM
american_scientific_journal-3703	480	2	proposition	proposition	NOUN
american_scientific_journal-3703	480	3	let	let	VERB
american_scientific_journal-3703	480	4	is	be	AUX
american_scientific_journal-3703	480	5	defined	define	VERB
american_scientific_journal-3703	480	6	by	by	ADP
american_scientific_journal-3703	480	7	is	be	AUX
american_scientific_journal-3703	480	8	conjugate	conjugate	ADJ
american_scientific_journal-3703	480	9	to	to	ADP
american_scientific_journal-3703	480	10	logistic	logistic	ADJ
american_scientific_journal-3703	480	11	map	map	NOUN
american_scientific_journal-3703	480	12	.	.	PUNCT
american_scientific_journal-3703	481	1	5.1	5.1	NUM
american_scientific_journal-3703	481	2	chaotic	chaotic	ADJ
american_scientific_journal-3703	481	3	behavior	behavior	NOUN
american_scientific_journal-3703	481	4	of	of	ADP
american_scientific_journal-3703	481	5	doubling	double	VERB
american_scientific_journal-3703	481	6	map	map	NOUN
american_scientific_journal-3703	481	7	considering	consider	VERB
american_scientific_journal-3703	481	8	initial	initial	ADJ
american_scientific_journal-3703	481	9	seeds	seed	NOUN
american_scientific_journal-3703	481	10	but	but	CCONJ
american_scientific_journal-3703	481	11	we	we	PRON
american_scientific_journal-3703	481	12	can	can	AUX
american_scientific_journal-3703	481	13	see	see	VERB
american_scientific_journal-3703	481	14	that	that	PRON
american_scientific_journal-3703	481	15	for	for	ADP
american_scientific_journal-3703	481	16	initial	initial	ADJ
american_scientific_journal-3703	481	17	seed	seed	NOUN
american_scientific_journal-3703	481	18	,	,	PUNCT
american_scientific_journal-3703	481	19	this	this	PRON
american_scientific_journal-3703	481	20	is	be	AUX
american_scientific_journal-3703	481	21	a	a	DET
american_scientific_journal-3703	481	22	periodic	periodic	ADJ
american_scientific_journal-3703	481	23	point	point	NOUN
american_scientific_journal-3703	481	24	with	with	ADP
american_scientific_journal-3703	481	25	prime	prime	ADJ
american_scientific_journal-3703	481	26	period-3	period-3	PROPN
american_scientific_journal-3703	481	27	and	and	CCONJ
american_scientific_journal-3703	481	28	therefore	therefore	ADV
american_scientific_journal-3703	481	29	the	the	DET
american_scientific_journal-3703	481	30	doubling	double	VERB
american_scientific_journal-3703	481	31	map	map	NOUN
american_scientific_journal-3703	481	32	is	be	AUX
american_scientific_journal-3703	481	33	chaotic	chaotic	ADJ
american_scientific_journal-3703	481	34	by	by	ADP
american_scientific_journal-3703	481	35	the	the	DET
american_scientific_journal-3703	481	36	period	period	NOUN
american_scientific_journal-3703	481	37	three	three	NUM
american_scientific_journal-3703	481	38	theorem	theorem	NOUN
american_scientific_journal-3703	481	39	[	[	X
american_scientific_journal-3703	481	40	7	7	NUM
american_scientific_journal-3703	481	41	]	]	PUNCT
american_scientific_journal-3703	481	42	.	.	PUNCT
american_scientific_journal-3703	482	1	5.2	5.2	NUM
american_scientific_journal-3703	482	2	orbit	orbit	NOUN
american_scientific_journal-3703	482	3	analysis	analysis	NOUN
american_scientific_journal-3703	482	4	of	of	ADP
american_scientific_journal-3703	482	5	doubling	double	VERB
american_scientific_journal-3703	482	6	map	map	NOUN
american_scientific_journal-3703	482	7	by	by	ADP
american_scientific_journal-3703	482	8	newton	newton	PROPN
american_scientific_journal-3703	482	9	’s	’s	PART
american_scientific_journal-3703	482	10	iteration	iteration	NOUN
american_scientific_journal-3703	482	11	the	the	DET
american_scientific_journal-3703	482	12	behavior	behavior	NOUN
american_scientific_journal-3703	482	13	of	of	ADP
american_scientific_journal-3703	482	14	orbit	orbit	NOUN
american_scientific_journal-3703	482	15	of	of	ADP
american_scientific_journal-3703	482	16	newton	newton	PROPN
american_scientific_journal-3703	482	17	iteration	iteration	PROPN
american_scientific_journal-3703	482	18	function	function	NOUN
american_scientific_journal-3703	482	19	associated	associate	VERB
american_scientific_journal-3703	482	20	to	to	ADP
american_scientific_journal-3703	482	21	doubling	double	VERB
american_scientific_journal-3703	482	22	function	function	NOUN
american_scientific_journal-3703	482	23	the	the	DET
american_scientific_journal-3703	482	24	doubling	double	VERB
american_scientific_journal-3703	482	25	mapis	mapis	NOUN
american_scientific_journal-3703	482	26	very	very	ADV
american_scientific_journal-3703	482	27	sensitive	sensitive	ADJ
american_scientific_journal-3703	482	28	to	to	ADP
american_scientific_journal-3703	482	29	numerical	numerical	ADJ
american_scientific_journal-3703	482	30	inaccuracies	inaccuracy	NOUN
american_scientific_journal-3703	482	31	.	.	PUNCT
american_scientific_journal-3703	483	1	to	to	PART
american_scientific_journal-3703	483	2	see	see	VERB
american_scientific_journal-3703	483	3	this	this	PRON
american_scientific_journal-3703	483	4	,	,	PUNCT
american_scientific_journal-3703	483	5	we	we	PRON
american_scientific_journal-3703	483	6	calculate	calculate	VERB
american_scientific_journal-3703	483	7	100	100	NUM
american_scientific_journal-3703	483	8	values	value	NOUN
american_scientific_journal-3703	483	9	from	from	ADP
american_scientific_journal-3703	483	10	the	the	DET
american_scientific_journal-3703	483	11	map	map	NOUN
american_scientific_journal-3703	483	12	,	,	PUNCT
american_scientific_journal-3703	483	13	the	the	DET
american_scientific_journal-3703	483	14	first	first	ADJ
american_scientific_journal-3703	483	15	by	by	ADP
american_scientific_journal-3703	483	16	using	use	VERB
american_scientific_journal-3703	483	17	normal	normal	ADJ
american_scientific_journal-3703	483	18	decimal	decimal	ADJ
american_scientific_journal-3703	483	19	numbers	number	NOUN
american_scientific_journal-3703	483	20	and	and	CCONJ
american_scientific_journal-3703	483	21	then	then	ADV
american_scientific_journal-3703	483	22	by	by	ADP
american_scientific_journal-3703	483	23	using	use	VERB
american_scientific_journal-3703	483	24	high	high	ADJ
american_scientific_journal-3703	483	25	-	-	PUNCT
american_scientific_journal-3703	483	26	precision	precision	NOUN
american_scientific_journal-3703	483	27	numbers	number	NOUN
american_scientific_journal-3703	483	28	.	.	PUNCT
american_scientific_journal-3703	484	1	in	in	ADP
american_scientific_journal-3703	484	2	the	the	DET
american_scientific_journal-3703	484	3	latter	latter	ADJ
american_scientific_journal-3703	484	4	case	case	NOUN
american_scientific_journal-3703	484	5	,	,	PUNCT
american_scientific_journal-3703	484	6	we	we	PRON
american_scientific_journal-3703	484	7	start	start	VERB
american_scientific_journal-3703	484	8	with	with	ADP
american_scientific_journal-3703	484	9	numbers	number	NOUN
american_scientific_journal-3703	484	10	that	that	PRON
american_scientific_journal-3703	484	11	have	have	VERB
american_scientific_journal-3703	484	12	a	a	DET
american_scientific_journal-3703	484	13	p	p	NOUN
american_scientific_journal-3703	484	14	...	...	PUNCT
american_scientific_journal-3703	484	15	figure	figure	NOUN
american_scientific_journal-3703	484	16	4	4	NUM
american_scientific_journal-3703	484	17	:	:	PUNCT
american_scientific_journal-3703	484	18	the	the	DET
american_scientific_journal-3703	484	19	initial	initial	ADJ
american_scientific_journal-3703	484	20	x=1/3	x=1/3	PROPN
american_scientific_journal-3703	484	21	and	and	CCONJ
american_scientific_journal-3703	484	22	0.1/5`65	0.1/5`65	PROPN
american_scientific_journal-3703	484	23	,	,	PUNCT
american_scientific_journal-3703	484	24	n=100	n=100	X
american_scientific_journal-3703	484	25	figure	figure	VERB
american_scientific_journal-3703	484	26	5	5	NUM
american_scientific_journal-3703	484	27	:	:	PUNCT
american_scientific_journal-3703	484	28	the	the	DET
american_scientific_journal-3703	484	29	initial	initial	ADJ
american_scientific_journal-3703	484	30	x=0.003	x=0.003	PROPN
american_scientific_journal-3703	484	31	and	and	CCONJ
american_scientific_journal-3703	484	32	0.0003`65	0.0003`65	NUM
american_scientific_journal-3703	484	33	,	,	PUNCT
american_scientific_journal-3703	484	34	n=100	n=100	NUM
american_scientific_journal-3703	484	35	we	we	PRON
american_scientific_journal-3703	484	36	see	see	VERB
american_scientific_journal-3703	484	37	that	that	DET
american_scientific_journal-3703	484	38	figure	figure	NOUN
american_scientific_journal-3703	484	39	3	3	NUM
american_scientific_journal-3703	484	40	and	and	CCONJ
american_scientific_journal-3703	484	41	figure	figure	VERB
american_scientific_journal-3703	484	42	4	4	NUM
american_scientific_journal-3703	484	43	are	be	AUX
american_scientific_journal-3703	484	44	regular	regular	ADJ
american_scientific_journal-3703	484	45	which	which	PRON
american_scientific_journal-3703	484	46	means	mean	VERB
american_scientific_journal-3703	484	47	that	that	SCONJ
american_scientific_journal-3703	484	48	numerical	numerical	ADJ
american_scientific_journal-3703	484	49	accuracy	accuracy	NOUN
american_scientific_journal-3703	484	50	.	.	PUNCT
american_scientific_journal-3703	485	1	but	but	CCONJ
american_scientific_journal-3703	485	2	the	the	DET
american_scientific_journal-3703	485	3	figure	figure	NOUN
american_scientific_journal-3703	485	4	5	5	NUM
american_scientific_journal-3703	485	5	shows	show	VERB
american_scientific_journal-3703	485	6	that	that	SCONJ
american_scientific_journal-3703	485	7	the	the	DET
american_scientific_journal-3703	485	8	behavior	behavior	NOUN
american_scientific_journal-3703	485	9	is	be	AUX
american_scientific_journal-3703	485	10	irregular	irregular	ADJ
american_scientific_journal-3703	485	11	which	which	PRON
american_scientific_journal-3703	485	12	means	mean	VERB
american_scientific_journal-3703	485	13	numerical	numerical	ADJ
american_scientific_journal-3703	485	14	inaccuracies	inaccuracy	NOUN
american_scientific_journal-3703	485	15	.	.	PUNCT
american_scientific_journal-3703	486	1	in	in	ADP
american_scientific_journal-3703	486	2	other	other	ADJ
american_scientific_journal-3703	486	3	words	word	NOUN
american_scientific_journal-3703	486	4	,	,	PUNCT
american_scientific_journal-3703	486	5	it	it	PRON
american_scientific_journal-3703	486	6	is	be	AUX
american_scientific_journal-3703	486	7	called	call	VERB
american_scientific_journal-3703	486	8	chaotic	chaotic	ADJ
american_scientific_journal-3703	486	9	behavior	behavior	NOUN
american_scientific_journal-3703	486	10	of	of	ADP
american_scientific_journal-3703	486	11	doubling	double	VERB
american_scientific_journal-3703	486	12	map	map	NOUN
american_scientific_journal-3703	486	13	[	[	X
american_scientific_journal-3703	486	14	5	5	NUM
american_scientific_journal-3703	486	15	]	]	PUNCT
american_scientific_journal-3703	486	16	.	.	PUNCT
american_scientific_journal-3703	487	1	5.4	5.4	NUM
american_scientific_journal-3703	487	2	sensitivity	sensitivity	NOUN
american_scientific_journal-3703	487	3	analysis	analysis	NOUN
american_scientific_journal-3703	487	4	to	to	ADP
american_scientific_journal-3703	487	5	initial	initial	ADJ
american_scientific_journal-3703	487	6	value	value	NOUN
american_scientific_journal-3703	487	7	of	of	ADP
american_scientific_journal-3703	487	8	doubling	double	VERB
american_scientific_journal-3703	487	9	map	map	NOUN
american_scientific_journal-3703	487	10	figure	figure	NOUN
american_scientific_journal-3703	487	11	6	6	NUM
american_scientific_journal-3703	487	12	:	:	PUNCT
american_scientific_journal-3703	487	13	the	the	DET
american_scientific_journal-3703	487	14	initial	initial	ADJ
american_scientific_journal-3703	487	15	x=0.02	x=0.02	PROPN
american_scientific_journal-3703	487	16	,	,	PUNCT
american_scientific_journal-3703	487	17	n=50	n=50	ADJ
american_scientific_journal-3703	487	18	figure	figure	NOUN
american_scientific_journal-3703	487	19	7	7	NUM
american_scientific_journal-3703	487	20	:	:	PUNCT
american_scientific_journal-3703	487	21	the	the	DET
american_scientific_journal-3703	487	22	initial	initial	ADJ
american_scientific_journal-3703	487	23	x=0.02`50	x=0.02`50	ADJ
american_scientific_journal-3703	487	24	,	,	PUNCT
american_scientific_journal-3703	487	25	n=50	n=50	ADJ
american_scientific_journal-3703	487	26	figure	figure	NOUN
american_scientific_journal-3703	487	27	8	8	NUM
american_scientific_journal-3703	487	28	:	:	PUNCT
american_scientific_journal-3703	487	29	the	the	DET
american_scientific_journal-3703	487	30	initial	initial	ADJ
american_scientific_journal-3703	487	31	x=0.02	x=0.02	PROPN
american_scientific_journal-3703	487	32	,	,	PUNCT
american_scientific_journal-3703	487	33	n=50	n=50	ADJ
american_scientific_journal-3703	487	34	figure	figure	NOUN
american_scientific_journal-3703	487	35	9	9	NUM
american_scientific_journal-3703	487	36	:	:	PUNCT
american_scientific_journal-3703	487	37	the	the	DET
american_scientific_journal-3703	487	38	initial	initial	ADJ
american_scientific_journal-3703	487	39	x=0.02`50	x=0.02`50	PROPN
american_scientific_journal-3703	487	40	,	,	PUNCT
american_scientific_journal-3703	487	41	n=50	n=50	ADJ
american_scientific_journal-3703	487	42	5.5	5.5	NUM
american_scientific_journal-3703	487	43	trajectories	trajectory	NOUN
american_scientific_journal-3703	487	44	of	of	ADP
american_scientific_journal-3703	487	45	doubling	double	VERB
american_scientific_journal-3703	487	46	map	map	NOUN
american_scientific_journal-3703	487	47	5.6	5.6	NUM
american_scientific_journal-3703	487	48	orbit	orbit	NOUN
american_scientific_journal-3703	487	49	analysis	analysis	NOUN
american_scientific_journal-3703	487	50	of	of	ADP
american_scientific_journal-3703	487	51	doubling	double	VERB
american_scientific_journal-3703	487	52	map	map	NOUN
american_scientific_journal-3703	487	53	graphically	graphically	ADV
american_scientific_journal-3703	487	54	the	the	DET
american_scientific_journal-3703	487	55	doubling	double	VERB
american_scientific_journal-3703	487	56	map	map	NOUN
american_scientific_journal-3703	487	57	is	be	AUX
american_scientific_journal-3703	487	58	defined	define	VERB
american_scientific_journal-3703	487	59	by	by	ADP