id	sid	tid	token	lemma	pos
ejde-637	1	1	electronic	electronic	ADJ
ejde-637	1	2	journal	journal	NOUN
ejde-637	1	3	of	of	ADP
ejde-637	1	4	differential	differential	ADJ
ejde-637	1	5	equations	equation	NOUN
ejde-637	1	6	,	,	PUNCT
ejde-637	1	7	vol	vol	NOUN
ejde-637	1	8	.	.	NOUN
ejde-637	1	9	2024	2024	NUM
ejde-637	1	10	(	(	PUNCT
ejde-637	1	11	2024	2024	NUM
ejde-637	1	12	)	)	PUNCT
ejde-637	1	13	,	,	PUNCT
ejde-637	1	14	no	no	INTJ
ejde-637	1	15	.	.	NOUN
ejde-637	1	16	57	57	NUM
ejde-637	1	17	,	,	PUNCT
ejde-637	1	18	pp	pp	PROPN
ejde-637	1	19	.	.	PUNCT
ejde-637	2	1	1–23	1–23	PROPN
ejde-637	2	2	.	.	PUNCT
ejde-637	3	1	issn	issn	PROPN
ejde-637	3	2	:	:	PUNCT
ejde-637	3	3	1072	1072	NUM
ejde-637	3	4	-	-	SYM
ejde-637	3	5	6691	6691	NUM
ejde-637	3	6	.	.	PUNCT
ejde-637	4	1	url	url	PROPN
ejde-637	4	2	:	:	PUNCT
ejde-637	4	3	https://ejde.math.txstate.edu	https://ejde.math.txstate.edu	PROPN
ejde-637	4	4	,	,	PUNCT
ejde-637	4	5	https://ejde.math.unt.edu	https://ejde.math.unt.edu	PROPN
ejde-637	4	6	doi	doi	PROPN
ejde-637	4	7	:	:	PUNCT
ejde-637	4	8	10.58997	10.58997	NUM
ejde-637	4	9	/	/	SYM
ejde-637	4	10	ejde.2024.57	ejde.2024.57	ADP
ejde-637	4	11	global	global	ADJ
ejde-637	4	12	dynamics	dynamic	NOUN
ejde-637	4	13	of	of	ADP
ejde-637	4	14	a	a	DET
ejde-637	4	15	special	special	ADJ
ejde-637	4	16	class	class	NOUN
ejde-637	4	17	of	of	ADP
ejde-637	4	18	planar	planar	ADJ
ejde-637	4	19	sector	sector	NOUN
ejde-637	4	20	-	-	PUNCT
ejde-637	4	21	wise	wise	ADJ
ejde-637	4	22	linear	linear	PROPN
ejde-637	4	23	systems	system	NOUN
ejde-637	4	24	qian	qian	PROPN
ejde-637	4	25	-	-	PUNCT
ejde-637	4	26	qian	qian	PROPN
ejde-637	4	27	han	han	PROPN
ejde-637	4	28	,	,	PUNCT
ejde-637	4	29	song	song	PROPN
ejde-637	4	30	-	-	PUNCT
ejde-637	4	31	mei	mei	PROPN
ejde-637	4	32	huan	huan	PROPN
ejde-637	4	33	abstract	abstract	PROPN
ejde-637	4	34	.	.	PUNCT
ejde-637	5	1	in	in	ADP
ejde-637	5	2	this	this	DET
ejde-637	5	3	article	article	NOUN
ejde-637	5	4	,	,	PUNCT
ejde-637	5	5	we	we	PRON
ejde-637	5	6	study	study	VERB
ejde-637	5	7	the	the	DET
ejde-637	5	8	global	global	ADJ
ejde-637	5	9	dynamics	dynamic	NOUN
ejde-637	5	10	of	of	ADP
ejde-637	5	11	a	a	DET
ejde-637	5	12	special	special	ADJ
ejde-637	5	13	class	class	NOUN
ejde-637	5	14	of	of	ADP
ejde-637	5	15	planar	planar	ADJ
ejde-637	5	16	sector	sector	NOUN
ejde-637	5	17	-	-	PUNCT
ejde-637	5	18	wise	wise	ADJ
ejde-637	5	19	linear	linear	ADJ
ejde-637	5	20	differential	differential	NOUN
ejde-637	5	21	systems	system	NOUN
ejde-637	5	22	with	with	ADP
ejde-637	5	23	two	two	NUM
ejde-637	5	24	subsystems	subsystem	NOUN
ejde-637	5	25	being	be	AUX
ejde-637	5	26	the	the	DET
ejde-637	5	27	same	same	ADJ
ejde-637	5	28	except	except	SCONJ
ejde-637	5	29	for	for	ADP
ejde-637	5	30	their	their	PRON
ejde-637	5	31	equilibriums	equilibrium	NOUN
ejde-637	5	32	.	.	PUNCT
ejde-637	6	1	taking	take	VERB
ejde-637	6	2	the	the	DET
ejde-637	6	3	position	position	NOUN
ejde-637	6	4	of	of	ADP
ejde-637	6	5	one	one	NUM
ejde-637	6	6	equilibrium	equilibrium	NOUN
ejde-637	6	7	as	as	ADP
ejde-637	6	8	the	the	DET
ejde-637	6	9	bifurcation	bifurcation	NOUN
ejde-637	6	10	parameter	parameter	NOUN
ejde-637	6	11	,	,	PUNCT
ejde-637	6	12	we	we	PRON
ejde-637	6	13	provide	provide	VERB
ejde-637	6	14	a	a	DET
ejde-637	6	15	complete	complete	ADJ
ejde-637	6	16	analysis	analysis	NOUN
ejde-637	6	17	about	about	ADP
ejde-637	6	18	sliding	slide	VERB
ejde-637	6	19	cycle	cycle	NOUN
ejde-637	6	20	bifurcation	bifurcation	NOUN
ejde-637	6	21	and	and	CCONJ
ejde-637	6	22	sliding	slide	VERB
ejde-637	6	23	homoclinic	homoclinic	ADJ
ejde-637	6	24	bifurcation	bifurcation	NOUN
ejde-637	6	25	.	.	PUNCT
ejde-637	7	1	moreover	moreover	ADV
ejde-637	7	2	,	,	PUNCT
ejde-637	7	3	we	we	PRON
ejde-637	7	4	obtain	obtain	VERB
ejde-637	7	5	the	the	DET
ejde-637	7	6	existence	existence	NOUN
ejde-637	7	7	of	of	ADP
ejde-637	7	8	all	all	DET
ejde-637	7	9	important	important	ADJ
ejde-637	7	10	separatrix	separatrix	NOUN
ejde-637	7	11	orbits	orbit	NOUN
ejde-637	7	12	and	and	CCONJ
ejde-637	7	13	their	their	PRON
ejde-637	7	14	dependence	dependence	NOUN
ejde-637	7	15	on	on	ADP
ejde-637	7	16	the	the	DET
ejde-637	7	17	bifurcation	bifurcation	NOUN
ejde-637	7	18	parameter	parameter	NOUN
ejde-637	7	19	,	,	PUNCT
ejde-637	7	20	including	include	VERB
ejde-637	7	21	sliding	slide	VERB
ejde-637	7	22	heteroclinic	heteroclinic	ADJ
ejde-637	7	23	orbit	orbit	NOUN
ejde-637	7	24	,	,	PUNCT
ejde-637	7	25	heteroclinic	heteroclinic	ADJ
ejde-637	7	26	cycle	cycle	NOUN
ejde-637	7	27	,	,	PUNCT
ejde-637	7	28	limit	limit	VERB
ejde-637	7	29	cycle	cycle	NOUN
ejde-637	7	30	,	,	PUNCT
ejde-637	7	31	sliding	slide	VERB
ejde-637	7	32	homoclinic	homoclinic	ADJ
ejde-637	7	33	cycle	cycle	NOUN
ejde-637	7	34	and	and	CCONJ
ejde-637	7	35	sliding	slide	VERB
ejde-637	7	36	cycle	cycle	NOUN
ejde-637	7	37	.	.	PUNCT
ejde-637	8	1	1	1	X
ejde-637	8	2	.	.	X
ejde-637	8	3	introduction	introduction	NOUN
ejde-637	8	4	piecewise	piecewise	NOUN
ejde-637	8	5	smooth	smooth	ADJ
ejde-637	8	6	dynamical	dynamical	ADJ
ejde-637	8	7	systems	system	NOUN
ejde-637	8	8	arise	arise	VERB
ejde-637	8	9	in	in	ADP
ejde-637	8	10	applications	application	NOUN
ejde-637	8	11	,	,	PUNCT
ejde-637	8	12	see	see	VERB
ejde-637	8	13	[	[	X
ejde-637	8	14	1	1	NUM
ejde-637	8	15	,	,	PUNCT
ejde-637	8	16	2	2	NUM
ejde-637	8	17	,	,	PUNCT
ejde-637	8	18	3	3	NUM
ejde-637	8	19	,	,	PUNCT
ejde-637	8	20	4	4	NUM
ejde-637	8	21	,	,	PUNCT
ejde-637	8	22	6	6	NUM
ejde-637	8	23	,	,	PUNCT
ejde-637	8	24	9	9	NUM
ejde-637	8	25	,	,	PUNCT
ejde-637	8	26	10	10	NUM
ejde-637	8	27	,	,	PUNCT
ejde-637	8	28	13	13	NUM
ejde-637	8	29	,	,	PUNCT
ejde-637	8	30	32	32	NUM
ejde-637	8	31	,	,	PUNCT
ejde-637	8	32	33	33	NUM
ejde-637	8	33	,	,	PUNCT
ejde-637	8	34	34	34	NUM
ejde-637	8	35	,	,	PUNCT
ejde-637	8	36	35	35	NUM
ejde-637	8	37	,	,	PUNCT
ejde-637	8	38	45	45	NUM
ejde-637	8	39	,	,	PUNCT
ejde-637	8	40	46	46	NUM
ejde-637	8	41	,	,	PUNCT
ejde-637	8	42	47	47	NUM
ejde-637	8	43	,	,	PUNCT
ejde-637	8	44	51	51	NUM
ejde-637	8	45	,	,	PUNCT
ejde-637	8	46	52	52	NUM
ejde-637	8	47	]	]	PUNCT
ejde-637	8	48	.	.	PUNCT
ejde-637	9	1	as	as	ADP
ejde-637	9	2	the	the	DET
ejde-637	9	3	simplest	simple	ADJ
ejde-637	9	4	piecewise	piecewise	NOUN
ejde-637	9	5	smooth	smooth	ADJ
ejde-637	9	6	dynamical	dynamical	ADJ
ejde-637	9	7	system	system	NOUN
ejde-637	9	8	,	,	PUNCT
ejde-637	9	9	planar	planar	ADJ
ejde-637	9	10	piecewise	piecewise	NOUN
ejde-637	9	11	linear	linear	NOUN
ejde-637	9	12	systems	system	NOUN
ejde-637	9	13	(	(	PUNCT
ejde-637	9	14	hereafter	hereafter	ADV
ejde-637	9	15	referred	refer	VERB
ejde-637	9	16	as	as	ADP
ejde-637	9	17	pwlss	pwlss	ADV
ejde-637	9	18	)	)	PUNCT
ejde-637	9	19	with	with	SCONJ
ejde-637	9	20	two	two	NUM
ejde-637	9	21	pieces	piece	NOUN
ejde-637	9	22	separated	separate	VERB
ejde-637	9	23	by	by	ADP
ejde-637	9	24	a	a	DET
ejde-637	9	25	straight	straight	ADJ
ejde-637	9	26	line	line	NOUN
ejde-637	9	27	has	have	AUX
ejde-637	9	28	been	be	AUX
ejde-637	9	29	deeply	deeply	ADV
ejde-637	9	30	studied	study	VERB
ejde-637	9	31	in	in	ADP
ejde-637	9	32	recent	recent	ADJ
ejde-637	9	33	years	year	NOUN
ejde-637	10	1	[	[	X
ejde-637	10	2	12	12	NUM
ejde-637	10	3	,	,	PUNCT
ejde-637	10	4	14	14	NUM
ejde-637	10	5	,	,	PUNCT
ejde-637	10	6	15	15	NUM
ejde-637	10	7	,	,	PUNCT
ejde-637	10	8	16	16	NUM
ejde-637	10	9	,	,	PUNCT
ejde-637	10	10	17	17	NUM
ejde-637	10	11	,	,	PUNCT
ejde-637	10	12	19	19	NUM
ejde-637	10	13	,	,	PUNCT
ejde-637	10	14	23	23	NUM
ejde-637	10	15	,	,	PUNCT
ejde-637	10	16	29	29	NUM
ejde-637	10	17	,	,	PUNCT
ejde-637	10	18	30	30	NUM
ejde-637	10	19	,	,	PUNCT
ejde-637	10	20	36	36	NUM
ejde-637	10	21	,	,	PUNCT
ejde-637	10	22	42	42	NUM
ejde-637	10	23	]	]	PUNCT
ejde-637	10	24	,	,	PUNCT
ejde-637	10	25	mainly	mainly	ADV
ejde-637	10	26	due	due	ADP
ejde-637	10	27	to	to	ADP
ejde-637	10	28	their	their	PRON
ejde-637	10	29	use	use	NOUN
ejde-637	10	30	in	in	ADP
ejde-637	10	31	analyzing	analyze	VERB
ejde-637	10	32	the	the	DET
ejde-637	10	33	dynamics	dynamic	NOUN
ejde-637	10	34	of	of	ADP
ejde-637	10	35	complex	complex	ADJ
ejde-637	10	36	systems	system	NOUN
ejde-637	10	37	locally	locally	ADV
ejde-637	10	38	,	,	PUNCT
ejde-637	10	39	the	the	DET
ejde-637	10	40	explicit	explicit	ADJ
ejde-637	10	41	solvability	solvability	NOUN
ejde-637	10	42	of	of	ADP
ejde-637	10	43	each	each	DET
ejde-637	10	44	linear	linear	ADJ
ejde-637	10	45	subsystem	subsystem	NOUN
ejde-637	10	46	and	and	CCONJ
ejde-637	10	47	their	their	PRON
ejde-637	10	48	own	own	ADJ
ejde-637	10	49	applications	application	NOUN
ejde-637	10	50	in	in	ADP
ejde-637	10	51	modeling	model	VERB
ejde-637	10	52	real	real	ADJ
ejde-637	10	53	systems	system	NOUN
ejde-637	10	54	.	.	PUNCT
ejde-637	11	1	the	the	DET
ejde-637	11	2	discontinuity	discontinuity	NOUN
ejde-637	11	3	of	of	ADP
ejde-637	11	4	vector	vector	NOUN
ejde-637	11	5	field	field	NOUN
ejde-637	11	6	appeared	appear	VERB
ejde-637	11	7	in	in	ADP
ejde-637	11	8	piecewise	piecewise	NOUN
ejde-637	11	9	smooth	smooth	ADJ
ejde-637	11	10	systems	system	NOUN
ejde-637	11	11	induces	induce	VERB
ejde-637	11	12	many	many	ADJ
ejde-637	11	13	dynamics	dynamic	NOUN
ejde-637	11	14	that	that	PRON
ejde-637	11	15	are	be	AUX
ejde-637	11	16	more	more	ADV
ejde-637	11	17	complicated	complicated	ADJ
ejde-637	11	18	and	and	CCONJ
ejde-637	11	19	a	a	DET
ejde-637	11	20	lot	lot	NOUN
ejde-637	11	21	of	of	ADP
ejde-637	11	22	dibs	dib	NOUN
ejde-637	11	23	having	have	VERB
ejde-637	11	24	new	new	ADJ
ejde-637	11	25	bifurcation	bifurcation	NOUN
ejde-637	11	26	mechanisms	mechanism	NOUN
ejde-637	11	27	,	,	PUNCT
ejde-637	11	28	see	see	VERB
ejde-637	11	29	[	[	X
ejde-637	11	30	18	18	NUM
ejde-637	11	31	,	,	PUNCT
ejde-637	11	32	36	36	NUM
ejde-637	11	33	,	,	PUNCT
ejde-637	11	34	50	50	NUM
ejde-637	11	35	,	,	PUNCT
ejde-637	11	36	53	53	NUM
ejde-637	11	37	]	]	PUNCT
ejde-637	11	38	.	.	PUNCT
ejde-637	12	1	even	even	ADV
ejde-637	12	2	in	in	ADP
ejde-637	12	3	planar	planar	ADJ
ejde-637	12	4	pwlss	pwlss	PROPN
ejde-637	12	5	,	,	PUNCT
ejde-637	12	6	we	we	PRON
ejde-637	12	7	can	can	AUX
ejde-637	12	8	see	see	VERB
ejde-637	12	9	some	some	DET
ejde-637	12	10	kind	kind	NOUN
ejde-637	12	11	of	of	ADP
ejde-637	12	12	sliding	slide	VERB
ejde-637	12	13	cycles	cycle	NOUN
ejde-637	12	14	,	,	PUNCT
ejde-637	12	15	for	for	ADP
ejde-637	12	16	example	example	NOUN
ejde-637	12	17	,	,	PUNCT
ejde-637	12	18	sliding	slide	VERB
ejde-637	12	19	homoclinic	homoclinic	ADJ
ejde-637	12	20	cycles	cycle	NOUN
ejde-637	12	21	[	[	X
ejde-637	12	22	21	21	NUM
ejde-637	12	23	,	,	PUNCT
ejde-637	12	24	22	22	NUM
ejde-637	12	25	]	]	PUNCT
ejde-637	12	26	and	and	CCONJ
ejde-637	12	27	even	even	ADV
ejde-637	12	28	double	double	ADJ
ejde-637	12	29	homoclinic	homoclinic	ADJ
ejde-637	12	30	loops	loop	NOUN
ejde-637	12	31	,	,	PUNCT
ejde-637	12	32	which	which	PRON
ejde-637	12	33	can	can	AUX
ejde-637	12	34	be	be	AUX
ejde-637	12	35	found	find	VERB
ejde-637	12	36	in	in	ADP
ejde-637	12	37	some	some	DET
ejde-637	12	38	engineering	engineering	NOUN
ejde-637	12	39	models	model	NOUN
ejde-637	12	40	such	such	ADJ
ejde-637	12	41	as	as	ADP
ejde-637	12	42	valve	valve	NOUN
ejde-637	12	43	oscillators	oscillator	NOUN
ejde-637	12	44	[	[	X
ejde-637	12	45	37	37	NUM
ejde-637	12	46	]	]	PUNCT
ejde-637	12	47	,	,	PUNCT
ejde-637	12	48	coulomb	coulomb	NOUN
ejde-637	12	49	friction	friction	NOUN
ejde-637	12	50	[	[	X
ejde-637	12	51	51	51	NUM
ejde-637	12	52	]	]	PUNCT
ejde-637	12	53	and	and	CCONJ
ejde-637	12	54	so	so	ADV
ejde-637	12	55	on	on	ADV
ejde-637	12	56	.	.	PUNCT
ejde-637	13	1	in	in	ADP
ejde-637	13	2	recent	recent	ADJ
ejde-637	13	3	years	year	NOUN
ejde-637	13	4	,	,	PUNCT
ejde-637	13	5	the	the	DET
ejde-637	13	6	main	main	ADJ
ejde-637	13	7	research	research	NOUN
ejde-637	13	8	focus	focus	NOUN
ejde-637	13	9	about	about	ADP
ejde-637	13	10	planar	planar	ADJ
ejde-637	13	11	pwlss	pwlss	ADV
ejde-637	13	12	with	with	ADP
ejde-637	13	13	a	a	DET
ejde-637	13	14	straight	straight	ADJ
ejde-637	13	15	line	line	NOUN
ejde-637	13	16	separation	separation	NOUN
ejde-637	13	17	has	have	AUX
ejde-637	13	18	been	be	AUX
ejde-637	13	19	transformed	transform	VERB
ejde-637	13	20	from	from	ADP
ejde-637	13	21	the	the	DET
ejde-637	13	22	study	study	NOUN
ejde-637	13	23	of	of	ADP
ejde-637	13	24	the	the	DET
ejde-637	13	25	existence	existence	NOUN
ejde-637	13	26	and	and	CCONJ
ejde-637	13	27	bifurcation	bifurcation	NOUN
ejde-637	13	28	of	of	ADP
ejde-637	13	29	crossing	crossing	NOUN
ejde-637	13	30	limit	limit	NOUN
ejde-637	13	31	cycles	cycle	NOUN
ejde-637	13	32	(	(	PUNCT
ejde-637	13	33	see	see	VERB
ejde-637	13	34	[	[	X
ejde-637	13	35	5	5	NUM
ejde-637	13	36	,	,	PUNCT
ejde-637	13	37	11	11	NUM
ejde-637	13	38	,	,	PUNCT
ejde-637	13	39	12	12	NUM
ejde-637	13	40	,	,	PUNCT
ejde-637	13	41	21	21	NUM
ejde-637	13	42	,	,	PUNCT
ejde-637	13	43	23	23	NUM
ejde-637	13	44	,	,	PUNCT
ejde-637	13	45	25	25	NUM
ejde-637	13	46	,	,	PUNCT
ejde-637	13	47	26	26	NUM
ejde-637	13	48	,	,	PUNCT
ejde-637	13	49	27	27	NUM
ejde-637	13	50	,	,	PUNCT
ejde-637	13	51	38	38	NUM
ejde-637	13	52	,	,	PUNCT
ejde-637	13	53	39	39	NUM
ejde-637	13	54	,	,	PUNCT
ejde-637	13	55	40	40	NUM
ejde-637	13	56	,	,	PUNCT
ejde-637	13	57	41	41	NUM
ejde-637	13	58	,	,	PUNCT
ejde-637	13	59	42	42	NUM
ejde-637	13	60	,	,	PUNCT
ejde-637	13	61	43	43	NUM
ejde-637	13	62	,	,	PUNCT
ejde-637	13	63	47	47	NUM
ejde-637	13	64	]	]	PUNCT
ejde-637	13	65	)	)	PUNCT
ejde-637	13	66	into	into	ADP
ejde-637	13	67	the	the	DET
ejde-637	13	68	study	study	NOUN
ejde-637	13	69	of	of	ADP
ejde-637	13	70	some	some	DET
ejde-637	13	71	critical	critical	ADJ
ejde-637	13	72	sliding	slide	VERB
ejde-637	13	73	orbits	orbit	NOUN
ejde-637	13	74	and	and	CCONJ
ejde-637	13	75	their	their	PRON
ejde-637	13	76	bifurcations	bifurcation	NOUN
ejde-637	13	77	.	.	PUNCT
ejde-637	14	1	for	for	ADP
ejde-637	14	2	example	example	NOUN
ejde-637	14	3	,	,	PUNCT
ejde-637	14	4	appearance	appearance	NOUN
ejde-637	14	5	of	of	ADP
ejde-637	14	6	crossing	crossing	NOUN
ejde-637	14	7	-	-	PUNCT
ejde-637	14	8	sliding	slide	VERB
ejde-637	14	9	bifurcation	bifurcation	NOUN
ejde-637	14	10	and	and	CCONJ
ejde-637	14	11	a	a	DET
ejde-637	14	12	double	double	ADJ
ejde-637	14	13	tangency	tangency	NOUN
ejde-637	14	14	,	,	PUNCT
ejde-637	14	15	pseudo	pseudo	NOUN
ejde-637	14	16	-	-	ADJ
ejde-637	14	17	heteroclinic	heteroclinic	ADJ
ejde-637	14	18	bifurcations	bifurcation	NOUN
ejde-637	14	19	,	,	PUNCT
ejde-637	14	20	pseudo	pseudo	NOUN
ejde-637	14	21	-	-	ADJ
ejde-637	14	22	homoclinic	homoclinic	ADJ
ejde-637	14	23	bifurcation	bifurcation	NOUN
ejde-637	14	24	,	,	PUNCT
ejde-637	14	25	pseudo	pseudo	NOUN
ejde-637	14	26	-	-	ADJ
ejde-637	14	27	hopf	hopf	ADJ
ejde-637	14	28	bifurcation	bifurcation	NOUN
ejde-637	14	29	and	and	CCONJ
ejde-637	14	30	so	so	ADV
ejde-637	14	31	on	on	ADV
ejde-637	14	32	(	(	PUNCT
ejde-637	14	33	[	[	X
ejde-637	14	34	8	8	NUM
ejde-637	14	35	,	,	PUNCT
ejde-637	14	36	20	20	NUM
ejde-637	14	37	,	,	PUNCT
ejde-637	14	38	36	36	NUM
ejde-637	14	39	]	]	PUNCT
ejde-637	14	40	)	)	PUNCT
ejde-637	14	41	.	.	PUNCT
ejde-637	15	1	2020	2020	NUM
ejde-637	15	2	mathematics	mathematic	NOUN
ejde-637	15	3	subject	subject	ADJ
ejde-637	15	4	classification	classification	NOUN
ejde-637	15	5	.	.	PUNCT
ejde-637	16	1	34c23	34c23	NUM
ejde-637	16	2	,	,	PUNCT
ejde-637	16	3	34c60	34c60	NUM
ejde-637	16	4	,	,	PUNCT
ejde-637	16	5	34c37	34c37	NUM
ejde-637	16	6	.	.	PUNCT
ejde-637	17	1	key	key	ADJ
ejde-637	17	2	words	word	NOUN
ejde-637	17	3	and	and	CCONJ
ejde-637	17	4	phrases	phrase	NOUN
ejde-637	17	5	.	.	PUNCT
ejde-637	18	1	sector	sector	NOUN
ejde-637	18	2	-	-	PUNCT
ejde-637	18	3	wise	wise	ADJ
ejde-637	18	4	linear	linear	NOUN
ejde-637	18	5	systems	system	NOUN
ejde-637	18	6	;	;	PUNCT
ejde-637	18	7	sliding	slide	VERB
ejde-637	18	8	cycle	cycle	NOUN
ejde-637	18	9	bifurcation	bifurcation	NOUN
ejde-637	18	10	;	;	PUNCT
ejde-637	18	11	sliding	slide	VERB
ejde-637	18	12	homoclinic	homoclinic	ADJ
ejde-637	18	13	bifurcation	bifurcation	NOUN
ejde-637	18	14	;	;	PUNCT
ejde-637	18	15	heteroclinic	heteroclinic	ADJ
ejde-637	18	16	cycle	cycle	NOUN
ejde-637	18	17	;	;	PUNCT
ejde-637	18	18	non	non	ADJ
ejde-637	18	19	-	-	ADJ
ejde-637	18	20	regular	regular	ADJ
ejde-637	18	21	point	point	NOUN
ejde-637	18	22	.	.	PUNCT
ejde-637	19	1	©	©	ADP
ejde-637	19	2	2024	2024	NUM
ejde-637	19	3	.	.	PUNCT
ejde-637	20	1	this	this	DET
ejde-637	20	2	work	work	NOUN
ejde-637	20	3	is	be	AUX
ejde-637	20	4	licensed	license	VERB
ejde-637	20	5	under	under	ADP
ejde-637	20	6	a	a	DET
ejde-637	20	7	cc	cc	NOUN
ejde-637	20	8	by	by	ADP
ejde-637	20	9	4.0	4.0	NUM
ejde-637	20	10	license	license	NOUN
ejde-637	20	11	.	.	PUNCT
ejde-637	21	1	submitted	submit	VERB
ejde-637	21	2	april	april	PROPN
ejde-637	21	3	2	2	NUM
ejde-637	21	4	,	,	PUNCT
ejde-637	21	5	2024	2024	NUM
ejde-637	21	6	.	.	PUNCT
ejde-637	22	1	published	publish	VERB
ejde-637	22	2	september	september	PROPN
ejde-637	22	3	30	30	NUM
ejde-637	22	4	,	,	PUNCT
ejde-637	22	5	2024	2024	NUM
ejde-637	22	6	.	.	PUNCT
ejde-637	22	7	1	1	NUM
ejde-637	22	8	2	2	NUM
ejde-637	22	9	q.-q	q.-q	NOUN
ejde-637	22	10	.	.	PUNCT
ejde-637	23	1	han	han	PROPN
ejde-637	23	2	,	,	PUNCT
ejde-637	23	3	s.-m	s.-m	PROPN
ejde-637	23	4	.	.	PUNCT
ejde-637	24	1	huan	huan	PROPN
ejde-637	24	2	ejde-2024/57	ejde-2024/57	PROPN
ejde-637	24	3	in	in	ADP
ejde-637	24	4	addition	addition	NOUN
ejde-637	24	5	to	to	ADP
ejde-637	24	6	this	this	PRON
ejde-637	24	7	,	,	PUNCT
ejde-637	24	8	the	the	DET
ejde-637	24	9	perturbation	perturbation	NOUN
ejde-637	24	10	to	to	ADP
ejde-637	24	11	discontinuity	discontinuity	NOUN
ejde-637	24	12	boundary	boundary	ADJ
ejde-637	24	13	as	as	ADP
ejde-637	24	14	an	an	DET
ejde-637	24	15	important	important	ADJ
ejde-637	24	16	common	common	ADJ
ejde-637	24	17	phenomenon	phenomenon	NOUN
ejde-637	24	18	should	should	AUX
ejde-637	24	19	also	also	ADV
ejde-637	24	20	be	be	AUX
ejde-637	24	21	taken	take	VERB
ejde-637	24	22	into	into	ADP
ejde-637	24	23	consideration	consideration	NOUN
ejde-637	24	24	,	,	PUNCT
ejde-637	24	25	since	since	SCONJ
ejde-637	24	26	which	which	PRON
ejde-637	24	27	can	can	AUX
ejde-637	24	28	lead	lead	VERB
ejde-637	24	29	to	to	ADP
ejde-637	24	30	many	many	ADJ
ejde-637	24	31	new	new	ADJ
ejde-637	24	32	interesting	interesting	ADJ
ejde-637	24	33	phenomena	phenomenon	NOUN
ejde-637	24	34	and	and	CCONJ
ejde-637	24	35	affect	affect	VERB
ejde-637	24	36	both	both	DET
ejde-637	24	37	the	the	DET
ejde-637	24	38	number	number	NOUN
ejde-637	24	39	and	and	CCONJ
ejde-637	24	40	type	type	NOUN
ejde-637	24	41	of	of	ADP
ejde-637	24	42	crossing	crossing	NOUN
ejde-637	24	43	limit	limit	NOUN
ejde-637	24	44	cycles	cycle	NOUN
ejde-637	24	45	,	,	PUNCT
ejde-637	24	46	see	see	VERB
ejde-637	24	47	[	[	X
ejde-637	24	48	7	7	NUM
ejde-637	24	49	,	,	PUNCT
ejde-637	24	50	24	24	NUM
ejde-637	24	51	,	,	PUNCT
ejde-637	24	52	28	28	NUM
ejde-637	24	53	,	,	PUNCT
ejde-637	24	54	29	29	NUM
ejde-637	24	55	,	,	PUNCT
ejde-637	24	56	44	44	NUM
ejde-637	24	57	,	,	PUNCT
ejde-637	24	58	46	46	NUM
ejde-637	24	59	,	,	PUNCT
ejde-637	24	60	54	54	NUM
ejde-637	24	61	,	,	PUNCT
ejde-637	24	62	55	55	NUM
ejde-637	24	63	,	,	PUNCT
ejde-637	24	64	56	56	NUM
ejde-637	24	65	]	]	PUNCT
ejde-637	24	66	.	.	PUNCT
ejde-637	25	1	therefore	therefore	ADV
ejde-637	25	2	,	,	PUNCT
ejde-637	25	3	in	in	ADP
ejde-637	25	4	this	this	DET
ejde-637	25	5	article	article	NOUN
ejde-637	25	6	,	,	PUNCT
ejde-637	25	7	we	we	PRON
ejde-637	25	8	study	study	VERB
ejde-637	25	9	a	a	DET
ejde-637	25	10	special	special	ADJ
ejde-637	25	11	family	family	NOUN
ejde-637	25	12	of	of	ADP
ejde-637	25	13	planar	planar	ADJ
ejde-637	25	14	pwlss	pwlss	ADV
ejde-637	25	15	with	with	ADP
ejde-637	25	16	two	two	NUM
ejde-637	25	17	zones	zone	NOUN
ejde-637	25	18	under	under	ADP
ejde-637	25	19	two	two	NUM
ejde-637	25	20	considerations	consideration	NOUN
ejde-637	25	21	,	,	PUNCT
ejde-637	25	22	i.e.	i.e.	X
ejde-637	25	23	,	,	PUNCT
ejde-637	25	24	the	the	DET
ejde-637	25	25	discontinuity	discontinuity	NOUN
ejde-637	25	26	boundary	boundary	NOUN
ejde-637	25	27	is	be	AUX
ejde-637	25	28	given	give	VERB
ejde-637	25	29	by	by	ADP
ejde-637	25	30	two	two	NUM
ejde-637	25	31	rays	ray	NOUN
ejde-637	25	32	starting	start	VERB
ejde-637	25	33	from	from	ADP
ejde-637	25	34	the	the	DET
ejde-637	25	35	same	same	ADJ
ejde-637	25	36	point	point	NOUN
ejde-637	25	37	(	(	PUNCT
ejde-637	25	38	which	which	PRON
ejde-637	25	39	are	be	AUX
ejde-637	25	40	called	call	VERB
ejde-637	25	41	planar	planar	ADJ
ejde-637	25	42	sector	sector	NOUN
ejde-637	25	43	-	-	PUNCT
ejde-637	25	44	wise	wise	ADJ
ejde-637	25	45	linear	linear	NOUN
ejde-637	25	46	systems	system	NOUN
ejde-637	25	47	in	in	ADP
ejde-637	25	48	[	[	X
ejde-637	25	49	30	30	NUM
ejde-637	25	50	]	]	PUNCT
ejde-637	25	51	)	)	PUNCT
ejde-637	25	52	and	and	CCONJ
ejde-637	25	53	investigate	investigate	VERB
ejde-637	25	54	the	the	DET
ejde-637	25	55	global	global	ADJ
ejde-637	25	56	qualitative	qualitative	ADJ
ejde-637	25	57	dynamics	dynamic	NOUN
ejde-637	25	58	of	of	ADP
ejde-637	25	59	such	such	ADJ
ejde-637	25	60	systems	system	NOUN
ejde-637	25	61	.	.	PUNCT
ejde-637	26	1	particularly	particularly	ADV
ejde-637	26	2	,	,	PUNCT
ejde-637	26	3	we	we	PRON
ejde-637	26	4	have	have	AUX
ejde-637	26	5	obtained	obtain	VERB
ejde-637	26	6	explicit	explicit	ADJ
ejde-637	26	7	dependence	dependence	NOUN
ejde-637	26	8	on	on	ADP
ejde-637	26	9	system	system	NOUN
ejde-637	26	10	parameters	parameter	NOUN
ejde-637	26	11	of	of	ADP
ejde-637	26	12	the	the	DET
ejde-637	26	13	existence	existence	NOUN
ejde-637	26	14	,	,	PUNCT
ejde-637	26	15	stability	stability	NOUN
ejde-637	26	16	and	and	CCONJ
ejde-637	26	17	number	number	NOUN
ejde-637	26	18	of	of	ADP
ejde-637	26	19	all	all	DET
ejde-637	26	20	kinds	kind	NOUN
ejde-637	26	21	of	of	ADP
ejde-637	26	22	special	special	ADJ
ejde-637	26	23	sliding	slide	VERB
ejde-637	26	24	points	point	NOUN
ejde-637	26	25	for	for	ADP
ejde-637	26	26	these	these	DET
ejde-637	26	27	planar	planar	ADJ
ejde-637	26	28	sector	sector	NOUN
ejde-637	26	29	-	-	PUNCT
ejde-637	26	30	wise	wise	ADJ
ejde-637	26	31	linear	linear	NOUN
ejde-637	26	32	systems	system	NOUN
ejde-637	26	33	in	in	ADP
ejde-637	26	34	[	[	X
ejde-637	26	35	31	31	NUM
ejde-637	26	36	]	]	PUNCT
ejde-637	26	37	.	.	PUNCT
ejde-637	27	1	notice	notice	VERB
ejde-637	27	2	that	that	SCONJ
ejde-637	27	3	the	the	DET
ejde-637	27	4	discontinuity	discontinuity	NOUN
ejde-637	27	5	boundary	boundary	NOUN
ejde-637	27	6	of	of	ADP
ejde-637	27	7	planar	planar	ADJ
ejde-637	27	8	sector	sector	NOUN
ejde-637	27	9	-	-	PUNCT
ejde-637	27	10	wise	wise	ADJ
ejde-637	27	11	linear	linear	NOUN
ejde-637	27	12	systems	system	NOUN
ejde-637	27	13	can	can	AUX
ejde-637	27	14	be	be	AUX
ejde-637	27	15	written	write	VERB
ejde-637	27	16	as	as	ADP
ejde-637	27	17	σπ/2	σπ/2	PROPN
ejde-637	27	18	(	(	PUNCT
ejde-637	27	19	see	see	VERB
ejde-637	27	20	[	[	X
ejde-637	27	21	28	28	NUM
ejde-637	27	22	,	,	PUNCT
ejde-637	27	23	theorem	theorem	VERB
ejde-637	27	24	1	1	NUM
ejde-637	27	25	]	]	PUNCT
ejde-637	27	26	)	)	PUNCT
ejde-637	27	27	,	,	PUNCT
ejde-637	27	28	i.e.	i.e.	X
ejde-637	27	29	,	,	PUNCT
ejde-637	27	30	σπ/2	σπ/2	PROPN
ejde-637	27	31	=	=	SYM
ejde-637	27	32	{	{	PUNCT
ejde-637	27	33	(	(	PUNCT
ejde-637	27	34	x	x	NOUN
ejde-637	27	35	,	,	PUNCT
ejde-637	27	36	y	y	PROPN
ejde-637	27	37	)	)	PUNCT
ejde-637	27	38	:	:	PUNCT
ejde-637	27	39	x	x	X
ejde-637	27	40	≥	≥	X
ejde-637	27	41	0	0	NUM
ejde-637	27	42	and	and	CCONJ
ejde-637	27	43	y	y	PROPN
ejde-637	27	44	=	=	SYM
ejde-637	27	45	0	0	NUM
ejde-637	27	46	}	}	PUNCT
ejde-637	27	47	∪	∪	X
ejde-637	27	48	{	{	PUNCT
ejde-637	27	49	(	(	PUNCT
ejde-637	27	50	x	x	NOUN
ejde-637	27	51	,	,	PUNCT
ejde-637	27	52	y	y	PROPN
ejde-637	27	53	)	)	PUNCT
ejde-637	27	54	:	:	PUNCT
ejde-637	28	1	x	x	SYM
ejde-637	28	2	=	=	SYM
ejde-637	28	3	0	0	NUM
ejde-637	28	4	and	and	CCONJ
ejde-637	28	5	y	y	PROPN
ejde-637	28	6	≥	≥	NUM
ejde-637	28	7	0	0	NUM
ejde-637	28	8	}	}	PUNCT
ejde-637	28	9	.	.	PUNCT
ejde-637	29	1	so	so	ADV
ejde-637	29	2	,	,	PUNCT
ejde-637	29	3	here	here	ADV
ejde-637	29	4	we	we	PRON
ejde-637	29	5	consider	consider	VERB
ejde-637	29	6	the	the	DET
ejde-637	29	7	planar	planar	ADJ
ejde-637	29	8	pwlss	pwlss	ADJ
ejde-637	29	9	ẋ	ẋ	PUNCT
ejde-637	30	1	=	=	PRON
ejde-637	30	2	{	{	PUNCT
ejde-637	30	3	f+(x	f+(x	PROPN
ejde-637	30	4	)	)	PUNCT
ejde-637	30	5	=	=	SYM
ejde-637	30	6	(	(	PUNCT
ejde-637	30	7	f+	f+	PROPN
ejde-637	30	8	1	1	NUM
ejde-637	30	9	(	(	PUNCT
ejde-637	30	10	x	x	NOUN
ejde-637	30	11	)	)	PUNCT
ejde-637	30	12	,	,	PUNCT
ejde-637	30	13	f+	f+	X
ejde-637	30	14	2	2	NUM
ejde-637	30	15	(	(	PUNCT
ejde-637	30	16	x))t	x))t	PROPN
ejde-637	30	17	=	=	PUNCT
ejde-637	30	18	a	a	X
ejde-637	30	19	·	·	PUNCT
ejde-637	30	20	(	(	PUNCT
ejde-637	30	21	x−	x−	PROPN
ejde-637	30	22	x+	x+	X
ejde-637	30	23	e	e	X
ejde-637	30	24	)	)	PUNCT
ejde-637	30	25	,	,	PUNCT
ejde-637	30	26	if	if	SCONJ
ejde-637	30	27	x	x	SYM
ejde-637	30	28	∈	∈	PROPN
ejde-637	30	29	rπ/2	rπ/2	NOUN
ejde-637	30	30	,	,	PUNCT
ejde-637	30	31	f−(x	f−(x	PROPN
ejde-637	30	32	)	)	PUNCT
ejde-637	30	33	=	=	SYM
ejde-637	30	34	(	(	PUNCT
ejde-637	30	35	f−	f−	PROPN
ejde-637	30	36	1	1	NUM
ejde-637	30	37	(	(	PUNCT
ejde-637	30	38	x	x	NOUN
ejde-637	30	39	)	)	PUNCT
ejde-637	30	40	,	,	PUNCT
ejde-637	30	41	f−	f−	PROPN
ejde-637	30	42	2	2	NUM
ejde-637	30	43	(	(	PUNCT
ejde-637	30	44	x))t	x))t	NOUN
ejde-637	30	45	=	=	PUNCT
ejde-637	30	46	a	a	X
ejde-637	30	47	·	·	PUNCT
ejde-637	30	48	(	(	PUNCT
ejde-637	30	49	x−	x−	PROPN
ejde-637	30	50	x−	x−	PROPN
ejde-637	30	51	e	e	PROPN
ejde-637	30	52	)	)	PUNCT
ejde-637	30	53	,	,	PUNCT
ejde-637	30	54	if	if	SCONJ
ejde-637	30	55	x	x	PROPN
ejde-637	30	56	∈	∈	NOUN
ejde-637	30	57	r3π/2	r3π/2	NUM
ejde-637	30	58	,	,	PUNCT
ejde-637	30	59	(	(	PUNCT
ejde-637	30	60	1.1	1.1	NUM
ejde-637	30	61	)	)	PUNCT
ejde-637	30	62	where	where	SCONJ
ejde-637	30	63	x	x	X
ejde-637	30	64	=	=	PRON
ejde-637	30	65	(	(	PUNCT
ejde-637	30	66	x	x	X
ejde-637	30	67	,	,	PUNCT
ejde-637	30	68	y)t	y)t	PUNCT
ejde-637	30	69	∈	∈	NOUN
ejde-637	30	70	r2	r2	PROPN
ejde-637	30	71	,	,	PUNCT
ejde-637	30	72	x±	x±	PROPN
ejde-637	30	73	e	e	X
ejde-637	30	74	=	=	PRON
ejde-637	30	75	(	(	PUNCT
ejde-637	30	76	x±	x±	PROPN
ejde-637	30	77	e	e	NOUN
ejde-637	30	78	,	,	PUNCT
ejde-637	30	79	y	y	PROPN
ejde-637	30	80	±	±	NUM
ejde-637	30	81	e	e	NOUN
ejde-637	30	82	)	)	PUNCT
ejde-637	30	83	t	t	PROPN
ejde-637	30	84	∈	∈	PROPN
ejde-637	30	85	r2	r2	NOUN
ejde-637	30	86	,	,	PUNCT
ejde-637	30	87	x+	x+	X
ejde-637	30	88	e	e	X
ejde-637	30	89	>	>	X
ejde-637	30	90	0	0	NUM
ejde-637	30	91	,	,	PUNCT
ejde-637	30	92	y+e	y+e	NUM
ejde-637	30	93	=	=	SYM
ejde-637	31	1	−y−e	−y−e	ADJ
ejde-637	31	2	>	>	X
ejde-637	31	3	0	0	PROPN
ejde-637	31	4	,	,	PUNCT
ejde-637	31	5	a	a	PRON
ejde-637	31	6	=	=	X
ejde-637	32	1	[	[	X
ejde-637	32	2	aij	aij	X
ejde-637	32	3	]	]	PUNCT
ejde-637	32	4	are	be	AUX
ejde-637	32	5	2×	2×	NUM
ejde-637	32	6	2	2	NUM
ejde-637	32	7	real	real	ADV
ejde-637	32	8	invertible	invertible	ADJ
ejde-637	32	9	matrices	matrix	NOUN
ejde-637	32	10	,	,	PUNCT
ejde-637	32	11	and	and	CCONJ
ejde-637	32	12	rπ/2	rπ/2	NOUN
ejde-637	32	13	=	=	PUNCT
ejde-637	32	14	{	{	PUNCT
ejde-637	32	15	(	(	PUNCT
ejde-637	32	16	x	x	NOUN
ejde-637	32	17	,	,	PUNCT
ejde-637	32	18	y	y	PROPN
ejde-637	32	19	)	)	PUNCT
ejde-637	32	20	:	:	PUNCT
ejde-637	33	1	x	x	X
ejde-637	33	2	>	>	X
ejde-637	33	3	0	0	PUNCT
ejde-637	33	4	and	and	CCONJ
ejde-637	33	5	y	y	PROPN
ejde-637	33	6	>	>	X
ejde-637	33	7	0	0	NUM
ejde-637	33	8	}	}	PUNCT
ejde-637	33	9	,	,	PUNCT
ejde-637	33	10	r3π/2	r3π/2	NUM
ejde-637	33	11	=	=	SYM
ejde-637	33	12	{	{	PUNCT
ejde-637	33	13	(	(	PUNCT
ejde-637	33	14	x	x	NOUN
ejde-637	33	15	,	,	PUNCT
ejde-637	33	16	y	y	PROPN
ejde-637	33	17	)	)	PUNCT
ejde-637	33	18	:	:	PUNCT
ejde-637	34	1	xy	xy	PROPN
ejde-637	34	2	=	=	SYM
ejde-637	34	3	0	0	PROPN
ejde-637	34	4	,	,	PUNCT
ejde-637	34	5	or	or	CCONJ
ejde-637	34	6	x	x	X
ejde-637	34	7	<	<	X
ejde-637	34	8	0	0	NUM
ejde-637	34	9	ory	ory	NOUN
ejde-637	34	10	<	<	X
ejde-637	34	11	0	0	NUM
ejde-637	34	12	}	}	PUNCT
ejde-637	34	13	.	.	PUNCT
ejde-637	35	1	we	we	PRON
ejde-637	35	2	will	will	AUX
ejde-637	35	3	investigate	investigate	VERB
ejde-637	35	4	the	the	DET
ejde-637	35	5	global	global	ADJ
ejde-637	35	6	dynamics	dynamic	NOUN
ejde-637	35	7	of	of	ADP
ejde-637	35	8	system	system	NOUN
ejde-637	35	9	(	(	PUNCT
ejde-637	35	10	1.1	1.1	NUM
ejde-637	35	11	)	)	PUNCT
ejde-637	35	12	as	as	ADP
ejde-637	35	13	the	the	DET
ejde-637	35	14	value	value	NOUN
ejde-637	35	15	of	of	ADP
ejde-637	35	16	x−	x−	PROPN
ejde-637	35	17	e	e	PROPN
ejde-637	35	18	changes	change	NOUN
ejde-637	35	19	when	when	SCONJ
ejde-637	35	20	both	both	DET
ejde-637	35	21	a	a	PRON
ejde-637	35	22	have	have	VERB
ejde-637	35	23	two	two	NUM
ejde-637	35	24	different	different	ADJ
ejde-637	35	25	real	real	ADJ
ejde-637	35	26	eigenvalues	eigenvalue	NOUN
ejde-637	35	27	and	and	CCONJ
ejde-637	35	28	a12a21	a12a21	ADJ
ejde-637	35	29	̸=	̸=	PROPN
ejde-637	35	30	0	0	NUM
ejde-637	35	31	.	.	PUNCT
ejde-637	36	1	for	for	ADP
ejde-637	36	2	convenience	convenience	NOUN
ejde-637	36	3	,	,	PUNCT
ejde-637	36	4	we	we	PRON
ejde-637	36	5	refer	refer	VERB
ejde-637	36	6	to	to	ADP
ejde-637	36	7	the	the	DET
ejde-637	36	8	systems	system	NOUN
ejde-637	36	9	ẋ	ẋ	PUNCT
ejde-637	37	1	=	=	PUNCT
ejde-637	37	2	a	a	X
ejde-637	37	3	·	·	PUNCT
ejde-637	37	4	(	(	PUNCT
ejde-637	37	5	x	x	SYM
ejde-637	37	6	−	−	NOUN
ejde-637	37	7	x+	x+	ADJ
ejde-637	37	8	e	e	NOUN
ejde-637	37	9	)	)	PUNCT
ejde-637	37	10	,	,	PUNCT
ejde-637	37	11	x	x	PUNCT
ejde-637	37	12	∈	∈	NOUN
ejde-637	37	13	rπ/2	rπ/2	NOUN
ejde-637	37	14	and	and	CCONJ
ejde-637	37	15	ẋ	ẋ	PROPN
ejde-637	37	16	=	=	PRON
ejde-637	38	1	a	a	PRON
ejde-637	38	2	·	·	PUNCT
ejde-637	38	3	(	(	PUNCT
ejde-637	38	4	x−	x−	PROPN
ejde-637	38	5	x−	x−	PROPN
ejde-637	38	6	e	e	PROPN
ejde-637	38	7	)	)	PUNCT
ejde-637	38	8	,	,	PUNCT
ejde-637	38	9	x	x	PUNCT
ejde-637	38	10	∈	∈	NOUN
ejde-637	38	11	r3π/2	r3π/2	NOUN
ejde-637	38	12	as	as	ADP
ejde-637	38	13	the	the	DET
ejde-637	38	14	⊕-system	⊕-system	NOUN
ejde-637	38	15	and	and	CCONJ
ejde-637	38	16	the	the	DET
ejde-637	38	17	⊖-system	⊖-system	NOUN
ejde-637	38	18	,	,	PUNCT
ejde-637	38	19	respectively	respectively	ADV
ejde-637	38	20	.	.	PUNCT
ejde-637	39	1	the	the	DET
ejde-637	39	2	remainder	remainder	NOUN
ejde-637	39	3	of	of	ADP
ejde-637	39	4	this	this	DET
ejde-637	39	5	article	article	NOUN
ejde-637	39	6	is	be	AUX
ejde-637	39	7	organized	organize	VERB
ejde-637	39	8	as	as	SCONJ
ejde-637	39	9	follows	follow	VERB
ejde-637	39	10	.	.	PUNCT
ejde-637	40	1	some	some	DET
ejde-637	40	2	preliminaries	preliminary	NOUN
ejde-637	40	3	are	be	AUX
ejde-637	40	4	given	give	VERB
ejde-637	40	5	in	in	ADP
ejde-637	40	6	section	section	NOUN
ejde-637	40	7	2	2	NUM
ejde-637	40	8	.	.	PUNCT
ejde-637	41	1	the	the	DET
ejde-637	41	2	main	main	ADJ
ejde-637	41	3	results	result	NOUN
ejde-637	41	4	can	can	AUX
ejde-637	41	5	be	be	AUX
ejde-637	41	6	found	find	VERB
ejde-637	41	7	in	in	ADP
ejde-637	41	8	section	section	NOUN
ejde-637	41	9	3	3	NUM
ejde-637	41	10	.	.	PUNCT
ejde-637	42	1	the	the	DET
ejde-637	42	2	proofs	proof	NOUN
ejde-637	42	3	of	of	ADP
ejde-637	42	4	the	the	DET
ejde-637	42	5	main	main	ADJ
ejde-637	42	6	results	result	NOUN
ejde-637	42	7	and	and	CCONJ
ejde-637	42	8	some	some	DET
ejde-637	42	9	examples	example	NOUN
ejde-637	42	10	can	can	AUX
ejde-637	42	11	be	be	AUX
ejde-637	42	12	found	find	VERB
ejde-637	42	13	in	in	ADP
ejde-637	42	14	section	section	NOUN
ejde-637	42	15	4	4	NUM
ejde-637	42	16	and	and	CCONJ
ejde-637	42	17	section	section	NOUN
ejde-637	42	18	5	5	NUM
ejde-637	42	19	.	.	PUNCT
ejde-637	43	1	our	our	PRON
ejde-637	43	2	conclusions	conclusion	NOUN
ejde-637	43	3	are	be	AUX
ejde-637	43	4	provided	provide	VERB
ejde-637	43	5	in	in	ADP
ejde-637	43	6	section	section	NOUN
ejde-637	43	7	6	6	NUM
ejde-637	43	8	.	.	NOUN
ejde-637	43	9	2	2	NUM
ejde-637	43	10	.	.	X
ejde-637	43	11	preliminaries	preliminary	NOUN
ejde-637	43	12	let	let	VERB
ejde-637	43	13	σ	σ	NOUN
ejde-637	43	14	:	:	PUNCT
ejde-637	43	15	h(x	h(x	PROPN
ejde-637	43	16	,	,	PUNCT
ejde-637	43	17	y	y	PROPN
ejde-637	43	18	)	)	PUNCT
ejde-637	43	19	=	=	SYM
ejde-637	43	20	0	0	NUM
ejde-637	43	21	be	be	AUX
ejde-637	43	22	the	the	DET
ejde-637	43	23	discontinuity	discontinuity	NOUN
ejde-637	43	24	boundary	boundary	NOUN
ejde-637	43	25	of	of	ADP
ejde-637	43	26	the	the	DET
ejde-637	43	27	planar	planar	ADJ
ejde-637	43	28	pwlss	pwlss	ADJ
ejde-637	43	29	with	with	ADP
ejde-637	43	30	two	two	NUM
ejde-637	43	31	zones	zone	NOUN
ejde-637	43	32	ẋ	ẋ	PUNCT
ejde-637	44	1	=	=	PRON
ejde-637	44	2	{	{	PUNCT
ejde-637	44	3	f+(x	f+(x	PROPN
ejde-637	44	4	)	)	PUNCT
ejde-637	44	5	=	=	SYM
ejde-637	44	6	(	(	PUNCT
ejde-637	44	7	f+	f+	PROPN
ejde-637	44	8	1	1	NUM
ejde-637	44	9	(	(	PUNCT
ejde-637	44	10	x	x	NOUN
ejde-637	44	11	)	)	PUNCT
ejde-637	44	12	,	,	PUNCT
ejde-637	44	13	f+	f+	X
ejde-637	44	14	2	2	NUM
ejde-637	44	15	(	(	PUNCT
ejde-637	44	16	x))t	x))t	NOUN
ejde-637	44	17	,	,	PUNCT
ejde-637	44	18	if	if	SCONJ
ejde-637	44	19	x	x	SYM
ejde-637	44	20	∈	∈	NOUN
ejde-637	44	21	σ+	σ+	NOUN
ejde-637	44	22	=	=	SYM
ejde-637	44	23	{	{	PUNCT
ejde-637	44	24	(	(	PUNCT
ejde-637	44	25	x	x	NOUN
ejde-637	44	26	,	,	PUNCT
ejde-637	44	27	y	y	PROPN
ejde-637	44	28	)	)	PUNCT
ejde-637	44	29	:	:	PUNCT
ejde-637	45	1	h(x	h(x	PROPN
ejde-637	45	2	,	,	PUNCT
ejde-637	45	3	y	y	PROPN
ejde-637	45	4	)	)	PUNCT
ejde-637	45	5	>	>	X
ejde-637	45	6	0	0	NUM
ejde-637	45	7	}	}	PUNCT
ejde-637	45	8	,	,	PUNCT
ejde-637	45	9	f−(x	f−(x	PROPN
ejde-637	45	10	)	)	PUNCT
ejde-637	45	11	=	=	SYM
ejde-637	45	12	(	(	PUNCT
ejde-637	45	13	f−	f−	PROPN
ejde-637	45	14	1	1	NUM
ejde-637	45	15	(	(	PUNCT
ejde-637	45	16	x	x	NOUN
ejde-637	45	17	)	)	PUNCT
ejde-637	45	18	,	,	PUNCT
ejde-637	45	19	f−	f−	PROPN
ejde-637	45	20	2	2	NUM
ejde-637	45	21	(	(	PUNCT
ejde-637	45	22	x))t	x))t	NOUN
ejde-637	45	23	,	,	PUNCT
ejde-637	45	24	if	if	SCONJ
ejde-637	45	25	x	x	PUNCT
ejde-637	45	26	∈	∈	PROPN
ejde-637	45	27	σ−	σ−	NOUN
ejde-637	45	28	=	=	SYM
ejde-637	45	29	{	{	PUNCT
ejde-637	45	30	(	(	PUNCT
ejde-637	45	31	x	x	NOUN
ejde-637	45	32	,	,	PUNCT
ejde-637	45	33	y	y	PROPN
ejde-637	45	34	)	)	PUNCT
ejde-637	45	35	:	:	PUNCT
ejde-637	45	36	h(x	h(x	PROPN
ejde-637	45	37	,	,	PUNCT
ejde-637	45	38	y	y	PROPN
ejde-637	45	39	)	)	PUNCT
ejde-637	45	40	<	<	X
ejde-637	45	41	0	0	NUM
ejde-637	45	42	}	}	PUNCT
ejde-637	45	43	.	.	PUNCT
ejde-637	46	1	(	(	PUNCT
ejde-637	46	2	2.1	2.1	NUM
ejde-637	46	3	)	)	PUNCT
ejde-637	46	4	it	it	PRON
ejde-637	46	5	is	be	AUX
ejde-637	46	6	often	often	ADV
ejde-637	46	7	considered	consider	VERB
ejde-637	46	8	that	that	SCONJ
ejde-637	46	9	the	the	DET
ejde-637	46	10	curve	curve	NOUN
ejde-637	46	11	h(x	h(x	PROPN
ejde-637	46	12	,	,	PUNCT
ejde-637	46	13	y	y	PROPN
ejde-637	46	14	)	)	PUNCT
ejde-637	46	15	=	=	SYM
ejde-637	46	16	0	0	NUM
ejde-637	46	17	is	be	AUX
ejde-637	46	18	smooth	smooth	ADJ
ejde-637	46	19	,	,	PUNCT
ejde-637	46	20	although	although	SCONJ
ejde-637	46	21	it	it	PRON
ejde-637	46	22	maybe	maybe	ADV
ejde-637	46	23	piecewise	piecewise	VERB
ejde-637	46	24	smooth	smooth	ADJ
ejde-637	46	25	.	.	PUNCT
ejde-637	47	1	precisely	precisely	ADV
ejde-637	47	2	,	,	PUNCT
ejde-637	47	3	the	the	DET
ejde-637	47	4	points	point	NOUN
ejde-637	47	5	on	on	ADP
ejde-637	47	6	σ	σ	PROPN
ejde-637	47	7	can	can	AUX
ejde-637	47	8	be	be	AUX
ejde-637	47	9	divided	divide	VERB
ejde-637	47	10	into	into	ADP
ejde-637	47	11	two	two	NUM
ejde-637	47	12	kinds	kind	NOUN
ejde-637	47	13	:	:	PUNCT
ejde-637	47	14	regular	regular	ADJ
ejde-637	47	15	points	point	NOUN
ejde-637	47	16	of	of	ADP
ejde-637	47	17	the	the	DET
ejde-637	47	18	discontinuity	discontinuity	NOUN
ejde-637	47	19	boundary	boundary	NOUN
ejde-637	47	20	(	(	PUNCT
ejde-637	47	21	at	at	ADP
ejde-637	47	22	which	which	PRON
ejde-637	47	23	the	the	DET
ejde-637	47	24	curve	curve	NOUN
ejde-637	47	25	have	have	VERB
ejde-637	47	26	tangent	tangent	NOUN
ejde-637	47	27	lines	line	NOUN
ejde-637	47	28	)	)	PUNCT
ejde-637	47	29	and	and	CCONJ
ejde-637	47	30	non	non	ADJ
ejde-637	47	31	-	-	ADJ
ejde-637	47	32	regular	regular	ADJ
ejde-637	47	33	points	point	NOUN
ejde-637	47	34	of	of	ADP
ejde-637	47	35	the	the	DET
ejde-637	47	36	discontinuity	discontinuity	NOUN
ejde-637	47	37	boundary	boundary	NOUN
ejde-637	47	38	.	.	PUNCT
ejde-637	48	1	in	in	ADP
ejde-637	48	2	this	this	DET
ejde-637	48	3	article	article	NOUN
ejde-637	48	4	,	,	PUNCT
ejde-637	48	5	the	the	DET
ejde-637	48	6	discontinuity	discontinuity	NOUN
ejde-637	48	7	boundary	boundary	NOUN
ejde-637	48	8	we	we	PRON
ejde-637	48	9	considered	consider	VERB
ejde-637	48	10	in	in	ADP
ejde-637	48	11	system	system	NOUN
ejde-637	48	12	(	(	PUNCT
ejde-637	48	13	1.1	1.1	NUM
ejde-637	48	14	)	)	PUNCT
ejde-637	48	15	has	have	VERB
ejde-637	48	16	a	a	DET
ejde-637	48	17	unique	unique	ADJ
ejde-637	48	18	non	non	ADJ
ejde-637	48	19	-	-	ADJ
ejde-637	48	20	regular	regular	ADJ
ejde-637	48	21	point	point	NOUN
ejde-637	48	22	(	(	PUNCT
ejde-637	48	23	0	0	NUM
ejde-637	48	24	,	,	PUNCT
ejde-637	48	25	0	0	NUM
ejde-637	48	26	)	)	PUNCT
ejde-637	48	27	.	.	PUNCT
ejde-637	49	1	so	so	ADV
ejde-637	49	2	,	,	PUNCT
ejde-637	49	3	based	base	VERB
ejde-637	49	4	on	on	ADP
ejde-637	49	5	the	the	DET
ejde-637	49	6	existent	existent	ADJ
ejde-637	49	7	definitions	definition	NOUN
ejde-637	49	8	about	about	ADP
ejde-637	49	9	various	various	ADJ
ejde-637	49	10	peculiar	peculiar	ADJ
ejde-637	49	11	sliding	slide	VERB
ejde-637	49	12	points	point	NOUN
ejde-637	49	13	(	(	PUNCT
ejde-637	49	14	see	see	VERB
ejde-637	49	15	[	[	X
ejde-637	49	16	21	21	NUM
ejde-637	49	17	,	,	PUNCT
ejde-637	49	18	36	36	NUM
ejde-637	49	19	,	,	PUNCT
ejde-637	49	20	50	50	NUM
ejde-637	49	21	,	,	PUNCT
ejde-637	49	22	53	53	NUM
ejde-637	49	23	]	]	PUNCT
ejde-637	49	24	)	)	PUNCT
ejde-637	49	25	,	,	PUNCT
ejde-637	49	26	we	we	PRON
ejde-637	49	27	first	first	ADV
ejde-637	49	28	introduce	introduce	VERB
ejde-637	49	29	some	some	DET
ejde-637	49	30	kinds	kind	NOUN
ejde-637	49	31	of	of	ADP
ejde-637	49	32	regular	regular	ADJ
ejde-637	49	33	points	point	NOUN
ejde-637	49	34	of	of	ADP
ejde-637	49	35	σ	σ	PROPN
ejde-637	49	36	for	for	ADP
ejde-637	49	37	system	system	NOUN
ejde-637	49	38	(	(	PUNCT
ejde-637	49	39	2.1	2.1	NUM
ejde-637	49	40	)	)	PUNCT
ejde-637	49	41	,	,	PUNCT
ejde-637	49	42	and	and	CCONJ
ejde-637	49	43	then	then	ADV
ejde-637	49	44	study	study	VERB
ejde-637	49	45	the	the	DET
ejde-637	49	46	non	non	ADJ
ejde-637	49	47	-	-	ADJ
ejde-637	49	48	regular	regular	ADJ
ejde-637	49	49	point	point	NOUN
ejde-637	49	50	of	of	ADP
ejde-637	49	51	σ	σ	PROPN
ejde-637	49	52	for	for	ADP
ejde-637	49	53	system	system	NOUN
ejde-637	49	54	(	(	PUNCT
ejde-637	49	55	1.1	1.1	NUM
ejde-637	49	56	)	)	PUNCT
ejde-637	49	57	separately	separately	ADV
ejde-637	49	58	.	.	PUNCT
ejde-637	50	1	ejde-2024/57	ejde-2024/57	NOUN
ejde-637	50	2	planar	planar	ADJ
ejde-637	50	3	sector	sector	NOUN
ejde-637	50	4	-	-	PUNCT
ejde-637	50	5	wise	wise	ADJ
ejde-637	50	6	linear	linear	PROPN
ejde-637	50	7	systems	system	NOUN
ejde-637	50	8	3	3	NUM
ejde-637	50	9	definition	definition	NOUN
ejde-637	50	10	2.1	2.1	NUM
ejde-637	50	11	.	.	PUNCT
ejde-637	51	1	a	a	DET
ejde-637	51	2	regular	regular	ADJ
ejde-637	51	3	point	point	NOUN
ejde-637	51	4	p	p	X
ejde-637	51	5	∈	∈	PROPN
ejde-637	51	6	σ	σ	PROPN
ejde-637	51	7	is	be	AUX
ejde-637	51	8	called	call	VERB
ejde-637	51	9	a	a	DET
ejde-637	51	10	crossing	crossing	NOUN
ejde-637	51	11	point	point	NOUN
ejde-637	51	12	if	if	SCONJ
ejde-637	51	13	⟨f+(p	⟨f+(p	PROPN
ejde-637	51	14	)	)	PUNCT
ejde-637	51	15	,	,	PUNCT
ejde-637	51	16	hx(p)⟩	hx(p)⟩	PROPN
ejde-637	51	17	·	·	PUNCT
ejde-637	51	18	⟨f−(p	⟨f−(p	PROPN
ejde-637	51	19	)	)	PUNCT
ejde-637	51	20	,	,	PUNCT
ejde-637	51	21	hx(p)⟩	hx(p)⟩	PROPN
ejde-637	51	22	>	>	X
ejde-637	51	23	0	0	NUM
ejde-637	51	24	,	,	PUNCT
ejde-637	51	25	where	where	SCONJ
ejde-637	51	26	hx(p	hx(p	NOUN
ejde-637	51	27	)	)	PUNCT
ejde-637	51	28	is	be	AUX
ejde-637	51	29	the	the	DET
ejde-637	51	30	transpose	transpose	NOUN
ejde-637	51	31	of	of	ADP
ejde-637	51	32	the	the	DET
ejde-637	51	33	gradient	gradient	NOUN
ejde-637	51	34	of	of	ADP
ejde-637	51	35	the	the	DET
ejde-637	51	36	function	function	NOUN
ejde-637	51	37	h(x	h(x	PROPN
ejde-637	51	38	,	,	PUNCT
ejde-637	51	39	y	y	PROPN
ejde-637	51	40	)	)	PUNCT
ejde-637	51	41	at	at	ADP
ejde-637	51	42	p.	p.	NOUN
ejde-637	51	43	denoted	denote	VERB
ejde-637	51	44	by	by	ADP
ejde-637	51	45	σc	σc	PROPN
ejde-637	51	46	the	the	DET
ejde-637	51	47	set	set	NOUN
ejde-637	51	48	of	of	ADP
ejde-637	51	49	all	all	DET
ejde-637	51	50	crossing	crossing	NOUN
ejde-637	51	51	points	point	NOUN
ejde-637	51	52	.	.	PUNCT
ejde-637	52	1	then	then	ADV
ejde-637	52	2	σc	σc	PROPN
ejde-637	52	3	is	be	AUX
ejde-637	52	4	the	the	DET
ejde-637	52	5	crossing	crossing	NOUN
ejde-637	52	6	set	set	NOUN
ejde-637	52	7	of	of	ADP
ejde-637	52	8	system	system	NOUN
ejde-637	52	9	(	(	PUNCT
ejde-637	52	10	2.1	2.1	NUM
ejde-637	52	11	)	)	PUNCT
ejde-637	52	12	.	.	PUNCT
ejde-637	53	1	definition	definition	NOUN
ejde-637	53	2	2.2	2.2	NUM
ejde-637	53	3	.	.	PUNCT
ejde-637	54	1	a	a	DET
ejde-637	54	2	regular	regular	ADJ
ejde-637	54	3	point	point	NOUN
ejde-637	54	4	p	p	X
ejde-637	54	5	∈	∈	PROPN
ejde-637	54	6	σ	σ	PROPN
ejde-637	54	7	is	be	AUX
ejde-637	54	8	called	call	VERB
ejde-637	54	9	a	a	DET
ejde-637	54	10	sliding	slide	VERB
ejde-637	54	11	point	point	NOUN
ejde-637	54	12	if	if	SCONJ
ejde-637	54	13	⟨f+(p	⟨f+(p	PROPN
ejde-637	54	14	)	)	PUNCT
ejde-637	54	15	,	,	PUNCT
ejde-637	54	16	hx(p)⟩	hx(p)⟩	PROPN
ejde-637	54	17	·	·	PUNCT
ejde-637	54	18	⟨f−(p	⟨f−(p	PROPN
ejde-637	54	19	)	)	PUNCT
ejde-637	54	20	,	,	PUNCT
ejde-637	54	21	hx(p)⟩	hx(p)⟩	PROPN
ejde-637	54	22	<	<	X
ejde-637	54	23	0	0	X
ejde-637	54	24	.	.	PUNCT
ejde-637	55	1	we	we	PRON
ejde-637	55	2	denoted	denote	VERB
ejde-637	55	3	by	by	ADP
ejde-637	55	4	σs	σs	ADP
ejde-637	55	5	the	the	DET
ejde-637	55	6	set	set	NOUN
ejde-637	55	7	of	of	ADP
ejde-637	55	8	all	all	DET
ejde-637	55	9	sliding	slide	VERB
ejde-637	55	10	points	point	NOUN
ejde-637	55	11	.	.	PUNCT
ejde-637	56	1	then	then	ADV
ejde-637	56	2	σs	σs	ADP
ejde-637	56	3	is	be	AUX
ejde-637	56	4	the	the	DET
ejde-637	56	5	sliding	slide	VERB
ejde-637	56	6	set	set	NOUN
ejde-637	56	7	of	of	ADP
ejde-637	56	8	system	system	NOUN
ejde-637	56	9	(	(	PUNCT
ejde-637	56	10	2.1	2.1	NUM
ejde-637	56	11	)	)	PUNCT
ejde-637	56	12	.	.	PUNCT
ejde-637	57	1	moreover	moreover	ADV
ejde-637	57	2	,	,	PUNCT
ejde-637	57	3	σs	σs	ADP
ejde-637	57	4	is	be	AUX
ejde-637	57	5	attractive	attractive	ADJ
ejde-637	57	6	(	(	PUNCT
ejde-637	57	7	repulsive	repulsive	ADJ
ejde-637	57	8	)	)	PUNCT
ejde-637	57	9	if	if	SCONJ
ejde-637	57	10	⟨f+(p	⟨f+(p	PROPN
ejde-637	57	11	)	)	PUNCT
ejde-637	57	12	,	,	PUNCT
ejde-637	57	13	hx(p)⟩	hx(p)⟩	PROPN
ejde-637	57	14	<	<	X
ejde-637	57	15	0	0	NUM
ejde-637	57	16	(	(	PUNCT
ejde-637	57	17	>	>	X
ejde-637	57	18	0	0	NUM
ejde-637	57	19	)	)	PUNCT
ejde-637	57	20	,	,	PUNCT
ejde-637	57	21	⟨f−(p	⟨f−(p	PROPN
ejde-637	57	22	)	)	PUNCT
ejde-637	57	23	,	,	PUNCT
ejde-637	57	24	hx(p)⟩	hx(p)⟩	PROPN
ejde-637	57	25	>	>	X
ejde-637	57	26	0	0	NUM
ejde-637	57	27	(	(	PUNCT
ejde-637	57	28	<	<	NOUN
ejde-637	57	29	0	0	NUM
ejde-637	57	30	)	)	PUNCT
ejde-637	57	31	,	,	PUNCT
ejde-637	57	32	p	p	PROPN
ejde-637	57	33	∈	∈	PROPN
ejde-637	57	34	σs	σs	PROPN
ejde-637	57	35	.	.	PROPN
ejde-637	58	1	in	in	ADP
ejde-637	58	2	addition	addition	NOUN
ejde-637	58	3	to	to	ADP
ejde-637	58	4	this	this	PRON
ejde-637	58	5	,	,	PUNCT
ejde-637	58	6	the	the	DET
ejde-637	58	7	sliding	slide	VERB
ejde-637	58	8	vector	vector	NOUN
ejde-637	58	9	field	field	NOUN
ejde-637	58	10	fs	f	NOUN
ejde-637	58	11	on	on	ADP
ejde-637	58	12	σs	σs	ADP
ejde-637	58	13	is	be	AUX
ejde-637	58	14	often	often	ADV
ejde-637	58	15	defined	define	VERB
ejde-637	58	16	by	by	ADP
ejde-637	58	17	using	use	VERB
ejde-637	58	18	the	the	DET
ejde-637	58	19	filippov	filippov	ADJ
ejde-637	58	20	convex	convex	NOUN
ejde-637	58	21	method	method	NOUN
ejde-637	58	22	(	(	PUNCT
ejde-637	58	23	[	[	X
ejde-637	58	24	13	13	NUM
ejde-637	58	25	,	,	PUNCT
ejde-637	58	26	35	35	NUM
ejde-637	58	27	]	]	PUNCT
ejde-637	58	28	)	)	PUNCT
ejde-637	58	29	to	to	PART
ejde-637	58	30	be	be	AUX
ejde-637	58	31	fs(p	fs(p	NOUN
ejde-637	58	32	)	)	PUNCT
ejde-637	58	33	=	=	SYM
ejde-637	59	1	⟨f+(p	⟨f+(p	PROPN
ejde-637	59	2	)	)	PUNCT
ejde-637	59	3	,	,	PUNCT
ejde-637	59	4	hx(p)⟩f−(p)−	hx(p)⟩f−(p)−	ADJ
ejde-637	59	5	⟨f−(p	⟨f−(p	NOUN
ejde-637	59	6	)	)	PUNCT
ejde-637	59	7	,	,	PUNCT
ejde-637	59	8	hx(p)⟩f+(p	hx(p)⟩f+(p	NOUN
ejde-637	59	9	)	)	PUNCT
ejde-637	59	10	⟨f+(p)−	⟨f+(p)−	PROPN
ejde-637	59	11	f−(p	f−(p	PROPN
ejde-637	59	12	)	)	PUNCT
ejde-637	59	13	,	,	PUNCT
ejde-637	59	14	hx(p)⟩	hx(p)⟩	PROPN
ejde-637	59	15	,	,	PUNCT
ejde-637	59	16	p	p	PROPN
ejde-637	59	17	∈	∈	PROPN
ejde-637	59	18	σs	σs	PROPN
ejde-637	59	19	,	,	PUNCT
ejde-637	59	20	(	(	PUNCT
ejde-637	59	21	2.2	2.2	NUM
ejde-637	59	22	)	)	PUNCT
ejde-637	59	23	and	and	CCONJ
ejde-637	59	24	a	a	DET
ejde-637	59	25	point	point	NOUN
ejde-637	59	26	p	p	X
ejde-637	59	27	∈	∈	PROPN
ejde-637	59	28	σ	σ	NOUN
ejde-637	59	29	satisfying	satisfy	VERB
ejde-637	59	30	fs(p	fs(p	NOUN
ejde-637	59	31	)	)	PUNCT
ejde-637	59	32	=	=	SYM
ejde-637	59	33	0	0	NUM
ejde-637	59	34	is	be	AUX
ejde-637	59	35	called	call	VERB
ejde-637	59	36	a	a	DET
ejde-637	59	37	pseudo	pseudo	NOUN
ejde-637	59	38	-	-	NOUN
ejde-637	59	39	equilibrium	equilibrium	NOUN
ejde-637	59	40	.	.	PUNCT
ejde-637	60	1	when	when	SCONJ
ejde-637	60	2	p	p	PROPN
ejde-637	60	3	∈	∈	PROPN
ejde-637	60	4	σs	σs	ADP
ejde-637	60	5	is	be	AUX
ejde-637	60	6	a	a	DET
ejde-637	60	7	pseudo	pseudo	NOUN
ejde-637	60	8	-	-	NOUN
ejde-637	60	9	equilibrium	equilibrium	NOUN
ejde-637	60	10	,	,	PUNCT
ejde-637	60	11	p	p	PROPN
ejde-637	60	12	may	may	AUX
ejde-637	60	13	show	show	VERB
ejde-637	60	14	properties	property	NOUN
ejde-637	60	15	of	of	ADP
ejde-637	60	16	a	a	DET
ejde-637	60	17	node	node	NOUN
ejde-637	60	18	,	,	PUNCT
ejde-637	60	19	a	a	DET
ejde-637	60	20	saddle	saddle	NOUN
ejde-637	60	21	or	or	CCONJ
ejde-637	60	22	a	a	DET
ejde-637	60	23	focus	focus	NOUN
ejde-637	60	24	according	accord	VERB
ejde-637	60	25	to	to	ADP
ejde-637	60	26	the	the	DET
ejde-637	60	27	stability	stability	NOUN
ejde-637	60	28	of	of	ADP
ejde-637	60	29	p	p	NOUN
ejde-637	60	30	inside	inside	ADP
ejde-637	60	31	σs	σs	ADP
ejde-637	60	32	and	and	CCONJ
ejde-637	60	33	the	the	DET
ejde-637	60	34	attractivity	attractivity	NOUN
ejde-637	60	35	of	of	ADP
ejde-637	60	36	σs	σs	PROPN
ejde-637	60	37	,	,	PUNCT
ejde-637	60	38	which	which	PRON
ejde-637	60	39	induces	induce	VERB
ejde-637	60	40	the	the	DET
ejde-637	60	41	following	follow	VERB
ejde-637	60	42	definitions	definition	NOUN
ejde-637	60	43	.	.	PUNCT
ejde-637	61	1	definition	definition	NOUN
ejde-637	61	2	2.3	2.3	NUM
ejde-637	61	3	.	.	PUNCT
ejde-637	62	1	let	let	VERB
ejde-637	62	2	p	p	PRON
ejde-637	62	3	∈	∈	PROPN
ejde-637	62	4	σs	σs	SCONJ
ejde-637	62	5	be	be	AUX
ejde-637	62	6	an	an	DET
ejde-637	62	7	isolated	isolated	ADJ
ejde-637	62	8	pseudo	pseudo	NOUN
ejde-637	62	9	-	-	NOUN
ejde-637	62	10	equilibrium	equilibrium	NOUN
ejde-637	62	11	.	.	PUNCT
ejde-637	63	1	then	then	ADV
ejde-637	63	2	p	p	PRON
ejde-637	63	3	will	will	AUX
ejde-637	63	4	be	be	AUX
ejde-637	63	5	an	an	DET
ejde-637	63	6	unstable	unstable	ADJ
ejde-637	63	7	(	(	PUNCT
ejde-637	63	8	a	a	DET
ejde-637	63	9	stable	stable	ADJ
ejde-637	63	10	)	)	PUNCT
ejde-637	63	11	pseudo	pseudo	NOUN
ejde-637	63	12	-	-	NOUN
ejde-637	63	13	node	node	NOUN
ejde-637	63	14	of	of	ADP
ejde-637	63	15	system	system	NOUN
ejde-637	63	16	(	(	PUNCT
ejde-637	63	17	2.1	2.1	NUM
ejde-637	63	18	)	)	PUNCT
ejde-637	63	19	if	if	SCONJ
ejde-637	63	20	σs	σs	ADV
ejde-637	63	21	is	be	AUX
ejde-637	63	22	repulsive	repulsive	ADJ
ejde-637	63	23	(	(	PUNCT
ejde-637	63	24	attractive	attractive	ADJ
ejde-637	63	25	)	)	PUNCT
ejde-637	63	26	and	and	CCONJ
ejde-637	63	27	p	p	NOUN
ejde-637	63	28	is	be	AUX
ejde-637	63	29	unstable	unstable	ADJ
ejde-637	63	30	(	(	PUNCT
ejde-637	63	31	stable	stable	ADJ
ejde-637	63	32	)	)	PUNCT
ejde-637	63	33	inside	inside	ADP
ejde-637	63	34	σs	σs	PROPN
ejde-637	63	35	,	,	PUNCT
ejde-637	63	36	a	a	DET
ejde-637	63	37	pseudo	pseudo	NOUN
ejde-637	63	38	-	-	NOUN
ejde-637	63	39	saddle	saddle	NOUN
ejde-637	63	40	if	if	SCONJ
ejde-637	63	41	one	one	NUM
ejde-637	63	42	of	of	ADP
ejde-637	63	43	the	the	DET
ejde-637	63	44	followings	following	NOUN
ejde-637	63	45	is	be	AUX
ejde-637	63	46	true	true	ADJ
ejde-637	63	47	:	:	PUNCT
ejde-637	63	48	(	(	PUNCT
ejde-637	63	49	i	i	NOUN
ejde-637	63	50	)	)	PUNCT
ejde-637	63	51	σs	σs	ADP
ejde-637	63	52	is	be	AUX
ejde-637	63	53	attractive	attractive	ADJ
ejde-637	63	54	and	and	CCONJ
ejde-637	63	55	p	p	NOUN
ejde-637	63	56	is	be	AUX
ejde-637	63	57	unstable	unstable	ADJ
ejde-637	63	58	inside	inside	ADP
ejde-637	63	59	σs	σs	ADP
ejde-637	63	60	;	;	PUNCT
ejde-637	63	61	(	(	PUNCT
ejde-637	63	62	ii	ii	NOUN
ejde-637	63	63	)	)	PUNCT
ejde-637	63	64	σs	σs	ADP
ejde-637	63	65	is	be	AUX
ejde-637	63	66	repulsive	repulsive	ADJ
ejde-637	63	67	and	and	CCONJ
ejde-637	63	68	p	p	NOUN
ejde-637	63	69	is	be	AUX
ejde-637	63	70	stable	stable	ADJ
ejde-637	63	71	inside	inside	ADP
ejde-637	63	72	σs	σs	PROPN
ejde-637	63	73	.	.	PROPN
ejde-637	64	1	moreover	moreover	ADV
ejde-637	64	2	,	,	PUNCT
ejde-637	64	3	p	p	NOUN
ejde-637	64	4	will	will	AUX
ejde-637	64	5	be	be	AUX
ejde-637	64	6	a	a	DET
ejde-637	64	7	pseudo	pseudo	NOUN
ejde-637	64	8	-	-	ADJ
ejde-637	64	9	saddle	saddle	NOUN
ejde-637	64	10	-	-	PUNCT
ejde-637	64	11	node	node	NOUN
ejde-637	64	12	if	if	SCONJ
ejde-637	64	13	p	p	NOUN
ejde-637	64	14	is	be	AUX
ejde-637	64	15	half	half	ADJ
ejde-637	64	16	-	-	PUNCT
ejde-637	64	17	stable	stable	ADJ
ejde-637	64	18	inside	inside	ADP
ejde-637	64	19	σs	σs	PROPN
ejde-637	64	20	.	.	PROPN
ejde-637	64	21	definition	definition	NOUN
ejde-637	64	22	2.4	2.4	NUM
ejde-637	64	23	.	.	PUNCT
ejde-637	65	1	the	the	DET
ejde-637	65	2	point	point	NOUN
ejde-637	65	3	p	p	X
ejde-637	65	4	∈	∈	PROPN
ejde-637	65	5	σ̄	σ̄	PRON
ejde-637	65	6	is	be	AUX
ejde-637	65	7	called	call	VERB
ejde-637	65	8	a	a	DET
ejde-637	65	9	sliding	slide	VERB
ejde-637	65	10	boundary	boundary	ADJ
ejde-637	65	11	point	point	NOUN
ejde-637	65	12	if	if	SCONJ
ejde-637	65	13	⟨f+(p	⟨f+(p	PROPN
ejde-637	65	14	)	)	PUNCT
ejde-637	65	15	,	,	PUNCT
ejde-637	65	16	hx(p)⟩	hx(p)⟩	PROPN
ejde-637	65	17	·	·	PUNCT
ejde-637	65	18	⟨f−(p	⟨f−(p	PROPN
ejde-637	65	19	)	)	PUNCT
ejde-637	65	20	,	,	PUNCT
ejde-637	65	21	hx(p)⟩	hx(p)⟩	PROPN
ejde-637	65	22	=	=	SYM
ejde-637	65	23	0	0	X
ejde-637	65	24	.	.	PUNCT
ejde-637	66	1	the	the	DET
ejde-637	66	2	set	set	NOUN
ejde-637	66	3	of	of	ADP
ejde-637	66	4	all	all	DET
ejde-637	66	5	sliding	slide	VERB
ejde-637	66	6	boundary	boundary	ADJ
ejde-637	66	7	points	point	NOUN
ejde-637	66	8	,	,	PUNCT
ejde-637	66	9	denoted	denote	VERB
ejde-637	66	10	by	by	ADP
ejde-637	66	11	σsb	σsb	PROPN
ejde-637	66	12	,	,	PUNCT
ejde-637	66	13	is	be	AUX
ejde-637	66	14	called	call	VERB
ejde-637	66	15	the	the	DET
ejde-637	66	16	sliding	slide	VERB
ejde-637	66	17	boundary	boundary	ADJ
ejde-637	66	18	set	set	NOUN
ejde-637	66	19	of	of	ADP
ejde-637	66	20	system	system	NOUN
ejde-637	66	21	(	(	PUNCT
ejde-637	66	22	1.1	1.1	NUM
ejde-637	66	23	)	)	PUNCT
ejde-637	66	24	.	.	PUNCT
ejde-637	67	1	definition	definition	NOUN
ejde-637	67	2	2.5	2.5	NUM
ejde-637	67	3	.	.	PUNCT
ejde-637	68	1	let	let	VERB
ejde-637	68	2	p	p	PROPN
ejde-637	68	3	∈	∈	PROPN
ejde-637	68	4	σsb	σsb	PROPN
ejde-637	68	5	,	,	PUNCT
ejde-637	68	6	we	we	PRON
ejde-637	68	7	call	call	VERB
ejde-637	68	8	p	p	PRON
ejde-637	68	9	a	a	DET
ejde-637	68	10	boundary	boundary	ADJ
ejde-637	68	11	equilibrium	equilibrium	NOUN
ejde-637	68	12	of	of	ADP
ejde-637	68	13	system	system	NOUN
ejde-637	68	14	(	(	PUNCT
ejde-637	68	15	1.1	1.1	NUM
ejde-637	68	16	)	)	PUNCT
ejde-637	68	17	if	if	SCONJ
ejde-637	68	18	f+(p	f+(p	NOUN
ejde-637	68	19	)	)	PUNCT
ejde-637	68	20	=	=	SYM
ejde-637	68	21	0	0	NUM
ejde-637	68	22	or	or	CCONJ
ejde-637	68	23	f−(p	f−(p	ADJ
ejde-637	68	24	)	)	PUNCT
ejde-637	69	1	=	=	SYM
ejde-637	69	2	0	0	X
ejde-637	69	3	.	.	PUNCT
ejde-637	70	1	more	more	ADV
ejde-637	70	2	specifically	specifically	ADV
ejde-637	70	3	,	,	PUNCT
ejde-637	70	4	p	p	PROPN
ejde-637	70	5	is	be	AUX
ejde-637	70	6	called	call	VERB
ejde-637	70	7	a	a	DET
ejde-637	70	8	double	double	ADJ
ejde-637	70	9	boundary	boundary	ADJ
ejde-637	70	10	equilibrium	equilibrium	NOUN
ejde-637	70	11	when	when	SCONJ
ejde-637	70	12	f+(p	f+(p	NOUN
ejde-637	70	13	)	)	PUNCT
ejde-637	70	14	=	=	SYM
ejde-637	70	15	f−(p	f−(p	ADJ
ejde-637	70	16	)	)	PUNCT
ejde-637	70	17	=	=	SYM
ejde-637	70	18	0	0	NUM
ejde-637	70	19	,	,	PUNCT
ejde-637	70	20	and	and	CCONJ
ejde-637	70	21	a	a	DET
ejde-637	70	22	unilateral	unilateral	ADJ
ejde-637	70	23	boundary	boundary	ADJ
ejde-637	70	24	equilibrium	equilibrium	NOUN
ejde-637	70	25	induced	induce	VERB
ejde-637	70	26	by	by	ADP
ejde-637	70	27	the	the	DET
ejde-637	70	28	⊖−system	⊖−system	NOUN
ejde-637	70	29	(	(	PUNCT
ejde-637	70	30	⊕−system	⊕−system	ADJ
ejde-637	70	31	)	)	PUNCT
ejde-637	70	32	if	if	SCONJ
ejde-637	70	33	f−(p	f−(p	VERB
ejde-637	70	34	)	)	PUNCT
ejde-637	70	35	=	=	SYM
ejde-637	70	36	0	0	NUM
ejde-637	70	37	,	,	PUNCT
ejde-637	70	38	f+(p	f+(p	NOUN
ejde-637	70	39	)	)	PUNCT
ejde-637	70	40	̸=	̸=	PROPN
ejde-637	70	41	0	0	NUM
ejde-637	70	42	,	,	PUNCT
ejde-637	70	43	(	(	PUNCT
ejde-637	70	44	f+(p	f+(p	X
ejde-637	70	45	)	)	PUNCT
ejde-637	70	46	=	=	SYM
ejde-637	70	47	0	0	NUM
ejde-637	70	48	,	,	PUNCT
ejde-637	70	49	f−(p	f−(p	PROPN
ejde-637	70	50	)	)	PUNCT
ejde-637	70	51	̸=	̸=	PROPN
ejde-637	70	52	0	0	NUM
ejde-637	70	53	)	)	PUNCT
ejde-637	70	54	.	.	PUNCT
ejde-637	71	1	let	let	VERB
ejde-637	71	2	p0	p0	NOUN
ejde-637	71	3	=	=	SYM
ejde-637	71	4	(	(	PUNCT
ejde-637	71	5	0	0	NUM
ejde-637	71	6	,	,	PUNCT
ejde-637	71	7	0	0	NUM
ejde-637	71	8	)	)	PUNCT
ejde-637	71	9	and	and	CCONJ
ejde-637	71	10	fs(p),p	fs(p),p	NOUN
ejde-637	71	11	∈	∈	PROPN
ejde-637	71	12	σs	σs	ADP
ejde-637	71	13	be	be	AUX
ejde-637	71	14	the	the	DET
ejde-637	71	15	unique	unique	ADJ
ejde-637	71	16	non	non	ADJ
ejde-637	71	17	-	-	ADJ
ejde-637	71	18	regular	regular	ADJ
ejde-637	71	19	point	point	NOUN
ejde-637	71	20	of	of	ADP
ejde-637	71	21	the	the	DET
ejde-637	71	22	discontinuity	discontinuity	NOUN
ejde-637	71	23	boundary	boundary	NOUN
ejde-637	71	24	σ	σ	PROPN
ejde-637	71	25	and	and	CCONJ
ejde-637	71	26	the	the	DET
ejde-637	71	27	sliding	slide	VERB
ejde-637	71	28	vector	vector	NOUN
ejde-637	71	29	field	field	NOUN
ejde-637	71	30	of	of	ADP
ejde-637	71	31	system	system	NOUN
ejde-637	71	32	(	(	PUNCT
ejde-637	71	33	1.1	1.1	NUM
ejde-637	71	34	)	)	PUNCT
ejde-637	71	35	,	,	PUNCT
ejde-637	71	36	respectively	respectively	ADV
ejde-637	71	37	.	.	PUNCT
ejde-637	72	1	notice	notice	VERB
ejde-637	72	2	that	that	SCONJ
ejde-637	72	3	we	we	PRON
ejde-637	72	4	did	do	AUX
ejde-637	72	5	not	not	PART
ejde-637	72	6	discuss	discuss	VERB
ejde-637	72	7	the	the	DET
ejde-637	72	8	definition	definition	NOUN
ejde-637	72	9	of	of	ADP
ejde-637	72	10	the	the	DET
ejde-637	72	11	sliding	slide	VERB
ejde-637	72	12	field	field	NOUN
ejde-637	72	13	fs	f	NOUN
ejde-637	72	14	at	at	ADP
ejde-637	72	15	p0	p0	NOUN
ejde-637	72	16	.	.	PUNCT
ejde-637	73	1	in	in	ADP
ejde-637	73	2	fact	fact	NOUN
ejde-637	73	3	,	,	PUNCT
ejde-637	73	4	we	we	PRON
ejde-637	73	5	even	even	ADV
ejde-637	73	6	do	do	AUX
ejde-637	73	7	not	not	PART
ejde-637	73	8	care	care	VERB
ejde-637	73	9	about	about	ADP
ejde-637	73	10	whether	whether	SCONJ
ejde-637	73	11	or	or	CCONJ
ejde-637	73	12	not	not	PART
ejde-637	73	13	this	this	DET
ejde-637	73	14	point	point	NOUN
ejde-637	73	15	is	be	AUX
ejde-637	73	16	a	a	DET
ejde-637	73	17	sliding	slide	VERB
ejde-637	73	18	point	point	NOUN
ejde-637	73	19	,	,	PUNCT
ejde-637	73	20	which	which	PRON
ejde-637	73	21	we	we	PRON
ejde-637	73	22	think	think	VERB
ejde-637	73	23	is	be	AUX
ejde-637	73	24	not	not	PART
ejde-637	73	25	necessary	necessary	ADJ
ejde-637	73	26	at	at	ADP
ejde-637	73	27	least	least	ADJ
ejde-637	73	28	now	now	ADV
ejde-637	73	29	.	.	PUNCT
ejde-637	74	1	however	however	ADV
ejde-637	74	2	,	,	PUNCT
ejde-637	74	3	there	there	PRON
ejde-637	74	4	is	be	VERB
ejde-637	74	5	no	no	DET
ejde-637	74	6	doubt	doubt	NOUN
ejde-637	74	7	that	that	SCONJ
ejde-637	74	8	the	the	DET
ejde-637	74	9	dynamics	dynamic	NOUN
ejde-637	74	10	around	around	ADP
ejde-637	74	11	p0	p0	NOUN
ejde-637	74	12	play	play	VERB
ejde-637	74	13	an	an	DET
ejde-637	74	14	important	important	ADJ
ejde-637	74	15	role	role	NOUN
ejde-637	74	16	in	in	ADP
ejde-637	74	17	studying	study	VERB
ejde-637	74	18	the	the	DET
ejde-637	74	19	global	global	ADJ
ejde-637	74	20	dynamics	dynamic	NOUN
ejde-637	74	21	.	.	PUNCT
ejde-637	75	1	therefore	therefore	ADV
ejde-637	75	2	,	,	PUNCT
ejde-637	75	3	we	we	PRON
ejde-637	75	4	need	need	VERB
ejde-637	75	5	to	to	PART
ejde-637	75	6	consider	consider	VERB
ejde-637	75	7	fs	fs	ADP
ejde-637	75	8	around	around	ADP
ejde-637	75	9	this	this	DET
ejde-637	75	10	special	special	ADJ
ejde-637	75	11	point	point	NOUN
ejde-637	75	12	.	.	PUNCT
ejde-637	76	1	4	4	NUM
ejde-637	76	2	q.-q	q.-q	PROPN
ejde-637	76	3	.	.	PUNCT
ejde-637	77	1	han	han	PROPN
ejde-637	77	2	,	,	PUNCT
ejde-637	77	3	s.-m	s.-m	PROPN
ejde-637	77	4	.	.	PUNCT
ejde-637	78	1	huan	huan	PROPN
ejde-637	78	2	ejde-2024/57	ejde-2024/57	PROPN
ejde-637	78	3	suppose	suppose	VERB
ejde-637	78	4	that	that	SCONJ
ejde-637	78	5	the	the	DET
ejde-637	78	6	sliding	slide	VERB
ejde-637	78	7	field	field	NOUN
ejde-637	78	8	fs	f	NOUN
ejde-637	78	9	is	be	AUX
ejde-637	78	10	well	well	ADV
ejde-637	78	11	defined	define	VERB
ejde-637	78	12	on	on	ADP
ejde-637	78	13	iyb	iyb	NOUN
ejde-637	78	14	∪	∪	X
ejde-637	78	15	ixa	ixa	NOUN
ejde-637	78	16	with	with	ADP
ejde-637	78	17	iyb	iyb	NOUN
ejde-637	78	18	=	=	SYM
ejde-637	78	19	{	{	PUNCT
ejde-637	78	20	(	(	PUNCT
ejde-637	78	21	0	0	NUM
ejde-637	78	22	,	,	PUNCT
ejde-637	78	23	y	y	PROPN
ejde-637	78	24	)	)	PUNCT
ejde-637	78	25	:	:	PUNCT
ejde-637	79	1	y	y	PROPN
ejde-637	79	2	∈	∈	PROPN
ejde-637	79	3	(	(	PUNCT
ejde-637	79	4	0	0	NUM
ejde-637	79	5	,	,	PUNCT
ejde-637	79	6	b	b	NOUN
ejde-637	79	7	)	)	PUNCT
ejde-637	79	8	}	}	PUNCT
ejde-637	79	9	,	,	PUNCT
ejde-637	79	10	ixa	ixa	ADJ
ejde-637	79	11	=	=	SYM
ejde-637	79	12	{	{	PUNCT
ejde-637	79	13	(	(	PUNCT
ejde-637	79	14	x	x	X
ejde-637	79	15	,	,	PUNCT
ejde-637	79	16	0	0	NUM
ejde-637	79	17	)	)	PUNCT
ejde-637	79	18	:	:	PUNCT
ejde-637	79	19	x	x	X
ejde-637	79	20	∈	∈	NOUN
ejde-637	79	21	(	(	PUNCT
ejde-637	79	22	0	0	NUM
ejde-637	79	23	,	,	PUNCT
ejde-637	79	24	a	a	PRON
ejde-637	79	25	)	)	PUNCT
ejde-637	79	26	}	}	PUNCT
ejde-637	79	27	.	.	PUNCT
ejde-637	80	1	then	then	ADV
ejde-637	80	2	we	we	PRON
ejde-637	80	3	call	call	VERB
ejde-637	80	4	p0	p0	NOUN
ejde-637	80	5	a	a	DET
ejde-637	80	6	non	non	ADJ
ejde-637	80	7	-	-	ADJ
ejde-637	80	8	regular	regular	ADJ
ejde-637	80	9	boundary	boundary	ADJ
ejde-637	80	10	saddle	saddle	NOUN
ejde-637	80	11	of	of	ADP
ejde-637	80	12	system	system	NOUN
ejde-637	80	13	(	(	PUNCT
ejde-637	80	14	1.1	1.1	NUM
ejde-637	80	15	)	)	PUNCT
ejde-637	80	16	if	if	SCONJ
ejde-637	80	17	there	there	PRON
ejde-637	80	18	exist	exist	VERB
ejde-637	80	19	a	a	DET
ejde-637	80	20	>	>	X
ejde-637	80	21	0	0	NUM
ejde-637	80	22	,	,	PUNCT
ejde-637	80	23	b	b	X
ejde-637	80	24	>	>	X
ejde-637	80	25	0	0	NUM
ejde-637	80	26	such	such	ADJ
ejde-637	80	27	that	that	DET
ejde-637	80	28	⟨fs(p1	⟨fs(p1	NOUN
ejde-637	80	29	)	)	PUNCT
ejde-637	80	30	,	,	PUNCT
ejde-637	80	31	(	(	PUNCT
ejde-637	80	32	0	0	NUM
ejde-637	80	33	,	,	PUNCT
ejde-637	80	34	1)⟩	1)⟩	NUM
ejde-637	80	35	·	·	PUNCT
ejde-637	80	36	⟨fs(p2	⟨fs(p2	PROPN
ejde-637	80	37	)	)	PUNCT
ejde-637	80	38	,	,	PUNCT
ejde-637	80	39	(	(	PUNCT
ejde-637	80	40	1	1	NUM
ejde-637	80	41	,	,	PUNCT
ejde-637	80	42	0)⟩	0)⟩	NUM
ejde-637	80	43	<	<	X
ejde-637	80	44	0	0	NUM
ejde-637	80	45	,	,	PUNCT
ejde-637	80	46	∀p1	∀p1	PUNCT
ejde-637	80	47	∈	∈	NOUN
ejde-637	80	48	iyb	iyb	NOUN
ejde-637	80	49	,	,	PUNCT
ejde-637	80	50	∀p2	∀p2	NOUN
ejde-637	80	51	∈	∈	PROPN
ejde-637	80	52	ixa	ixa	NOUN
ejde-637	80	53	,	,	PUNCT
ejde-637	80	54	and	and	CCONJ
ejde-637	80	55	a	a	DET
ejde-637	80	56	non	non	ADJ
ejde-637	80	57	-	-	ADJ
ejde-637	80	58	regular	regular	ADJ
ejde-637	80	59	boundary	boundary	ADJ
ejde-637	80	60	source	source	NOUN
ejde-637	80	61	(	(	PUNCT
ejde-637	80	62	sink	sink	NOUN
ejde-637	80	63	)	)	PUNCT
ejde-637	80	64	if	if	SCONJ
ejde-637	80	65	there	there	PRON
ejde-637	80	66	exist	exist	VERB
ejde-637	80	67	a	a	DET
ejde-637	80	68	>	>	X
ejde-637	80	69	0	0	NUM
ejde-637	80	70	and	and	CCONJ
ejde-637	80	71	b	b	X
ejde-637	80	72	>	>	X
ejde-637	80	73	0	0	NUM
ejde-637	80	74	such	such	ADJ
ejde-637	80	75	that	that	DET
ejde-637	80	76	⟨fs(p1	⟨fs(p1	NOUN
ejde-637	80	77	)	)	PUNCT
ejde-637	80	78	,	,	PUNCT
ejde-637	80	79	(	(	PUNCT
ejde-637	80	80	0	0	NUM
ejde-637	80	81	,	,	PUNCT
ejde-637	80	82	1)⟩	1)⟩	NUM
ejde-637	80	83	·	·	PUNCT
ejde-637	80	84	⟨fs(p2	⟨fs(p2	PROPN
ejde-637	80	85	)	)	PUNCT
ejde-637	80	86	,	,	PUNCT
ejde-637	80	87	(	(	PUNCT
ejde-637	80	88	1	1	NUM
ejde-637	80	89	,	,	PUNCT
ejde-637	80	90	0)⟩	0)⟩	NUM
ejde-637	80	91	>	>	X
ejde-637	80	92	0	0	NUM
ejde-637	80	93	,	,	PUNCT
ejde-637	80	94	⟨fs(p1	⟨fs(p1	PROPN
ejde-637	80	95	)	)	PUNCT
ejde-637	80	96	,	,	PUNCT
ejde-637	80	97	(	(	PUNCT
ejde-637	80	98	0	0	NUM
ejde-637	80	99	,	,	PUNCT
ejde-637	80	100	1)⟩	1)⟩	X
ejde-637	80	101	>	>	X
ejde-637	80	102	0	0	PUNCT
ejde-637	81	1	(	(	PUNCT
ejde-637	81	2	<	<	X
ejde-637	81	3	0	0	NUM
ejde-637	81	4	)	)	PUNCT
ejde-637	81	5	,	,	PUNCT
ejde-637	81	6	for	for	ADP
ejde-637	81	7	all	all	DET
ejde-637	81	8	p1	p1	PROPN
ejde-637	81	9	∈	∈	PROPN
ejde-637	81	10	iyb	iyb	NOUN
ejde-637	81	11	and	and	CCONJ
ejde-637	81	12	all	all	DET
ejde-637	81	13	p2	p2	PROPN
ejde-637	81	14	∈	∈	PROPN
ejde-637	81	15	ixa	ixa	NOUN
ejde-637	81	16	.	.	PUNCT
ejde-637	82	1	in	in	ADP
ejde-637	82	2	addition	addition	NOUN
ejde-637	82	3	to	to	ADP
ejde-637	82	4	this	this	PRON
ejde-637	82	5	,	,	PUNCT
ejde-637	82	6	according	accord	VERB
ejde-637	82	7	to	to	ADP
ejde-637	82	8	[	[	X
ejde-637	82	9	36	36	NUM
ejde-637	82	10	,	,	PUNCT
ejde-637	82	11	48	48	NUM
ejde-637	82	12	,	,	PUNCT
ejde-637	82	13	49	49	NUM
ejde-637	82	14	]	]	PUNCT
ejde-637	82	15	,	,	PUNCT
ejde-637	82	16	we	we	PRON
ejde-637	82	17	obtain	obtain	VERB
ejde-637	82	18	that	that	SCONJ
ejde-637	82	19	an	an	DET
ejde-637	82	20	orbit	orbit	NOUN
ejde-637	82	21	which	which	PRON
ejde-637	82	22	has	have	VERB
ejde-637	82	23	a	a	DET
ejde-637	82	24	common	common	ADJ
ejde-637	82	25	segment	segment	NOUN
ejde-637	82	26	with	with	ADP
ejde-637	82	27	the	the	DET
ejde-637	82	28	sliding	slide	VERB
ejde-637	82	29	set	set	NOUN
ejde-637	82	30	is	be	AUX
ejde-637	82	31	called	call	VERB
ejde-637	82	32	a	a	DET
ejde-637	82	33	sliding	slide	VERB
ejde-637	82	34	orbit	orbit	NOUN
ejde-637	82	35	,	,	PUNCT
ejde-637	82	36	and	and	CCONJ
ejde-637	82	37	a	a	DET
ejde-637	82	38	closed	closed	ADJ
ejde-637	82	39	orbit	orbit	NOUN
ejde-637	82	40	with	with	ADP
ejde-637	82	41	sliding	slide	VERB
ejde-637	82	42	motion	motion	NOUN
ejde-637	82	43	is	be	AUX
ejde-637	82	44	called	call	VERB
ejde-637	82	45	a	a	DET
ejde-637	82	46	sliding	slide	VERB
ejde-637	82	47	cycle	cycle	NOUN
ejde-637	82	48	.	.	PUNCT
ejde-637	83	1	furthermore	furthermore	ADV
ejde-637	83	2	,	,	PUNCT
ejde-637	83	3	a	a	DET
ejde-637	83	4	sliding	slide	VERB
ejde-637	83	5	-	-	PUNCT
ejde-637	83	6	zero	zero	NUM
ejde-637	83	7	cycle	cycle	NOUN
ejde-637	83	8	is	be	AUX
ejde-637	83	9	a	a	DET
ejde-637	83	10	closed	closed	ADJ
ejde-637	83	11	orbit	orbit	NOUN
ejde-637	83	12	intersecting	intersect	VERB
ejde-637	83	13	σ	σ	NOUN
ejde-637	83	14	at	at	ADP
ejde-637	83	15	an	an	DET
ejde-637	83	16	end	end	NOUN
ejde-637	83	17	point	point	NOUN
ejde-637	83	18	of	of	ADP
ejde-637	83	19	the	the	DET
ejde-637	83	20	sliding	slide	VERB
ejde-637	83	21	region	region	NOUN
ejde-637	83	22	.	.	PUNCT
ejde-637	84	1	a	a	DET
ejde-637	84	2	sliding	slide	VERB
ejde-637	84	3	heteroclinic	heteroclinic	ADJ
ejde-637	84	4	orbit	orbit	NOUN
ejde-637	84	5	(	(	PUNCT
ejde-637	84	6	or	or	CCONJ
ejde-637	84	7	cycle	cycle	NOUN
ejde-637	84	8	)	)	PUNCT
ejde-637	84	9	is	be	AUX
ejde-637	84	10	a	a	DET
ejde-637	84	11	hereroclinic	hereroclinic	ADJ
ejde-637	84	12	one	one	NUM
ejde-637	84	13	with	with	ADP
ejde-637	84	14	sliding	slide	VERB
ejde-637	84	15	motion	motion	NOUN
ejde-637	84	16	.	.	PUNCT
ejde-637	85	1	a	a	DET
ejde-637	85	2	sliding	slide	VERB
ejde-637	85	3	homoclinic	homoclinic	ADJ
ejde-637	85	4	orbit	orbit	NOUN
ejde-637	85	5	(	(	PUNCT
ejde-637	85	6	or	or	CCONJ
ejde-637	85	7	cycle	cycle	NOUN
ejde-637	85	8	)	)	PUNCT
ejde-637	85	9	is	be	AUX
ejde-637	85	10	a	a	DET
ejde-637	85	11	homoclinic	homoclinic	ADJ
ejde-637	85	12	one	one	NUM
ejde-637	85	13	with	with	ADP
ejde-637	85	14	sliding	slide	VERB
ejde-637	85	15	motion	motion	NOUN
ejde-637	85	16	.	.	PUNCT
ejde-637	86	1	moreover	moreover	ADV
ejde-637	86	2	,	,	PUNCT
ejde-637	86	3	for	for	ADP
ejde-637	86	4	a	a	DET
ejde-637	86	5	piecewise	piecewise	NOUN
ejde-637	86	6	smooth	smooth	ADJ
ejde-637	86	7	dynamical	dynamical	ADJ
ejde-637	86	8	system	system	NOUN
ejde-637	86	9	with	with	ADP
ejde-637	86	10	a	a	DET
ejde-637	86	11	parameter	parameter	NOUN
ejde-637	86	12	µ	µ	NOUN
ejde-637	86	13	,	,	PUNCT
ejde-637	86	14	a	a	DET
ejde-637	86	15	sliding	slide	VERB
ejde-637	86	16	cycle	cycle	NOUN
ejde-637	86	17	bifurcation	bifurcation	NOUN
ejde-637	86	18	happens	happen	VERB
ejde-637	86	19	at	at	ADP
ejde-637	86	20	µ	µ	NOUN
ejde-637	86	21	=	=	SYM
ejde-637	86	22	µ0	µ0	NOUN
ejde-637	86	23	means	mean	VERB
ejde-637	86	24	that	that	SCONJ
ejde-637	86	25	there	there	PRON
ejde-637	86	26	is	be	VERB
ejde-637	86	27	a	a	DET
ejde-637	86	28	sliding	sliding	ADJ
ejde-637	86	29	-	-	PUNCT
ejde-637	86	30	zero	zero	NUM
ejde-637	86	31	cycle	cycle	NOUN
ejde-637	86	32	when	when	SCONJ
ejde-637	86	33	µ	µ	X
ejde-637	86	34	=	=	SYM
ejde-637	86	35	µ0	µ0	NOUN
ejde-637	86	36	,	,	PUNCT
ejde-637	86	37	while	while	SCONJ
ejde-637	86	38	for	for	ADP
ejde-637	86	39	0	0	NUM
ejde-637	86	40	<	<	X
ejde-637	86	41	|µ	|µ	NOUN
ejde-637	86	42	−	−	PROPN
ejde-637	86	43	µ0|	µ0|	ADJ
ejde-637	86	44	≪	≪	PUNCT
ejde-637	86	45	1	1	NUM
ejde-637	86	46	the	the	DET
ejde-637	86	47	sliding	slide	VERB
ejde-637	86	48	-	-	PUNCT
ejde-637	86	49	zero	zero	NUM
ejde-637	86	50	cycle	cycle	NOUN
ejde-637	86	51	disappears	disappear	VERB
ejde-637	86	52	,	,	PUNCT
ejde-637	86	53	and	and	CCONJ
ejde-637	86	54	instead	instead	ADV
ejde-637	86	55	there	there	PRON
ejde-637	86	56	appear	appear	VERB
ejde-637	86	57	a	a	DET
ejde-637	86	58	limit	limit	NOUN
ejde-637	86	59	cycle	cycle	NOUN
ejde-637	86	60	and	and	CCONJ
ejde-637	86	61	a	a	DET
ejde-637	86	62	sliding	slide	VERB
ejde-637	86	63	cycle	cycle	NOUN
ejde-637	86	64	when	when	SCONJ
ejde-637	86	65	µ	µ	X
ejde-637	86	66	crosses	crosse	NOUN
ejde-637	86	67	µ0	µ0	NOUN
ejde-637	86	68	in	in	ADP
ejde-637	86	69	opposite	opposite	ADJ
ejde-637	86	70	directions	direction	NOUN
ejde-637	86	71	,	,	PUNCT
ejde-637	86	72	respectively	respectively	ADV
ejde-637	86	73	.	.	PUNCT
ejde-637	87	1	and	and	CCONJ
ejde-637	87	2	a	a	DET
ejde-637	87	3	sliding	slide	VERB
ejde-637	87	4	homoclinic	homoclinic	ADJ
ejde-637	87	5	bifurcation	bifurcation	NOUN
ejde-637	87	6	of	of	ADP
ejde-637	87	7	the	the	DET
ejde-637	87	8	system	system	NOUN
ejde-637	87	9	at	at	ADP
ejde-637	87	10	µ	µ	NOUN
ejde-637	87	11	=	=	SYM
ejde-637	87	12	µ0	µ0	NOUN
ejde-637	87	13	means	mean	VERB
ejde-637	87	14	the	the	DET
ejde-637	87	15	system	system	NOUN
ejde-637	87	16	has	have	VERB
ejde-637	87	17	a	a	DET
ejde-637	87	18	sliding	slide	VERB
ejde-637	87	19	homoclinic	homoclinic	ADJ
ejde-637	87	20	cycle	cycle	NOUN
ejde-637	87	21	when	when	SCONJ
ejde-637	87	22	µ	µ	X
ejde-637	87	23	=	=	SYM
ejde-637	87	24	µ0	µ0	NOUN
ejde-637	87	25	,	,	PUNCT
ejde-637	87	26	while	while	SCONJ
ejde-637	87	27	for	for	ADP
ejde-637	87	28	0	0	NUM
ejde-637	87	29	<	<	X
ejde-637	87	30	|µ	|µ	NOUN
ejde-637	87	31	−	−	PROPN
ejde-637	87	32	µ0|	µ0|	ADJ
ejde-637	87	33	≪	≪	PUNCT
ejde-637	87	34	1	1	NUM
ejde-637	87	35	the	the	DET
ejde-637	87	36	sliding	slide	VERB
ejde-637	87	37	homoclinic	homoclinic	ADJ
ejde-637	87	38	cycle	cycle	NOUN
ejde-637	87	39	disappears	disappear	VERB
ejde-637	87	40	,	,	PUNCT
ejde-637	87	41	instead	instead	ADV
ejde-637	87	42	there	there	PRON
ejde-637	87	43	appears	appear	VERB
ejde-637	87	44	a	a	DET
ejde-637	87	45	sliding	slide	VERB
ejde-637	87	46	cycle	cycle	NOUN
ejde-637	87	47	when	when	SCONJ
ejde-637	87	48	µ	µ	X
ejde-637	87	49	varies	vary	VERB
ejde-637	87	50	in	in	ADP
ejde-637	87	51	one	one	NUM
ejde-637	87	52	direction	direction	NOUN
ejde-637	87	53	and	and	CCONJ
ejde-637	87	54	neither	neither	PRON
ejde-637	87	55	sliding	slide	VERB
ejde-637	87	56	homoclinic	homoclinic	ADJ
ejde-637	87	57	orbits	orbit	NOUN
ejde-637	87	58	nor	nor	CCONJ
ejde-637	87	59	sliding	slide	VERB
ejde-637	87	60	cycles	cycle	NOUN
ejde-637	87	61	when	when	SCONJ
ejde-637	87	62	µ	µ	X
ejde-637	87	63	varies	vary	VERB
ejde-637	87	64	in	in	ADP
ejde-637	87	65	another	another	DET
ejde-637	87	66	direction	direction	NOUN
ejde-637	87	67	.	.	PUNCT
ejde-637	88	1	finally	finally	ADV
ejde-637	88	2	,	,	PUNCT
ejde-637	88	3	to	to	PART
ejde-637	88	4	give	give	VERB
ejde-637	88	5	our	our	PRON
ejde-637	88	6	main	main	ADJ
ejde-637	88	7	results	result	NOUN
ejde-637	88	8	,	,	PUNCT
ejde-637	88	9	we	we	PRON
ejde-637	88	10	introduce	introduce	VERB
ejde-637	88	11	some	some	DET
ejde-637	88	12	notation	notation	NOUN
ejde-637	88	13	for	for	ADP
ejde-637	88	14	the	the	DET
ejde-637	88	15	planar	planar	ADJ
ejde-637	88	16	linear	linear	NOUN
ejde-637	88	17	system	system	NOUN
ejde-637	88	18	ẋ	ẋ	PUNCT
ejde-637	89	1	=	=	PUNCT
ejde-637	89	2	a	a	X
ejde-637	89	3	·	·	PUNCT
ejde-637	89	4	(	(	PUNCT
ejde-637	89	5	x−	x−	PROPN
ejde-637	89	6	x±	x±	PROPN
ejde-637	89	7	e	e	PROPN
ejde-637	89	8	)	)	PUNCT
ejde-637	89	9	,	,	PUNCT
ejde-637	89	10	(	(	PUNCT
ejde-637	89	11	2.3	2.3	NUM
ejde-637	89	12	)	)	PUNCT
ejde-637	90	1	where	where	SCONJ
ejde-637	90	2	det(a	det(a	NOUN
ejde-637	90	3	)	)	PUNCT
ejde-637	90	4	<	<	X
ejde-637	90	5	0	0	PUNCT
ejde-637	90	6	(	(	PUNCT
ejde-637	90	7	i.e.	i.e.	X
ejde-637	90	8	,	,	PUNCT
ejde-637	90	9	a	a	PRON
ejde-637	90	10	has	have	VERB
ejde-637	90	11	two	two	NUM
ejde-637	90	12	different	different	ADJ
ejde-637	90	13	real	real	ADJ
ejde-637	90	14	eigenvalues	eigenvalue	NOUN
ejde-637	90	15	having	have	VERB
ejde-637	90	16	opposite	opposite	ADJ
ejde-637	90	17	signs	sign	NOUN
ejde-637	90	18	:	:	PUNCT
ejde-637	90	19	λ1	λ1	PROPN
ejde-637	90	20	>	>	X
ejde-637	90	21	0	0	PUNCT
ejde-637	90	22	>	>	X
ejde-637	90	23	λ2	λ2	PROPN
ejde-637	90	24	)	)	PUNCT
ejde-637	90	25	and	and	CCONJ
ejde-637	91	1	[	[	X
ejde-637	91	2	tr(a)]2	tr(a)]2	X
ejde-637	91	3	>	>	X
ejde-637	91	4	4	4	NUM
ejde-637	91	5	det(a	det(a	NOUN
ejde-637	91	6	)	)	PUNCT
ejde-637	91	7	.	.	PUNCT
ejde-637	92	1	then	then	ADV
ejde-637	92	2	λ1	λ1	PROPN
ejde-637	92	3	=	=	PUNCT
ejde-637	92	4	tr(a	tr(a	NUM
ejde-637	92	5	)	)	PUNCT
ejde-637	93	1	+	+	CCONJ
ejde-637	93	2	√	√	NUM
ejde-637	94	1	[	[	X
ejde-637	94	2	tr(a)]2	tr(a)]2	NOUN
ejde-637	94	3	−	−	PROPN
ejde-637	94	4	4	4	NUM
ejde-637	94	5	det(a	det(a	NOUN
ejde-637	94	6	)	)	PUNCT
ejde-637	94	7	2	2	NUM
ejde-637	94	8	,	,	PUNCT
ejde-637	94	9	λ2	λ2	NOUN
ejde-637	94	10	=	=	SYM
ejde-637	94	11	tr(a)−	tr(a)−	NOUN
ejde-637	94	12	√	√	ADP
ejde-637	95	1	[	[	X
ejde-637	95	2	tr(a)]2	tr(a)]2	NOUN
ejde-637	95	3	−	−	PROPN
ejde-637	95	4	4	4	NUM
ejde-637	95	5	det(a	det(a	NOUN
ejde-637	95	6	)	)	PUNCT
ejde-637	95	7	2	2	NUM
ejde-637	95	8	.	.	PUNCT
ejde-637	96	1	moreover	moreover	ADV
ejde-637	96	2	,	,	PUNCT
ejde-637	96	3	denote	denote	VERB
ejde-637	96	4	the	the	DET
ejde-637	96	5	invariant	invariant	ADJ
ejde-637	96	6	manifolds	manifold	NOUN
ejde-637	96	7	of	of	ADP
ejde-637	96	8	x±	x±	PROPN
ejde-637	96	9	e	e	NOUN
ejde-637	96	10	by	by	ADP
ejde-637	96	11	l±1	l±1	NOUN
ejde-637	96	12	,	,	PUNCT
ejde-637	96	13	l	l	NOUN
ejde-637	96	14	±	±	NUM
ejde-637	96	15	2	2	NUM
ejde-637	96	16	.	.	PUNCT
ejde-637	97	1	let	let	VERB
ejde-637	97	2	k	k	PROPN
ejde-637	97	3	±	±	PROPN
ejde-637	97	4	1	1	NUM
ejde-637	97	5	,	,	PUNCT
ejde-637	97	6	k	k	PROPN
ejde-637	97	7	±	±	NUM
ejde-637	97	8	2	2	NUM
ejde-637	97	9	be	be	AUX
ejde-637	97	10	the	the	DET
ejde-637	97	11	slopes	slope	NOUN
ejde-637	97	12	of	of	ADP
ejde-637	97	13	l±1	l±1	NOUN
ejde-637	97	14	,	,	PUNCT
ejde-637	97	15	l	l	PROPN
ejde-637	97	16	±	±	NUM
ejde-637	97	17	2	2	NUM
ejde-637	97	18	,	,	PUNCT
ejde-637	97	19	y±	y±	PROPN
ejde-637	97	20	m1	m1	NOUN
ejde-637	97	21	=	=	SYM
ejde-637	97	22	(	(	PUNCT
ejde-637	97	23	0	0	NUM
ejde-637	97	24	,	,	PUNCT
ejde-637	97	25	y±m1	y±m1	PROPN
ejde-637	97	26	)	)	PUNCT
ejde-637	97	27	,	,	PUNCT
ejde-637	97	28	y±	y±	PROPN
ejde-637	97	29	m2	m2	PROPN
ejde-637	97	30	=	=	SYM
ejde-637	97	31	(	(	PUNCT
ejde-637	97	32	0	0	NUM
ejde-637	97	33	,	,	PUNCT
ejde-637	97	34	y±m2	y±m2	PROPN
ejde-637	97	35	)	)	PUNCT
ejde-637	97	36	and	and	CCONJ
ejde-637	97	37	x±	x±	PROPN
ejde-637	97	38	m1	m1	PROPN
ejde-637	97	39	=	=	PRON
ejde-637	97	40	(	(	PUNCT
ejde-637	97	41	x±	x±	PROPN
ejde-637	97	42	m1	m1	PROPN
ejde-637	97	43	,	,	PUNCT
ejde-637	97	44	0	0	NUM
ejde-637	97	45	)	)	PUNCT
ejde-637	97	46	,	,	PUNCT
ejde-637	97	47	x±	x±	PROPN
ejde-637	97	48	m2	m2	PROPN
ejde-637	97	49	=	=	PRON
ejde-637	97	50	(	(	PUNCT
ejde-637	97	51	x±	x±	PROPN
ejde-637	97	52	m2	m2	PROPN
ejde-637	97	53	,	,	PUNCT
ejde-637	97	54	0	0	NUM
ejde-637	97	55	)	)	PUNCT
ejde-637	97	56	be	be	VERB
ejde-637	97	57	the	the	DET
ejde-637	97	58	intersections	intersection	NOUN
ejde-637	97	59	of	of	ADP
ejde-637	97	60	l±1	l±1	NOUN
ejde-637	97	61	and	and	CCONJ
ejde-637	97	62	l±2	l±2	NOUN
ejde-637	97	63	with	with	ADP
ejde-637	97	64	the	the	DET
ejde-637	97	65	y	y	NOUN
ejde-637	97	66	-	-	PUNCT
ejde-637	97	67	axis	axis	NOUN
ejde-637	97	68	and	and	CCONJ
ejde-637	97	69	the	the	DET
ejde-637	97	70	x	x	NOUN
ejde-637	97	71	-	-	NOUN
ejde-637	97	72	axis	axis	ADJ
ejde-637	97	73	,	,	PUNCT
ejde-637	97	74	respectively	respectively	ADV
ejde-637	97	75	.	.	PUNCT
ejde-637	98	1	in	in	ADP
ejde-637	98	2	addition	addition	NOUN
ejde-637	98	3	to	to	ADP
ejde-637	98	4	this	this	PRON
ejde-637	98	5	,	,	PUNCT
ejde-637	98	6	let	let	VERB
ejde-637	98	7	y±	y±	PROPN
ejde-637	98	8	t	t	PROPN
ejde-637	98	9	=	=	SYM
ejde-637	98	10	(	(	PUNCT
ejde-637	98	11	0	0	NUM
ejde-637	98	12	,	,	PUNCT
ejde-637	98	13	y±t	y±t	NUM
ejde-637	98	14	)	)	PUNCT
ejde-637	99	1	and	and	CCONJ
ejde-637	99	2	x±	x±	PROPN
ejde-637	99	3	t	t	PROPN
ejde-637	99	4	=	=	SYM
ejde-637	100	1	(	(	PUNCT
ejde-637	100	2	x±	x±	PROPN
ejde-637	100	3	t	t	PROPN
ejde-637	100	4	,	,	PUNCT
ejde-637	100	5	0	0	NUM
ejde-637	100	6	)	)	PUNCT
ejde-637	100	7	be	be	VERB
ejde-637	100	8	the	the	DET
ejde-637	100	9	contact	contact	NOUN
ejde-637	100	10	points	point	NOUN
ejde-637	100	11	at	at	ADP
ejde-637	100	12	which	which	PRON
ejde-637	100	13	the	the	DET
ejde-637	100	14	trajectories	trajectory	NOUN
ejde-637	100	15	of	of	ADP
ejde-637	100	16	system	system	NOUN
ejde-637	100	17	(	(	PUNCT
ejde-637	100	18	2.3	2.3	NUM
ejde-637	100	19	)	)	PUNCT
ejde-637	100	20	being	be	AUX
ejde-637	100	21	tangent	tangent	ADJ
ejde-637	100	22	to	to	ADP
ejde-637	100	23	the	the	DET
ejde-637	100	24	y	y	NOUN
ejde-637	100	25	-	-	PUNCT
ejde-637	100	26	axis	axis	NOUN
ejde-637	100	27	and	and	CCONJ
ejde-637	100	28	the	the	DET
ejde-637	100	29	x	x	NOUN
ejde-637	100	30	-	-	NOUN
ejde-637	100	31	axis	axis	ADJ
ejde-637	100	32	,	,	PUNCT
ejde-637	100	33	respectively	respectively	ADV
ejde-637	100	34	.	.	PUNCT
ejde-637	101	1	then	then	ADV
ejde-637	101	2	by	by	ADP
ejde-637	101	3	simple	simple	ADJ
ejde-637	101	4	calculations	calculation	NOUN
ejde-637	101	5	,	,	PUNCT
ejde-637	101	6	it	it	PRON
ejde-637	101	7	follows	follow	VERB
ejde-637	101	8	that	that	SCONJ
ejde-637	101	9	k±1	k±1	NOUN
ejde-637	102	1	=	=	SYM
ejde-637	102	2	λ1	λ1	PROPN
ejde-637	102	3	−	−	PROPN
ejde-637	102	4	a11	a11	PROPN
ejde-637	102	5	a12	a12	NOUN
ejde-637	102	6	,	,	PUNCT
ejde-637	102	7	k±2	k±2	X
ejde-637	102	8	=	=	SYM
ejde-637	102	9	λ2	λ2	PROPN
ejde-637	102	10	−	−	PROPN
ejde-637	102	11	a11	a11	PROPN
ejde-637	102	12	a12	a12	NOUN
ejde-637	102	13	,	,	PUNCT
ejde-637	102	14	(	(	PUNCT
ejde-637	102	15	2.4	2.4	NUM
ejde-637	102	16	)	)	PUNCT
ejde-637	103	1	x±	x±	PROPN
ejde-637	103	2	t	t	PROPN
ejde-637	103	3	=	=	PUNCT
ejde-637	104	1	x±	x±	PROPN
ejde-637	104	2	e	e	X
ejde-637	104	3	+	+	CCONJ
ejde-637	104	4	a22	a22	PROPN
ejde-637	104	5	a21	a21	PROPN
ejde-637	104	6	y±e	y±e	PROPN
ejde-637	104	7	,	,	PUNCT
ejde-637	104	8	y±t	y±t	PROPN
ejde-637	104	9	=	=	SYM
ejde-637	104	10	y±e	y±e	PROPN
ejde-637	105	1	+	+	NUM
ejde-637	105	2	a11	a11	PROPN
ejde-637	105	3	a12	a12	NOUN
ejde-637	105	4	x±	x±	PROPN
ejde-637	106	1	e	e	PROPN
ejde-637	106	2	,	,	PUNCT
ejde-637	106	3	(	(	PUNCT
ejde-637	106	4	2.5	2.5	NUM
ejde-637	106	5	)	)	PUNCT
ejde-637	106	6	ejde-2024/57	ejde-2024/57	NOUN
ejde-637	106	7	planar	planar	ADJ
ejde-637	106	8	sector	sector	NOUN
ejde-637	106	9	-	-	PUNCT
ejde-637	106	10	wise	wise	ADJ
ejde-637	106	11	linear	linear	PROPN
ejde-637	106	12	systems	system	NOUN
ejde-637	106	13	5	5	NUM
ejde-637	106	14	x±	x±	NOUN
ejde-637	106	15	m1	m1	PROPN
ejde-637	106	16	=	=	PUNCT
ejde-637	107	1	x±	x±	PROPN
ejde-637	107	2	e	e	X
ejde-637	107	3	−	−	PROPN
ejde-637	107	4	a12	a12	PROPN
ejde-637	107	5	λ1	λ1	PROPN
ejde-637	107	6	−	−	PROPN
ejde-637	107	7	a11	a11	PROPN
ejde-637	107	8	y±e	y±e	PROPN
ejde-637	108	1	=	=	SYM
ejde-637	108	2	x±	x±	PROPN
ejde-637	108	3	t	t	PROPN
ejde-637	108	4	−	−	PROPN
ejde-637	109	1	λ1	λ1	PROPN
ejde-637	109	2	a21	a21	PROPN
ejde-637	109	3	y±e	y±e	PROPN
ejde-637	109	4	,	,	PUNCT
ejde-637	109	5	x±	x±	PROPN
ejde-637	110	1	m2	m2	PROPN
ejde-637	110	2	=	=	SYM
ejde-637	110	3	x±	x±	PROPN
ejde-637	110	4	e	e	NOUN
ejde-637	110	5	−	−	PROPN
ejde-637	110	6	a12	a12	NOUN
ejde-637	110	7	λ2	λ2	PROPN
ejde-637	110	8	−	−	PROPN
ejde-637	110	9	a11	a11	PROPN
ejde-637	110	10	y±e	y±e	PROPN
ejde-637	111	1	=	=	PUNCT
ejde-637	112	1	x±	x±	PROPN
ejde-637	112	2	t	t	NOUN
ejde-637	112	3	−	−	PROPN
ejde-637	112	4	λ2	λ2	PROPN
ejde-637	112	5	a21	a21	PROPN
ejde-637	112	6	y±e	y±e	PROPN
ejde-637	112	7	,	,	PUNCT
ejde-637	112	8	y±m1	y±m1	X
ejde-637	113	1	=	=	PUNCT
ejde-637	114	1	y±e	y±e	PROPN
ejde-637	114	2	−	−	PROPN
ejde-637	115	1	λ1	λ1	PROPN
ejde-637	115	2	−	−	PROPN
ejde-637	115	3	a11	a11	PROPN
ejde-637	115	4	a12	a12	NOUN
ejde-637	115	5	x±	x±	PROPN
ejde-637	116	1	e	e	PROPN
ejde-637	116	2	=	=	PUNCT
ejde-637	116	3	y±t	y±t	PROPN
ejde-637	117	1	−	−	PROPN
ejde-637	117	2	λ1	λ1	PROPN
ejde-637	117	3	a12	a12	NOUN
ejde-637	117	4	x±	x±	PROPN
ejde-637	117	5	e	e	PROPN
ejde-637	117	6	,	,	PUNCT
ejde-637	117	7	y±m2	y±m2	PROPN
ejde-637	117	8	=	=	PUNCT
ejde-637	118	1	y±e	y±e	NUM
ejde-637	118	2	−	−	NOUN
ejde-637	118	3	λ2	λ2	PROPN
ejde-637	118	4	−	−	PROPN
ejde-637	118	5	a11	a11	PROPN
ejde-637	118	6	a12	a12	NOUN
ejde-637	118	7	x±	x±	PROPN
ejde-637	119	1	e	e	PROPN
ejde-637	119	2	=	=	PUNCT
ejde-637	119	3	y±t	y±t	PROPN
ejde-637	120	1	−	−	PROPN
ejde-637	120	2	λ2	λ2	PROPN
ejde-637	120	3	a12	a12	NOUN
ejde-637	120	4	x±	x±	PROPN
ejde-637	121	1	e	e	PROPN
ejde-637	121	2	.	.	PUNCT
ejde-637	122	1	(	(	PUNCT
ejde-637	122	2	2.6	2.6	NUM
ejde-637	122	3	)	)	PUNCT
ejde-637	122	4	remark	remark	NOUN
ejde-637	122	5	2.6	2.6	NUM
ejde-637	122	6	.	.	PUNCT
ejde-637	123	1	it	it	PRON
ejde-637	123	2	should	should	AUX
ejde-637	123	3	be	be	AUX
ejde-637	123	4	noted	note	VERB
ejde-637	123	5	that	that	SCONJ
ejde-637	123	6	,	,	PUNCT
ejde-637	123	7	by	by	ADP
ejde-637	123	8	system	system	NOUN
ejde-637	123	9	(	(	PUNCT
ejde-637	123	10	1.1	1.1	NUM
ejde-637	123	11	)	)	PUNCT
ejde-637	123	12	with	with	ADP
ejde-637	123	13	λ1	λ1	PROPN
ejde-637	123	14	>	>	X
ejde-637	123	15	0	0	PUNCT
ejde-637	123	16	>	>	X
ejde-637	123	17	λ2	λ2	PROPN
ejde-637	123	18	,	,	PUNCT
ejde-637	123	19	we	we	PRON
ejde-637	123	20	obtain	obtain	VERB
ejde-637	123	21	f1(0	f1(0	PROPN
ejde-637	123	22	,	,	PUNCT
ejde-637	123	23	y	y	PROPN
ejde-637	123	24	±	±	PROPN
ejde-637	123	25	m1	m1	NOUN
ejde-637	123	26	)	)	PUNCT
ejde-637	124	1	=	=	SYM
ejde-637	124	2	−λ1x	−λ1x	X
ejde-637	124	3	±	±	NUM
ejde-637	124	4	e	e	NOUN
ejde-637	124	5	,	,	PUNCT
ejde-637	124	6	f1(0	f1(0	PROPN
ejde-637	124	7	,	,	PUNCT
ejde-637	124	8	y	y	PROPN
ejde-637	124	9	±	±	NUM
ejde-637	124	10	m2	m2	PROPN
ejde-637	124	11	)	)	PUNCT
ejde-637	124	12	=	=	PUNCT
ejde-637	125	1	−λ2x	−λ2x	NUM
ejde-637	125	2	±	±	NUM
ejde-637	125	3	e	e	NOUN
ejde-637	125	4	,	,	PUNCT
ejde-637	125	5	f2(x	f2(x	PROPN
ejde-637	125	6	±	±	NUM
ejde-637	125	7	m1	m1	NOUN
ejde-637	125	8	,	,	PUNCT
ejde-637	125	9	0	0	NUM
ejde-637	125	10	)	)	PUNCT
ejde-637	125	11	=	=	SYM
ejde-637	125	12	−λ1y	−λ1y	NUM
ejde-637	125	13	±	±	NUM
ejde-637	125	14	e	e	NOUN
ejde-637	125	15	,	,	PUNCT
ejde-637	125	16	f2(x	f2(x	PROPN
ejde-637	125	17	±	±	NUM
ejde-637	125	18	m2	m2	PROPN
ejde-637	125	19	,	,	PUNCT
ejde-637	125	20	0	0	NUM
ejde-637	125	21	)	)	PUNCT
ejde-637	125	22	=	=	SYM
ejde-637	125	23	−λ2y	−λ2y	NUM
ejde-637	125	24	±	±	NUM
ejde-637	125	25	e	e	NOUN
ejde-637	125	26	,	,	PUNCT
ejde-637	125	27	which	which	PRON
ejde-637	125	28	means	mean	VERB
ejde-637	125	29	l±1	l±1	NOUN
ejde-637	125	30	and	and	CCONJ
ejde-637	125	31	l±2	l±2	NOUN
ejde-637	125	32	are	be	AUX
ejde-637	125	33	the	the	DET
ejde-637	125	34	unstable	unstable	ADJ
ejde-637	125	35	and	and	CCONJ
ejde-637	125	36	stable	stable	ADJ
ejde-637	125	37	invariant	invariant	ADJ
ejde-637	125	38	manifolds	manifold	NOUN
ejde-637	125	39	of	of	ADP
ejde-637	125	40	x±	x±	PROPN
ejde-637	125	41	e	e	PROPN
ejde-637	125	42	,	,	PUNCT
ejde-637	125	43	respectively	respectively	ADV
ejde-637	125	44	.	.	PUNCT
ejde-637	126	1	3	3	X
ejde-637	126	2	.	.	X
ejde-637	126	3	main	main	ADJ
ejde-637	126	4	results	result	NOUN
ejde-637	126	5	in	in	ADP
ejde-637	126	6	this	this	DET
ejde-637	126	7	paper	paper	NOUN
ejde-637	126	8	,	,	PUNCT
ejde-637	126	9	we	we	PRON
ejde-637	126	10	give	give	VERB
ejde-637	126	11	the	the	DET
ejde-637	126	12	qualitative	qualitative	ADJ
ejde-637	126	13	analysis	analysis	NOUN
ejde-637	126	14	of	of	ADP
ejde-637	126	15	system	system	NOUN
ejde-637	126	16	(	(	PUNCT
ejde-637	126	17	1.1	1.1	NUM
ejde-637	126	18	)	)	PUNCT
ejde-637	126	19	under	under	ADP
ejde-637	126	20	the	the	DET
ejde-637	126	21	following	follow	VERB
ejde-637	126	22	set	set	NOUN
ejde-637	126	23	of	of	ADP
ejde-637	126	24	conditions	condition	NOUN
ejde-637	126	25	(	(	PUNCT
ejde-637	126	26	h	h	NOUN
ejde-637	126	27	):	):	PUNCT
ejde-637	126	28	det(a	det(a	PROPN
ejde-637	126	29	)	)	PUNCT
ejde-637	126	30	=	=	SYM
ejde-637	126	31	a11a22	a11a22	PROPN
ejde-637	126	32	−	−	PROPN
ejde-637	126	33	a12a21	a12a21	ADJ
ejde-637	126	34	<	<	X
ejde-637	126	35	0	0	NUM
ejde-637	126	36	,	,	PUNCT
ejde-637	126	37	a12a21	a12a21	ADJ
ejde-637	126	38	̸=	̸=	PROPN
ejde-637	126	39	0	0	NUM
ejde-637	126	40	,	,	PUNCT
ejde-637	126	41	a21	a21	X
ejde-637	126	42	>	>	X
ejde-637	126	43	0	0	PROPN
ejde-637	126	44	,	,	PUNCT
ejde-637	126	45	a22	a22	X
ejde-637	126	46	>	>	X
ejde-637	126	47	0	0	PROPN
ejde-637	126	48	,	,	PUNCT
ejde-637	126	49	x+	x+	X
ejde-637	126	50	e	e	X
ejde-637	126	51	>	>	X
ejde-637	126	52	0	0	NUM
ejde-637	126	53	,	,	PUNCT
ejde-637	126	54	y+e	y+e	NUM
ejde-637	127	1	=	=	SYM
ejde-637	128	1	−y−e	−y−e	ADJ
ejde-637	128	2	>	>	X
ejde-637	128	3	0	0	NUM
ejde-637	128	4	,	,	PUNCT
ejde-637	128	5	(	(	PUNCT
ejde-637	128	6	3.1	3.1	NUM
ejde-637	128	7	)	)	PUNCT
ejde-637	128	8	for	for	ADP
ejde-637	128	9	which	which	PRON
ejde-637	128	10	,	,	PUNCT
ejde-637	128	11	we	we	PRON
ejde-637	128	12	have	have	VERB
ejde-637	128	13	the	the	DET
ejde-637	128	14	following	follow	VERB
ejde-637	128	15	considerations	consideration	NOUN
ejde-637	128	16	.	.	PUNCT
ejde-637	129	1	first	first	ADV
ejde-637	129	2	,	,	PUNCT
ejde-637	129	3	in	in	ADP
ejde-637	129	4	this	this	DET
ejde-637	129	5	article	article	NOUN
ejde-637	129	6	we	we	PRON
ejde-637	129	7	want	want	VERB
ejde-637	129	8	to	to	PART
ejde-637	129	9	investigate	investigate	VERB
ejde-637	129	10	the	the	DET
ejde-637	129	11	dynamics	dynamic	NOUN
ejde-637	129	12	of	of	ADP
ejde-637	129	13	system	system	NOUN
ejde-637	129	14	(	(	PUNCT
ejde-637	129	15	1.1	1.1	NUM
ejde-637	129	16	)	)	PUNCT
ejde-637	129	17	related	relate	VERB
ejde-637	129	18	to	to	ADP
ejde-637	129	19	sliding	slide	VERB
ejde-637	129	20	homoclinic	homoclinic	ADJ
ejde-637	129	21	/	/	SYM
ejde-637	129	22	heteroclinic	heteroclinic	ADJ
ejde-637	129	23	orbits	orbit	NOUN
ejde-637	129	24	,	,	PUNCT
ejde-637	129	25	so	so	SCONJ
ejde-637	129	26	we	we	PRON
ejde-637	129	27	consider	consider	VERB
ejde-637	129	28	the	the	DET
ejde-637	129	29	case	case	NOUN
ejde-637	129	30	det(a	det(a	PROPN
ejde-637	129	31	)	)	PUNCT
ejde-637	129	32	<	<	X
ejde-637	129	33	0	0	X
ejde-637	129	34	.	.	PUNCT
ejde-637	130	1	the	the	DET
ejde-637	130	2	eigenvalues	eigenvalue	NOUN
ejde-637	130	3	of	of	ADP
ejde-637	130	4	a	a	PRON
ejde-637	130	5	will	will	AUX
ejde-637	130	6	be	be	AUX
ejde-637	130	7	denoted	denote	VERB
ejde-637	130	8	by	by	ADP
ejde-637	130	9	λ1	λ1	PROPN
ejde-637	130	10	>	>	X
ejde-637	130	11	0	0	PUNCT
ejde-637	130	12	>	>	X
ejde-637	130	13	λ2	λ2	PROPN
ejde-637	130	14	.	.	PUNCT
ejde-637	131	1	moreover	moreover	ADV
ejde-637	131	2	,	,	PUNCT
ejde-637	131	3	since	since	SCONJ
ejde-637	131	4	the	the	DET
ejde-637	131	5	discontinuity	discontinuity	NOUN
ejde-637	131	6	boundary	boundary	NOUN
ejde-637	131	7	of	of	ADP
ejde-637	131	8	system	system	NOUN
ejde-637	131	9	(	(	PUNCT
ejde-637	131	10	1.1	1.1	NUM
ejde-637	131	11	)	)	PUNCT
ejde-637	131	12	is	be	AUX
ejde-637	131	13	given	give	VERB
ejde-637	131	14	by	by	ADP
ejde-637	131	15	the	the	DET
ejde-637	131	16	positive	positive	ADJ
ejde-637	131	17	x	x	NOUN
ejde-637	131	18	-	-	NOUN
ejde-637	131	19	axis	axis	NOUN
ejde-637	131	20	and	and	CCONJ
ejde-637	131	21	the	the	DET
ejde-637	131	22	positive	positive	ADJ
ejde-637	131	23	y	y	NOUN
ejde-637	131	24	-	-	PUNCT
ejde-637	131	25	axis	axis	NOUN
ejde-637	131	26	,	,	PUNCT
ejde-637	131	27	we	we	PRON
ejde-637	131	28	use	use	VERB
ejde-637	131	29	a21a12	a21a12	NOUN
ejde-637	131	30	̸=	̸=	PROPN
ejde-637	131	31	0	0	NUM
ejde-637	131	32	to	to	PART
ejde-637	131	33	guarantee	guarantee	VERB
ejde-637	131	34	that	that	SCONJ
ejde-637	131	35	the	the	DET
ejde-637	131	36	section	section	NOUN
ejde-637	131	37	return	return	NOUN
ejde-637	131	38	maps	map	NOUN
ejde-637	131	39	can	can	AUX
ejde-637	131	40	be	be	AUX
ejde-637	131	41	well	well	ADV
ejde-637	131	42	defined	define	VERB
ejde-637	131	43	.	.	PUNCT
ejde-637	132	1	notice	notice	VERB
ejde-637	132	2	that	that	SCONJ
ejde-637	132	3	the	the	DET
ejde-637	132	4	first	first	ADJ
ejde-637	132	5	condition	condition	NOUN
ejde-637	132	6	in	in	ADP
ejde-637	132	7	(	(	PUNCT
ejde-637	132	8	3.1	3.1	NUM
ejde-637	132	9	)	)	PUNCT
ejde-637	132	10	implies	imply	VERB
ejde-637	132	11	a11a22	a11a22	PROPN
ejde-637	132	12	̸=	̸=	PROPN
ejde-637	132	13	0	0	NUM
ejde-637	132	14	.	.	PUNCT
ejde-637	133	1	moreover	moreover	ADV
ejde-637	133	2	,	,	PUNCT
ejde-637	133	3	the	the	DET
ejde-637	133	4	signs	sign	NOUN
ejde-637	133	5	of	of	ADP
ejde-637	133	6	a12	a12	NOUN
ejde-637	133	7	and	and	CCONJ
ejde-637	133	8	a21	a21	NOUN
ejde-637	133	9	will	will	AUX
ejde-637	133	10	be	be	AUX
ejde-637	133	11	changed	change	VERB
ejde-637	133	12	at	at	ADP
ejde-637	133	13	the	the	DET
ejde-637	133	14	same	same	ADJ
ejde-637	133	15	time	time	NOUN
ejde-637	133	16	under	under	ADP
ejde-637	133	17	the	the	DET
ejde-637	133	18	transformation	transformation	NOUN
ejde-637	133	19	(	(	PUNCT
ejde-637	133	20	x	x	X
ejde-637	133	21	,	,	PUNCT
ejde-637	133	22	y	y	PROPN
ejde-637	133	23	,	,	PUNCT
ejde-637	133	24	t	t	PROPN
ejde-637	133	25	)	)	PUNCT
ejde-637	133	26	→	→	SYM
ejde-637	133	27	(	(	PUNCT
ejde-637	133	28	−x	−x	NOUN
ejde-637	133	29	+	+	CCONJ
ejde-637	133	30	2x+	2x+	NUM
ejde-637	133	31	e	e	NOUN
ejde-637	133	32	,	,	PUNCT
ejde-637	133	33	y	y	PROPN
ejde-637	133	34	,	,	PUNCT
ejde-637	133	35	t	t	PROPN
ejde-637	133	36	)	)	PUNCT
ejde-637	133	37	with	with	ADP
ejde-637	133	38	the	the	DET
ejde-637	133	39	signs	sign	NOUN
ejde-637	133	40	of	of	ADP
ejde-637	133	41	a11	a11	PROPN
ejde-637	133	42	and	and	CCONJ
ejde-637	133	43	a22	a22	PROPN
ejde-637	133	44	unchanged	unchanged	ADJ
ejde-637	133	45	.	.	PUNCT
ejde-637	134	1	similarly	similarly	ADV
ejde-637	134	2	,	,	PUNCT
ejde-637	134	3	the	the	DET
ejde-637	134	4	signs	sign	NOUN
ejde-637	134	5	of	of	ADP
ejde-637	134	6	a11	a11	PROPN
ejde-637	134	7	and	and	CCONJ
ejde-637	134	8	a22	a22	PROPN
ejde-637	134	9	will	will	AUX
ejde-637	134	10	be	be	AUX
ejde-637	134	11	changed	change	VERB
ejde-637	134	12	simultaneously	simultaneously	ADV
ejde-637	134	13	under	under	ADP
ejde-637	134	14	the	the	DET
ejde-637	134	15	transformation	transformation	NOUN
ejde-637	134	16	(	(	PUNCT
ejde-637	134	17	x	x	X
ejde-637	134	18	,	,	PUNCT
ejde-637	134	19	y	y	PROPN
ejde-637	134	20	,	,	PUNCT
ejde-637	134	21	t	t	PROPN
ejde-637	134	22	)	)	PUNCT
ejde-637	134	23	→	→	SYM
ejde-637	134	24	(	(	PUNCT
ejde-637	134	25	−x	−x	NOUN
ejde-637	134	26	+	+	CCONJ
ejde-637	134	27	2x+	2x+	NUM
ejde-637	134	28	e	e	NOUN
ejde-637	134	29	,	,	PUNCT
ejde-637	134	30	y,−t	y,−t	PROPN
ejde-637	134	31	)	)	PUNCT
ejde-637	134	32	with	with	ADP
ejde-637	134	33	the	the	DET
ejde-637	134	34	signs	sign	NOUN
ejde-637	134	35	of	of	ADP
ejde-637	134	36	a12	a12	NOUN
ejde-637	134	37	and	and	CCONJ
ejde-637	134	38	a21	a21	NOUN
ejde-637	134	39	unchanged	unchanged	ADJ
ejde-637	134	40	.	.	PUNCT
ejde-637	135	1	therefore	therefore	ADV
ejde-637	135	2	,	,	PUNCT
ejde-637	135	3	when	when	SCONJ
ejde-637	135	4	we	we	PRON
ejde-637	135	5	need	need	VERB
ejde-637	135	6	to	to	PART
ejde-637	135	7	analyze	analyze	VERB
ejde-637	135	8	the	the	DET
ejde-637	135	9	section	section	NOUN
ejde-637	135	10	return	return	NOUN
ejde-637	135	11	maps	map	NOUN
ejde-637	135	12	defined	define	VERB
ejde-637	135	13	on	on	ADP
ejde-637	135	14	the	the	DET
ejde-637	135	15	discontinuity	discontinuity	NOUN
ejde-637	135	16	boundary	boundary	NOUN
ejde-637	135	17	,	,	PUNCT
ejde-637	135	18	we	we	PRON
ejde-637	135	19	only	only	ADV
ejde-637	135	20	need	need	VERB
ejde-637	135	21	to	to	PART
ejde-637	135	22	discuss	discuss	VERB
ejde-637	135	23	the	the	DET
ejde-637	135	24	case	case	NOUN
ejde-637	135	25	when	when	SCONJ
ejde-637	135	26	a21	a21	PROPN
ejde-637	135	27	>	>	X
ejde-637	135	28	0	0	PROPN
ejde-637	135	29	,	,	PUNCT
ejde-637	135	30	a22	a22	X
ejde-637	135	31	>	>	X
ejde-637	135	32	0	0	PROPN
ejde-637	135	33	.	.	PUNCT
ejde-637	136	1	more	more	ADV
ejde-637	136	2	precisely	precisely	ADV
ejde-637	136	3	,	,	PUNCT
ejde-637	136	4	we	we	PRON
ejde-637	136	5	only	only	ADV
ejde-637	136	6	consider	consider	VERB
ejde-637	136	7	the	the	DET
ejde-637	136	8	following	follow	VERB
ejde-637	136	9	two	two	NUM
ejde-637	136	10	cases	case	NOUN
ejde-637	136	11	:	:	PUNCT
ejde-637	136	12	ω1	ω1	PROPN
ejde-637	136	13	=	=	PUNCT
ejde-637	136	14	{	{	PUNCT
ejde-637	136	15	a	a	DET
ejde-637	136	16	:	:	PUNCT
ejde-637	136	17	a21	a21	X
ejde-637	136	18	>	>	X
ejde-637	136	19	0	0	PROPN
ejde-637	136	20	,	,	PUNCT
ejde-637	136	21	a22	a22	X
ejde-637	136	22	>	>	X
ejde-637	136	23	0	0	PROPN
ejde-637	136	24	,	,	PUNCT
ejde-637	136	25	a12a11	a12a11	VERB
ejde-637	136	26	>	>	X
ejde-637	136	27	0	0	NUM
ejde-637	136	28	}	}	PUNCT
ejde-637	136	29	,	,	PUNCT
ejde-637	136	30	ω2	ω2	NOUN
ejde-637	136	31	=	=	PUNCT
ejde-637	136	32	{	{	PUNCT
ejde-637	136	33	a	a	DET
ejde-637	136	34	:	:	PUNCT
ejde-637	136	35	a21	a21	X
ejde-637	136	36	>	>	X
ejde-637	136	37	0	0	PROPN
ejde-637	136	38	,	,	PUNCT
ejde-637	136	39	a22	a22	X
ejde-637	136	40	>	>	X
ejde-637	136	41	0	0	PROPN
ejde-637	136	42	,	,	PUNCT
ejde-637	136	43	a12a11	a12a11	VERB
ejde-637	136	44	<	<	X
ejde-637	136	45	0	0	NUM
ejde-637	136	46	}	}	PUNCT
ejde-637	136	47	.	.	PUNCT
ejde-637	137	1	finally	finally	ADV
ejde-637	137	2	,	,	PUNCT
ejde-637	137	3	because	because	SCONJ
ejde-637	137	4	the	the	DET
ejde-637	137	5	global	global	ADJ
ejde-637	137	6	dynamics	dynamic	NOUN
ejde-637	137	7	of	of	ADP
ejde-637	137	8	piecewise	piecewise	NOUN
ejde-637	137	9	smooth	smooth	ADJ
ejde-637	137	10	systems	system	NOUN
ejde-637	137	11	is	be	AUX
ejde-637	137	12	so	so	ADV
ejde-637	137	13	complex	complex	ADJ
ejde-637	137	14	that	that	SCONJ
ejde-637	137	15	we	we	PRON
ejde-637	137	16	put	put	VERB
ejde-637	137	17	x+	x+	ADJ
ejde-637	137	18	e	e	X
ejde-637	137	19	>	>	X
ejde-637	137	20	0	0	NUM
ejde-637	137	21	,	,	PUNCT
ejde-637	137	22	y+e	y+e	NUM
ejde-637	138	1	=	=	SYM
ejde-637	138	2	−y−e	−y−e	VERB
ejde-637	138	3	>	>	X
ejde-637	138	4	0	0	PUNCT
ejde-637	139	1	and	and	CCONJ
ejde-637	139	2	only	only	ADV
ejde-637	139	3	left	leave	VERB
ejde-637	139	4	x−	x−	PROPN
ejde-637	139	5	e	e	PROPN
ejde-637	139	6	as	as	ADP
ejde-637	139	7	a	a	DET
ejde-637	139	8	bifurcation	bifurcation	NOUN
ejde-637	139	9	parameter	parameter	NOUN
ejde-637	139	10	.	.	PUNCT
ejde-637	140	1	to	to	PART
ejde-637	140	2	state	state	VERB
ejde-637	140	3	our	our	PRON
ejde-637	140	4	main	main	ADJ
ejde-637	140	5	results	result	NOUN
ejde-637	140	6	about	about	ADP
ejde-637	140	7	the	the	DET
ejde-637	140	8	global	global	ADJ
ejde-637	140	9	dynamics	dynamic	NOUN
ejde-637	140	10	of	of	ADP
ejde-637	140	11	system	system	NOUN
ejde-637	140	12	(	(	PUNCT
ejde-637	140	13	1.1	1.1	NUM
ejde-637	140	14	)	)	PUNCT
ejde-637	140	15	under	under	ADP
ejde-637	140	16	(	(	PUNCT
ejde-637	140	17	3.1	3.1	NUM
ejde-637	140	18	)	)	PUNCT
ejde-637	140	19	by	by	ADP
ejde-637	140	20	means	mean	NOUN
ejde-637	140	21	of	of	ADP
ejde-637	140	22	providing	provide	VERB
ejde-637	140	23	the	the	DET
ejde-637	140	24	existence	existence	NOUN
ejde-637	140	25	of	of	ADP
ejde-637	140	26	all	all	DET
ejde-637	140	27	important	important	ADJ
ejde-637	140	28	separatrix	separatrix	NOUN
ejde-637	140	29	in	in	ADP
ejde-637	140	30	the	the	DET
ejde-637	140	31	state	state	NOUN
ejde-637	140	32	space	space	NOUN
ejde-637	140	33	,	,	PUNCT
ejde-637	140	34	we	we	PRON
ejde-637	140	35	first	first	ADV
ejde-637	140	36	give	give	VERB
ejde-637	140	37	the	the	DET
ejde-637	140	38	following	follow	VERB
ejde-637	140	39	propositions	proposition	NOUN
ejde-637	140	40	to	to	PART
ejde-637	140	41	clarify	clarify	VERB
ejde-637	140	42	the	the	DET
ejde-637	140	43	existence	existence	NOUN
ejde-637	140	44	of	of	ADP
ejde-637	140	45	sliding	slide	VERB
ejde-637	140	46	set	set	VERB
ejde-637	140	47	and	and	CCONJ
ejde-637	140	48	pseudo	pseudo	NOUN
ejde-637	140	49	-	-	NOUN
ejde-637	140	50	equilibrium	equilibrium	NOUN
ejde-637	140	51	points	point	NOUN
ejde-637	140	52	,	,	PUNCT
ejde-637	140	53	and	and	CCONJ
ejde-637	140	54	the	the	DET
ejde-637	140	55	properties	property	NOUN
ejde-637	140	56	of	of	ADP
ejde-637	140	57	the	the	DET
ejde-637	140	58	unique	unique	ADJ
ejde-637	140	59	non	non	ADJ
ejde-637	140	60	-	-	ADJ
ejde-637	140	61	regular	regular	ADJ
ejde-637	140	62	p0	p0	NOUN
ejde-637	140	63	=	=	SYM
ejde-637	140	64	(	(	PUNCT
ejde-637	140	65	0	0	NUM
ejde-637	140	66	,	,	PUNCT
ejde-637	140	67	0	0	NUM
ejde-637	140	68	)	)	PUNCT
ejde-637	140	69	.	.	PUNCT
ejde-637	141	1	6	6	NUM
ejde-637	141	2	q.-q	q.-q	PROPN
ejde-637	141	3	.	.	PUNCT
ejde-637	142	1	han	han	PROPN
ejde-637	142	2	,	,	PUNCT
ejde-637	142	3	s.-m	s.-m	PROPN
ejde-637	142	4	.	.	PUNCT
ejde-637	143	1	huan	huan	PROPN
ejde-637	143	2	ejde-2024/57	ejde-2024/57	PROPN
ejde-637	143	3	proposition	proposition	NOUN
ejde-637	143	4	3.1	3.1	NUM
ejde-637	143	5	.	.	PUNCT
ejde-637	143	6	suppose	suppose	VERB
ejde-637	143	7	that	that	SCONJ
ejde-637	143	8	condition	condition	NOUN
ejde-637	143	9	(	(	PUNCT
ejde-637	143	10	3.1	3.1	NUM
ejde-637	143	11	)	)	PUNCT
ejde-637	143	12	holds	hold	NOUN
ejde-637	143	13	and	and	CCONJ
ejde-637	143	14	a	a	DET
ejde-637	143	15	∈	∈	PROPN
ejde-637	143	16	ω1	ω1	PROPN
ejde-637	143	17	∪	∪	X
ejde-637	143	18	ω2	ω2	PROPN
ejde-637	143	19	.	.	PUNCT
ejde-637	144	1	let	let	VERB
ejde-637	144	2	µ1	µ1	VERB
ejde-637	144	3	:	:	PUNCT
ejde-637	144	4	=	=	NOUN
ejde-637	144	5	a22	a22	PROPN
ejde-637	144	6	a21	a21	PROPN
ejde-637	144	7	y+e	y+e	NUM
ejde-637	144	8	,	,	PUNCT
ejde-637	144	9	µ2	µ2	PROPN
ejde-637	144	10	:	:	PUNCT
ejde-637	144	11	=	=	PROPN
ejde-637	144	12	a12	a12	PROPN
ejde-637	144	13	a11	a11	PROPN
ejde-637	144	14	y+e	y+e	PROPN
ejde-637	144	15	.	.	PUNCT
ejde-637	145	1	then	then	ADV
ejde-637	145	2	the	the	DET
ejde-637	145	3	sliding	slide	VERB
ejde-637	145	4	set	set	NOUN
ejde-637	145	5	σs	σs	ADP
ejde-637	145	6	of	of	ADP
ejde-637	145	7	system	system	NOUN
ejde-637	145	8	(	(	PUNCT
ejde-637	145	9	1.1	1.1	NUM
ejde-637	145	10	)	)	PUNCT
ejde-637	145	11	is	be	AUX
ejde-637	145	12	σs	σs	ADP
ejde-637	145	13	=	=	PROPN
ejde-637	145	14	σx	σx	NOUN
ejde-637	145	15	s	s	PROPN
ejde-637	145	16	∪	∪	X
ejde-637	145	17	σy	σy	NOUN
ejde-637	145	18	s	s	NOUN
ejde-637	145	19	with	with	ADP
ejde-637	145	20	σx	σx	PROPN
ejde-637	145	21	s	s	PART
ejde-637	145	22	=	=	PUNCT
ejde-637	145	23	{	{	PUNCT
ejde-637	145	24	(	(	PUNCT
ejde-637	145	25	x	x	NOUN
ejde-637	145	26	,	,	PUNCT
ejde-637	145	27	0	0	NUM
ejde-637	145	28	)	)	PUNCT
ejde-637	145	29	:	:	PUNCT
ejde-637	146	1	x	x	SYM
ejde-637	146	2	>	>	X
ejde-637	146	3	0	0	NUM
ejde-637	146	4	,	,	PUNCT
ejde-637	146	5	x	x	SYM
ejde-637	146	6	∈	∈	PROPN
ejde-637	146	7	(	(	PUNCT
ejde-637	146	8	min{x−	min{x−	PROPN
ejde-637	146	9	t	t	PROPN
ejde-637	146	10	,	,	PUNCT
ejde-637	146	11	x	x	PROPN
ejde-637	146	12	+	+	NUM
ejde-637	146	13	t	t	NOUN
ejde-637	146	14	}	}	PUNCT
ejde-637	146	15	,	,	PUNCT
ejde-637	146	16	max{x−	max{x−	PROPN
ejde-637	146	17	t	t	PROPN
ejde-637	146	18	,	,	PUNCT
ejde-637	146	19	x	x	PROPN
ejde-637	146	20	+	+	NUM
ejde-637	146	21	t	t	NOUN
ejde-637	146	22	}	}	PUNCT
ejde-637	146	23	)	)	PUNCT
ejde-637	146	24	}	}	PUNCT
ejde-637	146	25	,	,	PUNCT
ejde-637	146	26	=	=	PUNCT
ejde-637	146	27			PROPN
ejde-637	146	28	{	{	PUNCT
ejde-637	146	29	(	(	PUNCT
ejde-637	146	30	x	x	X
ejde-637	146	31	,	,	PUNCT
ejde-637	146	32	0	0	NUM
ejde-637	146	33	)	)	PUNCT
ejde-637	146	34	:	:	PUNCT
ejde-637	146	35	0	0	NUM
ejde-637	146	36	≤	≤	NUM
ejde-637	146	37	x	x	PUNCT
ejde-637	146	38	<	<	X
ejde-637	146	39	x+	x+	PROPN
ejde-637	146	40	t	t	PROPN
ejde-637	146	41	}	}	PUNCT
ejde-637	146	42	,	,	PUNCT
ejde-637	146	43	if	if	SCONJ
ejde-637	146	44	x−	x−	PROPN
ejde-637	146	45	e	e	PROPN
ejde-637	146	46	<	<	X
ejde-637	146	47	µ1	µ1	PROPN
ejde-637	146	48	,	,	PUNCT
ejde-637	146	49	{	{	PUNCT
ejde-637	146	50	(	(	PUNCT
ejde-637	146	51	x	x	X
ejde-637	146	52	,	,	PUNCT
ejde-637	146	53	0	0	NUM
ejde-637	146	54	)	)	PUNCT
ejde-637	146	55	:	:	PUNCT
ejde-637	146	56	x−	x−	PROPN
ejde-637	146	57	t	t	PROPN
ejde-637	146	58	<	<	X
ejde-637	146	59	x	x	X
ejde-637	146	60	<	<	X
ejde-637	146	61	x+	x+	PROPN
ejde-637	146	62	t	t	PROPN
ejde-637	146	63	}	}	PUNCT
ejde-637	146	64	,	,	PUNCT
ejde-637	146	65	if	if	SCONJ
ejde-637	146	66	µ1	µ1	PROPN
ejde-637	146	67	≤	≤	X
ejde-637	146	68	x−	x−	PROPN
ejde-637	147	1	e	e	X
ejde-637	147	2	<	<	X
ejde-637	147	3	x+	x+	X
ejde-637	147	4	e	e	X
ejde-637	147	5	+	+	NOUN
ejde-637	147	6	2µ1	2µ1	NUM
ejde-637	147	7	,	,	PUNCT
ejde-637	147	8	∅	∅	NOUN
ejde-637	147	9	,	,	PUNCT
ejde-637	147	10	if	if	SCONJ
ejde-637	147	11	x−	x−	PROPN
ejde-637	147	12	e	e	PROPN
ejde-637	147	13	=	=	PUNCT
ejde-637	147	14	x+	x+	SYM
ejde-637	147	15	e	e	X
ejde-637	147	16	+	+	NOUN
ejde-637	147	17	2µ1	2µ1	NUM
ejde-637	147	18	,	,	PUNCT
ejde-637	147	19	{	{	PUNCT
ejde-637	147	20	(	(	PUNCT
ejde-637	147	21	x	x	X
ejde-637	147	22	,	,	PUNCT
ejde-637	147	23	0	0	NUM
ejde-637	147	24	)	)	PUNCT
ejde-637	147	25	:	:	PUNCT
ejde-637	148	1	x+	x+	PROPN
ejde-637	148	2	t	t	X
ejde-637	148	3	<	<	X
ejde-637	148	4	x	x	X
ejde-637	148	5	<	<	X
ejde-637	148	6	x−	x−	PROPN
ejde-637	148	7	t	t	PROPN
ejde-637	148	8	}	}	PUNCT
ejde-637	148	9	,	,	PUNCT
ejde-637	148	10	if	if	SCONJ
ejde-637	148	11	x−	x−	PROPN
ejde-637	148	12	e	e	PROPN
ejde-637	148	13	>	>	X
ejde-637	148	14	x+	x+	X
ejde-637	149	1	e	e	X
ejde-637	149	2	+	+	NOUN
ejde-637	149	3	2µ1	2µ1	NUM
ejde-637	149	4	,	,	PUNCT
ejde-637	149	5	(	(	PUNCT
ejde-637	149	6	3.2	3.2	NUM
ejde-637	149	7	)	)	PUNCT
ejde-637	149	8	and	and	CCONJ
ejde-637	149	9	σy	σy	NOUN
ejde-637	149	10	s	s	PROPN
ejde-637	149	11	=	=	X
ejde-637	149	12	{	{	PUNCT
ejde-637	149	13	(	(	PUNCT
ejde-637	149	14	0	0	NUM
ejde-637	149	15	,	,	PUNCT
ejde-637	149	16	y	y	PROPN
ejde-637	149	17	)	)	PUNCT
ejde-637	149	18	:	:	PUNCT
ejde-637	150	1	y	y	PROPN
ejde-637	150	2	>	>	X
ejde-637	150	3	0	0	PROPN
ejde-637	150	4	,	,	PUNCT
ejde-637	150	5	y	y	PROPN
ejde-637	150	6	∈	∈	PROPN
ejde-637	150	7	(	(	PUNCT
ejde-637	150	8	min{y−t	min{y−t	NOUN
ejde-637	150	9	,	,	PUNCT
ejde-637	150	10	y+t	y+t	PROPN
ejde-637	150	11	}	}	PUNCT
ejde-637	150	12	,	,	PUNCT
ejde-637	150	13	max{y−t	max{y−t	NOUN
ejde-637	150	14	,	,	PUNCT
ejde-637	150	15	y+t	y+t	PROPN
ejde-637	150	16	}	}	PUNCT
ejde-637	150	17	)	)	PUNCT
ejde-637	150	18	}	}	PUNCT
ejde-637	150	19	.	.	PUNCT
ejde-637	151	1	(	(	PUNCT
ejde-637	151	2	3.3	3.3	NUM
ejde-637	151	3	)	)	PUNCT
ejde-637	151	4	about	about	ADP
ejde-637	151	5	σy	σy	NOUN
ejde-637	151	6	s	s	PART
ejde-637	151	7	,	,	PUNCT
ejde-637	151	8	we	we	PRON
ejde-637	151	9	have	have	VERB
ejde-637	151	10	the	the	DET
ejde-637	151	11	following	following	ADJ
ejde-637	151	12	statements	statement	NOUN
ejde-637	151	13	:	:	PUNCT
ejde-637	151	14	(	(	PUNCT
ejde-637	151	15	a1	a1	NOUN
ejde-637	151	16	)	)	PUNCT
ejde-637	151	17	when	when	SCONJ
ejde-637	151	18	a	a	DET
ejde-637	151	19	∈	∈	PROPN
ejde-637	151	20	ω1	ω1	PROPN
ejde-637	151	21	,	,	PUNCT
ejde-637	151	22	we	we	PRON
ejde-637	151	23	have	have	VERB
ejde-637	151	24	σy	σy	NOUN
ejde-637	151	25	s	s	PART
ejde-637	151	26	=	=	SYM
ejde-637	151	27			PROPN
ejde-637	151	28	{	{	PUNCT
ejde-637	151	29	(	(	PUNCT
ejde-637	151	30	0	0	NUM
ejde-637	151	31	,	,	PUNCT
ejde-637	151	32	y	y	PROPN
ejde-637	151	33	)	)	PUNCT
ejde-637	151	34	:	:	PUNCT
ejde-637	152	1	0	0	NUM
ejde-637	152	2	≤	≤	NUM
ejde-637	152	3	y	y	PROPN
ejde-637	152	4	<	<	X
ejde-637	152	5	y+t	y+t	PROPN
ejde-637	152	6	}	}	PUNCT
ejde-637	152	7	,	,	PUNCT
ejde-637	152	8	if	if	SCONJ
ejde-637	152	9	x−	x−	PROPN
ejde-637	152	10	e	e	PROPN
ejde-637	152	11	<	<	X
ejde-637	152	12	µ2	µ2	PROPN
ejde-637	152	13	,	,	PUNCT
ejde-637	152	14	{	{	PUNCT
ejde-637	152	15	(	(	PUNCT
ejde-637	152	16	0	0	NUM
ejde-637	152	17	,	,	PUNCT
ejde-637	152	18	y	y	PROPN
ejde-637	152	19	)	)	PUNCT
ejde-637	152	20	:	:	PUNCT
ejde-637	152	21	y−t	y−t	VERB
ejde-637	152	22	<	<	X
ejde-637	152	23	y	y	X
ejde-637	152	24	<	<	X
ejde-637	152	25	y+t	y+t	PROPN
ejde-637	152	26	}	}	PUNCT
ejde-637	152	27	,	,	PUNCT
ejde-637	152	28	if	if	SCONJ
ejde-637	152	29	µ2	µ2	PROPN
ejde-637	152	30	≤	≤	NUM
ejde-637	152	31	x−	x−	PROPN
ejde-637	153	1	e	e	X
ejde-637	153	2	<	<	X
ejde-637	153	3	x+	x+	X
ejde-637	153	4	e	e	X
ejde-637	153	5	+	+	SYM
ejde-637	153	6	2µ2	2µ2	NUM
ejde-637	153	7	,	,	PUNCT
ejde-637	153	8	∅	∅	NOUN
ejde-637	153	9	,	,	PUNCT
ejde-637	153	10	if	if	SCONJ
ejde-637	153	11	x−	x−	PROPN
ejde-637	153	12	e	e	PROPN
ejde-637	153	13	=	=	PUNCT
ejde-637	153	14	x+	x+	SYM
ejde-637	153	15	e	e	X
ejde-637	153	16	+	+	NOUN
ejde-637	153	17	2µ2	2µ2	NUM
ejde-637	153	18	,	,	PUNCT
ejde-637	153	19	{	{	PUNCT
ejde-637	153	20	(	(	PUNCT
ejde-637	153	21	0	0	NUM
ejde-637	153	22	,	,	PUNCT
ejde-637	153	23	y	y	PROPN
ejde-637	153	24	)	)	PUNCT
ejde-637	153	25	:	:	PUNCT
ejde-637	153	26	y+t	y+t	X
ejde-637	153	27	<	<	X
ejde-637	154	1	y	y	X
ejde-637	154	2	<	<	X
ejde-637	154	3	y−t	y−t	PROPN
ejde-637	154	4	}	}	PUNCT
ejde-637	154	5	,	,	PUNCT
ejde-637	155	1	if	if	SCONJ
ejde-637	155	2	x−	x−	PROPN
ejde-637	155	3	e	e	PROPN
ejde-637	155	4	>	>	X
ejde-637	155	5	x+	x+	X
ejde-637	155	6	e	e	X
ejde-637	155	7	+	+	NOUN
ejde-637	155	8	2µ2	2µ2	NUM
ejde-637	155	9	.	.	PUNCT
ejde-637	156	1	(	(	PUNCT
ejde-637	156	2	3.4	3.4	NUM
ejde-637	156	3	)	)	PUNCT
ejde-637	156	4	(	(	PUNCT
ejde-637	156	5	a2	a2	PROPN
ejde-637	156	6	)	)	PUNCT
ejde-637	156	7	when	when	SCONJ
ejde-637	156	8	a	a	DET
ejde-637	156	9	∈	∈	NOUN
ejde-637	156	10	ω2	ω2	ADJ
ejde-637	156	11	with	with	ADP
ejde-637	156	12	x+	x+	ADJ
ejde-637	156	13	e	e	X
ejde-637	156	14	+	+	CCONJ
ejde-637	156	15	µ2	µ2	PROPN
ejde-637	156	16	>	>	X
ejde-637	156	17	0	0	PROPN
ejde-637	156	18	,	,	PUNCT
ejde-637	156	19	we	we	PRON
ejde-637	156	20	have	have	VERB
ejde-637	156	21	σy	σy	NOUN
ejde-637	156	22	s	s	PART
ejde-637	156	23	=	=	X
ejde-637	156	24	{	{	PUNCT
ejde-637	156	25	{	{	PUNCT
ejde-637	156	26	(	(	PUNCT
ejde-637	156	27	0	0	NUM
ejde-637	156	28	,	,	PUNCT
ejde-637	156	29	y	y	PROPN
ejde-637	156	30	)	)	PUNCT
ejde-637	156	31	:	:	PUNCT
ejde-637	157	1	0	0	NUM
ejde-637	157	2	≤	≤	NUM
ejde-637	157	3	y	y	PROPN
ejde-637	157	4	<	<	X
ejde-637	157	5	y−t	y−t	PROPN
ejde-637	157	6	}	}	PUNCT
ejde-637	157	7	,	,	PUNCT
ejde-637	157	8	if	if	SCONJ
ejde-637	157	9	x−	x−	PROPN
ejde-637	157	10	e	e	PROPN
ejde-637	157	11	<	<	X
ejde-637	157	12	µ2	µ2	PROPN
ejde-637	157	13	,	,	PUNCT
ejde-637	157	14	∅	∅	NOUN
ejde-637	157	15	,	,	PUNCT
ejde-637	157	16	if	if	SCONJ
ejde-637	157	17	x−	x−	PROPN
ejde-637	157	18	e	e	PROPN
ejde-637	157	19	≥	≥	NOUN
ejde-637	157	20	µ2	µ2	PROPN
ejde-637	157	21	.	.	PUNCT
ejde-637	158	1	(	(	PUNCT
ejde-637	158	2	3.5	3.5	NUM
ejde-637	158	3	)	)	PUNCT
ejde-637	158	4	(	(	PUNCT
ejde-637	158	5	a3	a3	NOUN
ejde-637	158	6	)	)	PUNCT
ejde-637	158	7	when	when	SCONJ
ejde-637	158	8	a	a	DET
ejde-637	158	9	∈	∈	NOUN
ejde-637	158	10	ω2	ω2	ADJ
ejde-637	158	11	with	with	ADP
ejde-637	158	12	x+	x+	ADJ
ejde-637	158	13	e	e	X
ejde-637	158	14	+	+	CCONJ
ejde-637	158	15	µ2	µ2	VERB
ejde-637	158	16	≤	≤	PROPN
ejde-637	158	17	0	0	NUM
ejde-637	158	18	,	,	PUNCT
ejde-637	158	19	we	we	PRON
ejde-637	158	20	have	have	VERB
ejde-637	158	21	σy	σy	NOUN
ejde-637	158	22	s	s	PART
ejde-637	158	23	=	=	SYM
ejde-637	158	24			PROPN
ejde-637	158	25	{	{	PUNCT
ejde-637	158	26	(	(	PUNCT
ejde-637	158	27	0	0	NUM
ejde-637	158	28	,	,	PUNCT
ejde-637	158	29	y	y	PROPN
ejde-637	158	30	)	)	PUNCT
ejde-637	158	31	:	:	PUNCT
ejde-637	158	32	y+t	y+t	X
ejde-637	158	33	<	<	X
ejde-637	159	1	y	y	X
ejde-637	159	2	<	<	X
ejde-637	159	3	y−t	y−t	PROPN
ejde-637	159	4	}	}	PUNCT
ejde-637	159	5	,	,	PUNCT
ejde-637	160	1	if	if	SCONJ
ejde-637	160	2	x−	x−	PROPN
ejde-637	160	3	e	e	PROPN
ejde-637	160	4	<	<	X
ejde-637	160	5	x+	x+	X
ejde-637	160	6	e	e	X
ejde-637	160	7	+	+	SYM
ejde-637	160	8	2µ2	2µ2	NUM
ejde-637	160	9	,	,	PUNCT
ejde-637	160	10	∅	∅	NOUN
ejde-637	160	11	,	,	PUNCT
ejde-637	160	12	if	if	SCONJ
ejde-637	160	13	x−	x−	PROPN
ejde-637	160	14	e	e	PROPN
ejde-637	160	15	=	=	PUNCT
ejde-637	160	16	x+	x+	SYM
ejde-637	160	17	e	e	X
ejde-637	160	18	+	+	NOUN
ejde-637	160	19	2µ2	2µ2	NUM
ejde-637	160	20	,	,	PUNCT
ejde-637	160	21	{	{	PUNCT
ejde-637	160	22	(	(	PUNCT
ejde-637	160	23	0	0	NUM
ejde-637	160	24	,	,	PUNCT
ejde-637	160	25	y	y	PROPN
ejde-637	160	26	)	)	PUNCT
ejde-637	160	27	:	:	PUNCT
ejde-637	160	28	y−t	y−t	VERB
ejde-637	160	29	<	<	X
ejde-637	160	30	y	y	X
ejde-637	160	31	<	<	X
ejde-637	160	32	y+t	y+t	PROPN
ejde-637	160	33	}	}	PUNCT
ejde-637	160	34	,	,	PUNCT
ejde-637	160	35	if	if	SCONJ
ejde-637	160	36	x+	x+	ADJ
ejde-637	160	37	e	e	NOUN
ejde-637	160	38	+	+	NOUN
ejde-637	160	39	2µ2	2µ2	NUM
ejde-637	160	40	<	<	X
ejde-637	160	41	x−	x−	PROPN
ejde-637	160	42	e	e	PROPN
ejde-637	160	43	≤	≤	PROPN
ejde-637	160	44	µ2	µ2	PROPN
ejde-637	160	45	,	,	PUNCT
ejde-637	160	46	{	{	PUNCT
ejde-637	160	47	(	(	PUNCT
ejde-637	160	48	0	0	NUM
ejde-637	160	49	,	,	PUNCT
ejde-637	160	50	y	y	PROPN
ejde-637	160	51	)	)	PUNCT
ejde-637	160	52	:	:	PUNCT
ejde-637	161	1	0	0	NUM
ejde-637	161	2	≤	≤	NUM
ejde-637	161	3	y	y	PROPN
ejde-637	161	4	<	<	X
ejde-637	161	5	y+t	y+t	PROPN
ejde-637	161	6	}	}	PUNCT
ejde-637	161	7	,	,	PUNCT
ejde-637	161	8	if	if	SCONJ
ejde-637	161	9	x−	x−	PROPN
ejde-637	161	10	e	e	PROPN
ejde-637	161	11	>	>	X
ejde-637	161	12	µ2	µ2	PROPN
ejde-637	161	13	.	.	PUNCT
ejde-637	162	1	(	(	PUNCT
ejde-637	162	2	3.6	3.6	NUM
ejde-637	162	3	)	)	PUNCT
ejde-637	162	4	proof	proof	NOUN
ejde-637	162	5	.	.	PUNCT
ejde-637	163	1	note	note	VERB
ejde-637	163	2	that	that	SCONJ
ejde-637	163	3	the	the	DET
ejde-637	163	4	discontinuity	discontinuity	NOUN
ejde-637	163	5	boundary	boundary	NOUN
ejde-637	163	6	of	of	ADP
ejde-637	163	7	system	system	NOUN
ejde-637	163	8	(	(	PUNCT
ejde-637	163	9	1.1	1.1	NUM
ejde-637	163	10	)	)	PUNCT
ejde-637	163	11	is	be	AUX
ejde-637	163	12	composed	compose	VERB
ejde-637	163	13	of	of	ADP
ejde-637	163	14	the	the	DET
ejde-637	163	15	origin	origin	NOUN
ejde-637	163	16	,	,	PUNCT
ejde-637	163	17	the	the	DET
ejde-637	163	18	positive	positive	ADJ
ejde-637	163	19	x	x	NOUN
ejde-637	163	20	-	-	NOUN
ejde-637	163	21	axis	axis	NOUN
ejde-637	163	22	and	and	CCONJ
ejde-637	163	23	the	the	DET
ejde-637	163	24	positive	positive	ADJ
ejde-637	163	25	y	y	NOUN
ejde-637	163	26	-	-	PUNCT
ejde-637	163	27	axis	axis	NOUN
ejde-637	163	28	.	.	PUNCT
ejde-637	164	1	so	so	ADV
ejde-637	164	2	according	accord	VERB
ejde-637	164	3	to	to	ADP
ejde-637	164	4	definition	definition	NOUN
ejde-637	164	5	2.2	2.2	NUM
ejde-637	164	6	,	,	PUNCT
ejde-637	164	7	when	when	SCONJ
ejde-637	164	8	x	x	X
ejde-637	164	9	=	=	SYM
ejde-637	164	10	(	(	PUNCT
ejde-637	164	11	x	x	X
ejde-637	164	12	,	,	PUNCT
ejde-637	164	13	0	0	NUM
ejde-637	164	14	)	)	PUNCT
ejde-637	164	15	is	be	AUX
ejde-637	164	16	on	on	ADP
ejde-637	164	17	the	the	DET
ejde-637	164	18	positive	positive	ADJ
ejde-637	164	19	x	x	NOUN
ejde-637	164	20	-	-	NOUN
ejde-637	164	21	axis	axis	ADJ
ejde-637	164	22	,	,	PUNCT
ejde-637	164	23	we	we	PRON
ejde-637	164	24	have	have	VERB
ejde-637	164	25	⟨f+(p	⟨f+(p	PROPN
ejde-637	164	26	)	)	PUNCT
ejde-637	164	27	,	,	PUNCT
ejde-637	164	28	hx(p)⟩	hx(p)⟩	PROPN
ejde-637	164	29	·	·	PUNCT
ejde-637	164	30	⟨f−(p	⟨f−(p	PROPN
ejde-637	164	31	)	)	PUNCT
ejde-637	164	32	,	,	PUNCT
ejde-637	164	33	hx(p)⟩	hx(p)⟩	PROPN
ejde-637	164	34	=	=	PRON
ejde-637	164	35	f+	f+	PROPN
ejde-637	164	36	2	2	NUM
ejde-637	164	37	(	(	PUNCT
ejde-637	164	38	x	x	NOUN
ejde-637	164	39	,	,	PUNCT
ejde-637	164	40	0)f−	0)f−	NOUN
ejde-637	164	41	2	2	NUM
ejde-637	164	42	(	(	PUNCT
ejde-637	164	43	x	x	NOUN
ejde-637	164	44	,	,	PUNCT
ejde-637	164	45	0	0	NUM
ejde-637	164	46	)	)	PUNCT
ejde-637	164	47	=	=	PRON
ejde-637	164	48	a221(x−	a221(x−	X
ejde-637	164	49	x+	x+	PUNCT
ejde-637	164	50	t	t	NOUN
ejde-637	164	51	)	)	PUNCT
ejde-637	164	52	(	(	PUNCT
ejde-637	164	53	x−	x−	PROPN
ejde-637	164	54	x−	x−	PROPN
ejde-637	164	55	t	t	PROPN
ejde-637	164	56	)	)	PUNCT
ejde-637	164	57	,	,	PUNCT
ejde-637	164	58	and	and	CCONJ
ejde-637	164	59	when	when	SCONJ
ejde-637	164	60	x	x	PART
ejde-637	164	61	=	=	SYM
ejde-637	164	62	(	(	PUNCT
ejde-637	164	63	0	0	NUM
ejde-637	164	64	,	,	PUNCT
ejde-637	164	65	y	y	NOUN
ejde-637	164	66	)	)	PUNCT
ejde-637	164	67	is	be	AUX
ejde-637	164	68	on	on	ADP
ejde-637	164	69	the	the	DET
ejde-637	164	70	positive	positive	ADJ
ejde-637	164	71	y	y	NOUN
ejde-637	164	72	-	-	PUNCT
ejde-637	164	73	axis	axis	NOUN
ejde-637	164	74	,	,	PUNCT
ejde-637	164	75	we	we	PRON
ejde-637	164	76	have	have	VERB
ejde-637	164	77	⟨f+(p	⟨f+(p	PROPN
ejde-637	164	78	)	)	PUNCT
ejde-637	164	79	,	,	PUNCT
ejde-637	164	80	hx(p)⟩	hx(p)⟩	PROPN
ejde-637	164	81	·	·	PUNCT
ejde-637	164	82	⟨f−(p	⟨f−(p	PROPN
ejde-637	164	83	)	)	PUNCT
ejde-637	164	84	,	,	PUNCT
ejde-637	164	85	hx(p)⟩	hx(p)⟩	PROPN
ejde-637	164	86	=	=	PRON
ejde-637	164	87	f+	f+	PROPN
ejde-637	164	88	1	1	NUM
ejde-637	164	89	(	(	PUNCT
ejde-637	164	90	0	0	NUM
ejde-637	164	91	,	,	PUNCT
ejde-637	164	92	y)f−	y)f−	PROPN
ejde-637	164	93	1	1	NUM
ejde-637	164	94	(	(	PUNCT
ejde-637	164	95	0	0	NUM
ejde-637	164	96	,	,	PUNCT
ejde-637	164	97	y	y	NOUN
ejde-637	164	98	)	)	PUNCT
ejde-637	164	99	=	=	SYM
ejde-637	165	1	a212(y	a212(y	PROPN
ejde-637	165	2	−	−	PROPN
ejde-637	165	3	y+t	y+t	PROPN
ejde-637	165	4	)	)	PUNCT
ejde-637	166	1	(	(	PUNCT
ejde-637	166	2	y	y	PROPN
ejde-637	166	3	−	−	PROPN
ejde-637	166	4	y−t	y−t	PROPN
ejde-637	166	5	)	)	PUNCT
ejde-637	166	6	.	.	PUNCT
ejde-637	167	1	moreover	moreover	ADV
ejde-637	167	2	,	,	PUNCT
ejde-637	167	3	when	when	SCONJ
ejde-637	167	4	a	a	DET
ejde-637	167	5	∈	∈	PROPN
ejde-637	167	6	ω1	ω1	PROPN
ejde-637	167	7	∪	∪	X
ejde-637	167	8	ω2	ω2	PROPN
ejde-637	167	9	,	,	PUNCT
ejde-637	167	10	we	we	PRON
ejde-637	167	11	have	have	VERB
ejde-637	167	12	x+	x+	PROPN
ejde-637	167	13	t	t	PROPN
ejde-637	167	14	>	>	X
ejde-637	167	15	0	0	PUNCT
ejde-637	168	1	and	and	CCONJ
ejde-637	168	2	0	0	NUM
ejde-637	168	3	<	<	X
ejde-637	168	4	µ1	µ1	PROPN
ejde-637	168	5	<	<	X
ejde-637	168	6	2µ1	2µ1	NUM
ejde-637	169	1	+	+	CCONJ
ejde-637	169	2	x+	x+	ADJ
ejde-637	169	3	e	e	X
ejde-637	169	4	under	under	ADP
ejde-637	169	5	the	the	DET
ejde-637	169	6	condition	condition	NOUN
ejde-637	169	7	(	(	PUNCT
ejde-637	169	8	3.1	3.1	NUM
ejde-637	169	9	)	)	PUNCT
ejde-637	169	10	.	.	PUNCT
ejde-637	170	1	and	and	CCONJ
ejde-637	170	2	by	by	ADP
ejde-637	170	3	easy	easy	ADJ
ejde-637	170	4	computations	computation	NOUN
ejde-637	170	5	,	,	PUNCT
ejde-637	170	6	it	it	PRON
ejde-637	170	7	follows	follow	VERB
ejde-637	170	8	that	that	SCONJ
ejde-637	170	9	x−	x−	PROPN
ejde-637	170	10	e	e	PROPN
ejde-637	170	11	=	=	PROPN
ejde-637	170	12	µ1	µ1	PROPN
ejde-637	170	13	⇔	⇔	PROPN
ejde-637	170	14	x−	x−	PROPN
ejde-637	170	15	t	t	PROPN
ejde-637	170	16	=	=	SYM
ejde-637	170	17	0	0	PROPN
ejde-637	170	18	,	,	PUNCT
ejde-637	170	19	x−	x−	PROPN
ejde-637	170	20	e	e	NOUN
ejde-637	170	21	=	=	PUNCT
ejde-637	170	22	x+	x+	PUNCT
ejde-637	170	23	e	e	X
ejde-637	170	24	+	+	NUM
ejde-637	170	25	2µ1	2µ1	NUM
ejde-637	170	26	⇔	⇔	PROPN
ejde-637	170	27	x−	x−	PROPN
ejde-637	170	28	t	t	PROPN
ejde-637	170	29	=	=	PUNCT
ejde-637	170	30	x+	x+	PROPN
ejde-637	170	31	t	t	NOUN
ejde-637	170	32	.	.	PUNCT
ejde-637	171	1	(	(	PUNCT
ejde-637	171	2	3.7	3.7	NUM
ejde-637	171	3	)	)	PUNCT
ejde-637	171	4	it	it	PRON
ejde-637	171	5	is	be	AUX
ejde-637	171	6	obvious	obvious	ADJ
ejde-637	171	7	that	that	SCONJ
ejde-637	171	8	x−	x−	PROPN
ejde-637	171	9	t	t	PROPN
ejde-637	171	10	increases	increase	VERB
ejde-637	171	11	with	with	ADP
ejde-637	171	12	respect	respect	NOUN
ejde-637	171	13	to	to	ADP
ejde-637	171	14	x−	x−	PROPN
ejde-637	171	15	e	e	PROPN
ejde-637	171	16	by	by	ADP
ejde-637	171	17	(	(	PUNCT
ejde-637	171	18	2.5	2.5	NUM
ejde-637	171	19	)	)	PUNCT
ejde-637	171	20	.	.	PUNCT
ejde-637	172	1	then	then	ADV
ejde-637	172	2	(	(	PUNCT
ejde-637	172	3	3.2	3.2	NUM
ejde-637	172	4	)	)	PUNCT
ejde-637	172	5	and	and	CCONJ
ejde-637	172	6	(	(	PUNCT
ejde-637	172	7	3.3	3.3	NUM
ejde-637	172	8	)	)	PUNCT
ejde-637	172	9	can	can	AUX
ejde-637	172	10	be	be	AUX
ejde-637	172	11	obtained	obtain	VERB
ejde-637	172	12	directly	directly	ADV
ejde-637	172	13	.	.	PUNCT
ejde-637	173	1	in	in	ADP
ejde-637	173	2	addition	addition	NOUN
ejde-637	173	3	,	,	PUNCT
ejde-637	173	4	by	by	ADP
ejde-637	173	5	simple	simple	ADJ
ejde-637	173	6	calculations	calculation	NOUN
ejde-637	173	7	,	,	PUNCT
ejde-637	173	8	we	we	PRON
ejde-637	173	9	obtain	obtain	VERB
ejde-637	173	10	x−	x−	PROPN
ejde-637	173	11	e	e	PROPN
ejde-637	174	1	=	=	PROPN
ejde-637	174	2	µ2	µ2	PROPN
ejde-637	174	3	⇔	⇔	PROPN
ejde-637	174	4	y−t	y−t	PROPN
ejde-637	174	5	=	=	SYM
ejde-637	174	6	0	0	NUM
ejde-637	174	7	,	,	PUNCT
ejde-637	174	8	x−	x−	PROPN
ejde-637	174	9	e	e	NOUN
ejde-637	174	10	=	=	PUNCT
ejde-637	174	11	x+	x+	SYM
ejde-637	175	1	e	e	X
ejde-637	175	2	+	+	NUM
ejde-637	175	3	2µ2	2µ2	NUM
ejde-637	175	4	⇔	⇔	NUM
ejde-637	175	5	y−t	y−t	PROPN
ejde-637	175	6	=	=	SYM
ejde-637	175	7	y+t	y+t	PROPN
ejde-637	175	8	.	.	PUNCT
ejde-637	176	1	(	(	PUNCT
ejde-637	176	2	3.8	3.8	NUM
ejde-637	176	3	)	)	PUNCT
ejde-637	176	4	ejde-2024/57	ejde-2024/57	NOUN
ejde-637	176	5	planar	planar	ADJ
ejde-637	176	6	sector	sector	NOUN
ejde-637	176	7	-	-	PUNCT
ejde-637	176	8	wise	wise	ADJ
ejde-637	176	9	linear	linear	NOUN
ejde-637	176	10	systems	system	NOUN
ejde-637	176	11	7	7	NUM
ejde-637	176	12	on	on	ADP
ejde-637	176	13	the	the	DET
ejde-637	176	14	one	one	NUM
ejde-637	176	15	hand	hand	NOUN
ejde-637	176	16	,	,	PUNCT
ejde-637	176	17	when	when	SCONJ
ejde-637	176	18	a	a	DET
ejde-637	176	19	∈	∈	PROPN
ejde-637	176	20	ω1	ω1	NOUN
ejde-637	176	21	,	,	PUNCT
ejde-637	176	22	by	by	ADP
ejde-637	176	23	(	(	PUNCT
ejde-637	176	24	2.5	2.5	NUM
ejde-637	176	25	)	)	PUNCT
ejde-637	176	26	,	,	PUNCT
ejde-637	176	27	we	we	PRON
ejde-637	176	28	have	have	VERB
ejde-637	176	29	y+t	y+t	PROPN
ejde-637	176	30	>	>	X
ejde-637	176	31	0	0	PROPN
ejde-637	176	32	,	,	PUNCT
ejde-637	176	33	and	and	CCONJ
ejde-637	176	34	y−t	y−t	NOUN
ejde-637	176	35	is	be	AUX
ejde-637	176	36	a	a	DET
ejde-637	176	37	linear	linear	ADJ
ejde-637	176	38	monotone	monotone	NOUN
ejde-637	176	39	increasing	increase	VERB
ejde-637	176	40	function	function	NOUN
ejde-637	176	41	with	with	ADP
ejde-637	176	42	respect	respect	NOUN
ejde-637	176	43	to	to	ADP
ejde-637	176	44	x−	x−	PROPN
ejde-637	176	45	e	e	PROPN
ejde-637	176	46	.	.	PUNCT
ejde-637	177	1	then	then	ADV
ejde-637	177	2	(	(	PUNCT
ejde-637	177	3	3.4	3.4	NUM
ejde-637	177	4	)	)	PUNCT
ejde-637	177	5	can	can	AUX
ejde-637	177	6	be	be	AUX
ejde-637	177	7	obtained	obtain	VERB
ejde-637	177	8	easily	easily	ADV
ejde-637	177	9	.	.	PUNCT
ejde-637	178	1	on	on	ADP
ejde-637	178	2	the	the	DET
ejde-637	178	3	other	other	ADJ
ejde-637	178	4	hand	hand	NOUN
ejde-637	178	5	,	,	PUNCT
ejde-637	178	6	when	when	SCONJ
ejde-637	178	7	a	a	DET
ejde-637	178	8	∈	∈	PROPN
ejde-637	178	9	ω2	ω2	NOUN
ejde-637	178	10	,	,	PUNCT
ejde-637	178	11	by	by	ADP
ejde-637	178	12	(	(	PUNCT
ejde-637	178	13	2.5	2.5	NUM
ejde-637	178	14	)	)	PUNCT
ejde-637	178	15	,	,	PUNCT
ejde-637	178	16	it	it	PRON
ejde-637	178	17	follows	follow	VERB
ejde-637	178	18	that	that	SCONJ
ejde-637	178	19	y+t	y+t	PROPN
ejde-637	178	20	{	{	PUNCT
ejde-637	178	21	<	<	X
ejde-637	178	22	0	0	NUM
ejde-637	178	23	,	,	PUNCT
ejde-637	178	24	if	if	SCONJ
ejde-637	178	25	x+	x+	ADJ
ejde-637	178	26	e	e	NOUN
ejde-637	178	27	+	+	CCONJ
ejde-637	178	28	µ2	µ2	PROPN
ejde-637	178	29	>	>	X
ejde-637	178	30	0	0	NUM
ejde-637	178	31	,	,	PUNCT
ejde-637	178	32	≥	≥	NOUN
ejde-637	178	33	0	0	NUM
ejde-637	178	34	,	,	PUNCT
ejde-637	178	35	if	if	SCONJ
ejde-637	178	36	x+	x+	ADJ
ejde-637	178	37	e	e	NOUN
ejde-637	179	1	+	+	CCONJ
ejde-637	179	2	µ2	µ2	VERB
ejde-637	179	3	≤	≤	PROPN
ejde-637	179	4	0	0	NUM
ejde-637	179	5	.	.	PUNCT
ejde-637	180	1	(	(	PUNCT
ejde-637	180	2	3.9	3.9	NUM
ejde-637	180	3	)	)	PUNCT
ejde-637	180	4	and	and	CCONJ
ejde-637	180	5	y−t	y−t	NOUN
ejde-637	180	6	is	be	AUX
ejde-637	180	7	a	a	DET
ejde-637	180	8	linear	linear	ADJ
ejde-637	180	9	monotone	monotone	NOUN
ejde-637	180	10	decreasing	decrease	VERB
ejde-637	180	11	function	function	NOUN
ejde-637	180	12	with	with	ADP
ejde-637	180	13	respect	respect	NOUN
ejde-637	180	14	to	to	ADP
ejde-637	180	15	x−	x−	PROPN
ejde-637	180	16	e	e	PROPN
ejde-637	180	17	.	.	PUNCT
ejde-637	181	1	then	then	ADV
ejde-637	181	2	(	(	PUNCT
ejde-637	181	3	3.5	3.5	NUM
ejde-637	181	4	)	)	PUNCT
ejde-637	181	5	and	and	CCONJ
ejde-637	181	6	(	(	PUNCT
ejde-637	181	7	3.6	3.6	NUM
ejde-637	181	8	)	)	PUNCT
ejde-637	181	9	can	can	AUX
ejde-637	181	10	be	be	AUX
ejde-637	181	11	proved	prove	VERB
ejde-637	181	12	directly	directly	ADV
ejde-637	181	13	.	.	PUNCT
ejde-637	182	1	□	□	PUNCT
ejde-637	182	2	based	base	VERB
ejde-637	182	3	on	on	ADP
ejde-637	182	4	the	the	DET
ejde-637	182	5	results	result	NOUN
ejde-637	182	6	about	about	ADP
ejde-637	182	7	sliding	slide	VERB
ejde-637	182	8	sets	set	NOUN
ejde-637	182	9	given	give	VERB
ejde-637	182	10	in	in	ADP
ejde-637	182	11	proposition	proposition	NOUN
ejde-637	182	12	3.1	3.1	NUM
ejde-637	182	13	,	,	PUNCT
ejde-637	182	14	we	we	PRON
ejde-637	182	15	can	can	AUX
ejde-637	182	16	now	now	ADV
ejde-637	182	17	write	write	VERB
ejde-637	182	18	out	out	ADP
ejde-637	182	19	the	the	DET
ejde-637	182	20	sliding	slide	VERB
ejde-637	182	21	vector	vector	NOUN
ejde-637	182	22	field	field	NOUN
ejde-637	182	23	of	of	ADP
ejde-637	182	24	system	system	NOUN
ejde-637	182	25	(	(	PUNCT
ejde-637	182	26	1.1	1.1	NUM
ejde-637	182	27	)	)	PUNCT
ejde-637	182	28	defined	define	VERB
ejde-637	182	29	by	by	ADP
ejde-637	182	30	using	use	VERB
ejde-637	182	31	the	the	DET
ejde-637	182	32	filippov	filippov	ADJ
ejde-637	182	33	convex	convex	NOUN
ejde-637	182	34	method	method	NOUN
ejde-637	182	35	as	as	SCONJ
ejde-637	182	36	follows	follow	VERB
ejde-637	182	37	:	:	PUNCT
ejde-637	182	38	fs(p	fs(p	X
ejde-637	182	39	)	)	PUNCT
ejde-637	182	40	=	=	PUNCT
ejde-637	183	1			NOUN
ejde-637	183	2	1	1	NUM
ejde-637	183	3	f+	f+	NUM
ejde-637	183	4	2	2	NUM
ejde-637	183	5	(	(	PUNCT
ejde-637	183	6	p)−f−	p)−f−	PROPN
ejde-637	183	7	2	2	NUM
ejde-637	183	8	(	(	PUNCT
ejde-637	183	9	p	p	NOUN
ejde-637	183	10	)	)	PUNCT
ejde-637	183	11	(	(	PUNCT
ejde-637	183	12	f+	f+	NUM
ejde-637	183	13	2	2	NUM
ejde-637	183	14	(	(	PUNCT
ejde-637	183	15	p)f−	p)f−	NOUN
ejde-637	183	16	1	1	NUM
ejde-637	183	17	(	(	PUNCT
ejde-637	183	18	p)−	p)−	NOUN
ejde-637	183	19	f−	f−	NOUN
ejde-637	183	20	2	2	NUM
ejde-637	183	21	(	(	PUNCT
ejde-637	183	22	p)f+	p)f+	PROPN
ejde-637	183	23	1	1	NUM
ejde-637	183	24	(	(	PUNCT
ejde-637	183	25	p	p	NOUN
ejde-637	183	26	)	)	PUNCT
ejde-637	183	27	0	0	NUM
ejde-637	183	28	)	)	PUNCT
ejde-637	183	29	,	,	PUNCT
ejde-637	183	30	if	if	SCONJ
ejde-637	183	31	p	p	PROPN
ejde-637	183	32	∈	∈	PROPN
ejde-637	183	33	σx	σx	NOUN
ejde-637	183	34	s	s	NOUN
ejde-637	183	35	;	;	PUNCT
ejde-637	183	36	1	1	NUM
ejde-637	183	37	f+	f+	NUM
ejde-637	183	38	1	1	NUM
ejde-637	183	39	(	(	PUNCT
ejde-637	183	40	p)−f−	p)−f−	NUM
ejde-637	183	41	1	1	NUM
ejde-637	183	42	(	(	PUNCT
ejde-637	183	43	p	p	NOUN
ejde-637	183	44	)	)	PUNCT
ejde-637	183	45	(	(	PUNCT
ejde-637	183	46	0	0	NUM
ejde-637	183	47	f+	f+	NUM
ejde-637	183	48	1	1	NUM
ejde-637	183	49	(	(	PUNCT
ejde-637	183	50	p)f−	p)f−	NOUN
ejde-637	183	51	2	2	NUM
ejde-637	183	52	(	(	PUNCT
ejde-637	183	53	p)−	p)−	NOUN
ejde-637	183	54	f−	f−	PROPN
ejde-637	183	55	1	1	NUM
ejde-637	183	56	(	(	PUNCT
ejde-637	183	57	p)f+	p)f+	PROPN
ejde-637	183	58	2	2	NUM
ejde-637	183	59	(	(	PUNCT
ejde-637	183	60	p	p	NOUN
ejde-637	183	61	)	)	PUNCT
ejde-637	183	62	)	)	PUNCT
ejde-637	183	63	,	,	PUNCT
ejde-637	183	64	if	if	SCONJ
ejde-637	183	65	p	p	PROPN
ejde-637	183	66	∈	∈	PROPN
ejde-637	183	67	σy	σy	NOUN
ejde-637	183	68	s	s	PROPN
ejde-637	183	69	.	.	PUNCT
ejde-637	184	1	(	(	PUNCT
ejde-637	184	2	3.10	3.10	NUM
ejde-637	184	3	)	)	PUNCT
ejde-637	184	4	then	then	ADV
ejde-637	184	5	the	the	DET
ejde-637	184	6	existence	existence	NOUN
ejde-637	184	7	,	,	PUNCT
ejde-637	184	8	number	number	NOUN
ejde-637	184	9	and	and	CCONJ
ejde-637	184	10	stability	stability	NOUN
ejde-637	184	11	of	of	ADP
ejde-637	184	12	pseudo	pseudo	NOUN
ejde-637	184	13	-	-	NOUN
ejde-637	184	14	equilibrium	equilibrium	NOUN
ejde-637	184	15	points	point	NOUN
ejde-637	184	16	(	(	PUNCT
ejde-637	184	17	i.e.	i.e.	X
ejde-637	184	18	,	,	PUNCT
ejde-637	184	19	the	the	DET
ejde-637	184	20	equilibrium	equilibrium	NOUN
ejde-637	184	21	points	point	NOUN
ejde-637	184	22	of	of	ADP
ejde-637	184	23	fs	f	NOUN
ejde-637	184	24	)	)	PUNCT
ejde-637	184	25	of	of	ADP
ejde-637	184	26	system	system	NOUN
ejde-637	184	27	(	(	PUNCT
ejde-637	184	28	1.1	1.1	NUM
ejde-637	184	29	)	)	PUNCT
ejde-637	184	30	are	be	AUX
ejde-637	184	31	provided	provide	VERB
ejde-637	184	32	in	in	ADP
ejde-637	184	33	the	the	DET
ejde-637	184	34	next	next	ADJ
ejde-637	184	35	proposition	proposition	NOUN
ejde-637	184	36	.	.	PUNCT
ejde-637	185	1	proposition	proposition	NOUN
ejde-637	185	2	3.2	3.2	NUM
ejde-637	185	3	.	.	PUNCT
ejde-637	185	4	suppose	suppose	VERB
ejde-637	185	5	that	that	SCONJ
ejde-637	185	6	condition	condition	NOUN
ejde-637	185	7	(	(	PUNCT
ejde-637	185	8	3.1	3.1	NUM
ejde-637	185	9	)	)	PUNCT
ejde-637	185	10	holds	hold	NOUN
ejde-637	185	11	and	and	CCONJ
ejde-637	185	12	a	a	DET
ejde-637	185	13	∈	∈	PROPN
ejde-637	185	14	ω1	ω1	PROPN
ejde-637	185	15	∪	∪	X
ejde-637	185	16	ω2	ω2	PROPN
ejde-637	185	17	.	.	PUNCT
ejde-637	186	1	there	there	PRON
ejde-637	186	2	exists	exist	VERB
ejde-637	186	3	at	at	ADP
ejde-637	186	4	most	most	ADV
ejde-637	186	5	one	one	NUM
ejde-637	186	6	pseudo	pseudo	NOUN
ejde-637	186	7	-	-	NOUN
ejde-637	186	8	equilibrium	equilibrium	NOUN
ejde-637	186	9	point	point	NOUN
ejde-637	186	10	in	in	ADP
ejde-637	186	11	system	system	NOUN
ejde-637	186	12	(	(	PUNCT
ejde-637	186	13	1.1	1.1	NUM
ejde-637	186	14	)	)	PUNCT
ejde-637	186	15	.	.	PUNCT
ejde-637	187	1	more	more	ADV
ejde-637	187	2	precisely	precisely	ADV
ejde-637	187	3	,	,	PUNCT
ejde-637	187	4	about	about	ADP
ejde-637	187	5	the	the	DET
ejde-637	187	6	pseudo	pseudo	NOUN
ejde-637	187	7	-	-	NOUN
ejde-637	187	8	equilibrium	equilibrium	NOUN
ejde-637	187	9	point	point	NOUN
ejde-637	187	10	in	in	ADP
ejde-637	187	11	σx	σx	ADP
ejde-637	187	12	s	s	PRON
ejde-637	187	13	,	,	PUNCT
ejde-637	187	14	we	we	PRON
ejde-637	187	15	have	have	VERB
ejde-637	187	16	:	:	PUNCT
ejde-637	187	17	(	(	PUNCT
ejde-637	187	18	a1	a1	NOUN
ejde-637	187	19	)	)	PUNCT
ejde-637	187	20	if	if	SCONJ
ejde-637	187	21	x−	x−	PROPN
ejde-637	187	22	e	e	PROPN
ejde-637	187	23	≥	≥	X
ejde-637	187	24	−x+	−x+	NUM
ejde-637	187	25	e	e	NOUN
ejde-637	187	26	and	and	CCONJ
ejde-637	187	27	x−	x−	PROPN
ejde-637	187	28	e	e	PROPN
ejde-637	187	29	̸=	̸=	PROPN
ejde-637	187	30	x+	x+	PUNCT
ejde-637	187	31	e	e	X
ejde-637	187	32	+	+	NOUN
ejde-637	187	33	2µ1	2µ1	NUM
ejde-637	187	34	,	,	PUNCT
ejde-637	187	35	there	there	PRON
ejde-637	187	36	exists	exist	VERB
ejde-637	187	37	a	a	DET
ejde-637	187	38	unique	unique	ADJ
ejde-637	187	39	pseudo	pseudo	NOUN
ejde-637	187	40	-	-	NOUN
ejde-637	187	41	equilibrium	equilibrium	NOUN
ejde-637	187	42	point	point	NOUN
ejde-637	187	43	(	(	PUNCT
ejde-637	187	44	x∗	x∗	PROPN
ejde-637	187	45	,	,	PUNCT
ejde-637	187	46	0	0	NUM
ejde-637	187	47	)	)	PUNCT
ejde-637	187	48	,	,	PUNCT
ejde-637	187	49	which	which	PRON
ejde-637	187	50	is	be	AUX
ejde-637	187	51	a	a	DET
ejde-637	187	52	stable	stable	ADJ
ejde-637	187	53	(	(	PUNCT
ejde-637	187	54	an	an	DET
ejde-637	187	55	unstable	unstable	ADJ
ejde-637	187	56	)	)	PUNCT
ejde-637	187	57	pseudo	pseudo	NOUN
ejde-637	187	58	-	-	NOUN
ejde-637	187	59	node	node	ADJ
ejde-637	187	60	when	when	SCONJ
ejde-637	187	61	x−	x−	PROPN
ejde-637	187	62	e	e	PROPN
ejde-637	188	1	<	<	X
ejde-637	188	2	x+	x+	X
ejde-637	188	3	e	e	X
ejde-637	188	4	+	+	NUM
ejde-637	188	5	2µ1	2µ1	NUM
ejde-637	188	6	(	(	PUNCT
ejde-637	188	7	x−	x−	PROPN
ejde-637	188	8	e	e	PROPN
ejde-637	188	9	>	>	X
ejde-637	188	10	x+	x+	X
ejde-637	188	11	e	e	X
ejde-637	188	12	+	+	NOUN
ejde-637	188	13	2µ1	2µ1	NUM
ejde-637	188	14	)	)	PUNCT
ejde-637	188	15	;	;	PUNCT
ejde-637	188	16	(	(	PUNCT
ejde-637	188	17	a2	a2	PROPN
ejde-637	188	18	)	)	PUNCT
ejde-637	189	1	if	if	SCONJ
ejde-637	189	2	x−	x−	PROPN
ejde-637	189	3	e	e	PROPN
ejde-637	189	4	<	<	X
ejde-637	189	5	−x+	−x+	X
ejde-637	189	6	e	e	NOUN
ejde-637	189	7	or	or	CCONJ
ejde-637	189	8	x−	x−	PROPN
ejde-637	189	9	e	e	PROPN
ejde-637	189	10	=	=	PUNCT
ejde-637	189	11	x+	x+	PUNCT
ejde-637	189	12	e	e	X
ejde-637	189	13	+	+	NOUN
ejde-637	189	14	2µ1	2µ1	NUM
ejde-637	189	15	,	,	PUNCT
ejde-637	189	16	there	there	PRON
ejde-637	189	17	exists	exist	VERB
ejde-637	189	18	no	no	DET
ejde-637	189	19	pseudo	pseudo	NOUN
ejde-637	189	20	-	-	NOUN
ejde-637	189	21	equilibrium	equilibrium	NOUN
ejde-637	189	22	point	point	NOUN
ejde-637	189	23	in	in	ADP
ejde-637	189	24	σx	σx	NOUN
ejde-637	189	25	s	s	PROPN
ejde-637	189	26	.	.	PUNCT
ejde-637	190	1	about	about	ADP
ejde-637	190	2	the	the	DET
ejde-637	190	3	pseudo	pseudo	NOUN
ejde-637	190	4	-	-	NOUN
ejde-637	190	5	equilibrium	equilibrium	NOUN
ejde-637	190	6	point	point	NOUN
ejde-637	190	7	in	in	ADP
ejde-637	190	8	σy	σy	PROPN
ejde-637	190	9	s	s	PART
ejde-637	190	10	,	,	PUNCT
ejde-637	190	11	we	we	PRON
ejde-637	190	12	have	have	VERB
ejde-637	190	13	:	:	PUNCT
ejde-637	190	14	(	(	PUNCT
ejde-637	190	15	b1	b1	NOUN
ejde-637	190	16	)	)	PUNCT
ejde-637	190	17	if	if	SCONJ
ejde-637	190	18	x−	x−	PROPN
ejde-637	190	19	e	e	PROPN
ejde-637	190	20	≤	≤	ADJ
ejde-637	190	21	−x+	−x+	NOUN
ejde-637	190	22	e	e	NOUN
ejde-637	190	23	and	and	CCONJ
ejde-637	190	24	x−	x−	PROPN
ejde-637	190	25	e	e	PROPN
ejde-637	190	26	̸=	̸=	PROPN
ejde-637	190	27	x+	x+	PUNCT
ejde-637	190	28	e	e	X
ejde-637	190	29	+	+	NOUN
ejde-637	190	30	2µ2	2µ2	NUM
ejde-637	190	31	,	,	PUNCT
ejde-637	190	32	there	there	PRON
ejde-637	190	33	exists	exist	VERB
ejde-637	190	34	a	a	DET
ejde-637	190	35	unique	unique	ADJ
ejde-637	190	36	pseudo	pseudo	NOUN
ejde-637	190	37	-	-	NOUN
ejde-637	190	38	equilibrium	equilibrium	NOUN
ejde-637	190	39	point	point	NOUN
ejde-637	190	40	(	(	PUNCT
ejde-637	190	41	0	0	NUM
ejde-637	190	42	,	,	PUNCT
ejde-637	190	43	y∗	y∗	PROPN
ejde-637	190	44	)	)	PUNCT
ejde-637	190	45	,	,	PUNCT
ejde-637	190	46	which	which	PRON
ejde-637	190	47	is	be	AUX
ejde-637	190	48	a	a	DET
ejde-637	190	49	stable	stable	ADJ
ejde-637	190	50	(	(	PUNCT
ejde-637	190	51	an	an	DET
ejde-637	190	52	unstable	unstable	ADJ
ejde-637	190	53	)	)	PUNCT
ejde-637	190	54	pseudo	pseudo	NOUN
ejde-637	190	55	-	-	NOUN
ejde-637	190	56	node	node	ADJ
ejde-637	190	57	when	when	SCONJ
ejde-637	190	58	a11[x	a11[x	NOUN
ejde-637	190	59	−	−	PROPN
ejde-637	190	60	e	e	NOUN
ejde-637	190	61	−	−	PROPN
ejde-637	190	62	(	(	PUNCT
ejde-637	190	63	x+	x+	X
ejde-637	190	64	e	e	X
ejde-637	190	65	+	+	NOUN
ejde-637	190	66	2µ2	2µ2	NUM
ejde-637	190	67	)	)	PUNCT
ejde-637	190	68	]	]	PUNCT
ejde-637	191	1	<	<	X
ejde-637	191	2	0	0	PUNCT
ejde-637	191	3	(	(	PUNCT
ejde-637	191	4	a11[x	a11[x	NOUN
ejde-637	191	5	−	−	PROPN
ejde-637	191	6	e	e	NOUN
ejde-637	191	7	−	−	PROPN
ejde-637	191	8	(	(	PUNCT
ejde-637	191	9	x+	x+	X
ejde-637	191	10	e	e	X
ejde-637	191	11	+	+	NOUN
ejde-637	191	12	2µ2	2µ2	NUM
ejde-637	191	13	)	)	PUNCT
ejde-637	191	14	]	]	PUNCT
ejde-637	192	1	>	>	X
ejde-637	192	2	0	0	NUM
ejde-637	192	3	)	)	PUNCT
ejde-637	192	4	;	;	PUNCT
ejde-637	192	5	(	(	PUNCT
ejde-637	192	6	b2	b2	NOUN
ejde-637	192	7	)	)	PUNCT
ejde-637	192	8	if	if	SCONJ
ejde-637	192	9	x−	x−	PROPN
ejde-637	192	10	e	e	PROPN
ejde-637	192	11	>	>	PUNCT
ejde-637	192	12	−x+	−x+	X
ejde-637	192	13	e	e	NOUN
ejde-637	192	14	or	or	CCONJ
ejde-637	192	15	x−	x−	PROPN
ejde-637	192	16	e	e	PROPN
ejde-637	192	17	=	=	SYM
ejde-637	192	18	x+	x+	SYM
ejde-637	192	19	e	e	X
ejde-637	192	20	+	+	NOUN
ejde-637	192	21	2µ2	2µ2	NUM
ejde-637	192	22	,	,	PUNCT
ejde-637	192	23	there	there	PRON
ejde-637	192	24	exists	exist	VERB
ejde-637	192	25	no	no	DET
ejde-637	192	26	pseudo	pseudo	NOUN
ejde-637	192	27	-	-	NOUN
ejde-637	192	28	equilibrium	equilibrium	NOUN
ejde-637	192	29	point	point	NOUN
ejde-637	192	30	in	in	ADP
ejde-637	192	31	σy	σy	PROPN
ejde-637	192	32	s	s	PART
ejde-637	192	33	.	.	PUNCT
ejde-637	193	1	proof	proof	NOUN
ejde-637	193	2	.	.	PUNCT
ejde-637	194	1	by	by	ADP
ejde-637	194	2	the	the	DET
ejde-637	194	3	definition	definition	NOUN
ejde-637	194	4	of	of	ADP
ejde-637	194	5	a	a	DET
ejde-637	194	6	pseudo	pseudo	NOUN
ejde-637	194	7	-	-	NOUN
ejde-637	194	8	equilibrium	equilibrium	NOUN
ejde-637	194	9	given	give	VERB
ejde-637	194	10	in	in	ADP
ejde-637	194	11	definition	definition	NOUN
ejde-637	194	12	2.2	2.2	NUM
ejde-637	194	13	and	and	CCONJ
ejde-637	194	14	(	(	PUNCT
ejde-637	194	15	3.10	3.10	NUM
ejde-637	194	16	)	)	PUNCT
ejde-637	194	17	,	,	PUNCT
ejde-637	194	18	we	we	PRON
ejde-637	194	19	know	know	VERB
ejde-637	194	20	that	that	SCONJ
ejde-637	194	21	pex	pex	PROPN
ejde-637	194	22	=	=	PUNCT
ejde-637	194	23	(	(	PUNCT
ejde-637	194	24	x∗	x∗	PROPN
ejde-637	194	25	,	,	PUNCT
ejde-637	194	26	0	0	NUM
ejde-637	194	27	)	)	PUNCT
ejde-637	194	28	is	be	AUX
ejde-637	194	29	a	a	DET
ejde-637	194	30	pseudo	pseudo	NOUN
ejde-637	194	31	-	-	NOUN
ejde-637	194	32	equilibrium	equilibrium	NOUN
ejde-637	194	33	of	of	ADP
ejde-637	194	34	system	system	NOUN
ejde-637	194	35	(	(	PUNCT
ejde-637	194	36	1.1	1.1	NUM
ejde-637	194	37	)	)	PUNCT
ejde-637	195	1	if	if	SCONJ
ejde-637	195	2	and	and	CCONJ
ejde-637	195	3	only	only	ADV
ejde-637	195	4	if	if	SCONJ
ejde-637	195	5	pex	pex	PROPN
ejde-637	195	6	∈	∈	PROPN
ejde-637	195	7	σx	σx	PROPN
ejde-637	195	8	s	s	PROPN
ejde-637	195	9	and	and	CCONJ
ejde-637	195	10	f+	f+	NUM
ejde-637	195	11	2	2	NUM
ejde-637	195	12	(	(	PUNCT
ejde-637	195	13	x∗	x∗	PROPN
ejde-637	195	14	,	,	PUNCT
ejde-637	195	15	0)f−	0)f−	PROPN
ejde-637	195	16	1	1	NUM
ejde-637	195	17	(	(	PUNCT
ejde-637	195	18	x∗	x∗	PROPN
ejde-637	195	19	,	,	PUNCT
ejde-637	195	20	0)−	0)−	PUNCT
ejde-637	195	21	f−	f−	PROPN
ejde-637	195	22	2	2	NUM
ejde-637	195	23	(	(	PUNCT
ejde-637	195	24	x∗	x∗	PROPN
ejde-637	195	25	,	,	PUNCT
ejde-637	195	26	0)f+	0)f+	NUM
ejde-637	195	27	1	1	NUM
ejde-637	195	28	(	(	PUNCT
ejde-637	195	29	x∗	x∗	PROPN
ejde-637	195	30	,	,	PUNCT
ejde-637	195	31	0	0	NUM
ejde-637	195	32	)	)	PUNCT
ejde-637	195	33	=	=	SYM
ejde-637	195	34	−2	−2	NOUN
ejde-637	195	35	det(a	det(a	PROPN
ejde-637	195	36	)	)	PUNCT
ejde-637	195	37	·	·	PUNCT
ejde-637	196	1	y+e	y+e	NOUN
ejde-637	196	2	·	·	PUNCT
ejde-637	196	3	(	(	PUNCT
ejde-637	196	4	x∗	x∗	PROPN
ejde-637	196	5	−	−	PROPN
ejde-637	196	6	x−	x−	PROPN
ejde-637	196	7	e	e	PROPN
ejde-637	197	1	+	+	CCONJ
ejde-637	197	2	x+	x+	PROPN
ejde-637	197	3	e	e	X
ejde-637	197	4	2	2	NUM
ejde-637	197	5	)	)	PUNCT
ejde-637	197	6	=	=	SYM
ejde-637	198	1	0	0	X
ejde-637	198	2	.	.	PUNCT
ejde-637	199	1	(	(	PUNCT
ejde-637	199	2	3.11	3.11	NUM
ejde-637	199	3	)	)	PUNCT
ejde-637	199	4	similarly	similarly	ADV
ejde-637	199	5	,	,	PUNCT
ejde-637	199	6	pey	pey	NOUN
ejde-637	199	7	=	=	SYM
ejde-637	199	8	(	(	PUNCT
ejde-637	199	9	0	0	NUM
ejde-637	199	10	,	,	PUNCT
ejde-637	199	11	y∗	y∗	PROPN
ejde-637	199	12	)	)	PUNCT
ejde-637	199	13	is	be	AUX
ejde-637	199	14	a	a	DET
ejde-637	199	15	pseudo	pseudo	NOUN
ejde-637	199	16	-	-	NOUN
ejde-637	199	17	equilibrium	equilibrium	NOUN
ejde-637	199	18	of	of	ADP
ejde-637	199	19	system	system	NOUN
ejde-637	199	20	(	(	PUNCT
ejde-637	199	21	1.1	1.1	NUM
ejde-637	199	22	)	)	PUNCT
ejde-637	199	23	if	if	SCONJ
ejde-637	199	24	and	and	CCONJ
ejde-637	199	25	only	only	ADV
ejde-637	199	26	if	if	SCONJ
ejde-637	199	27	pey	pey	PROPN
ejde-637	199	28	∈	∈	PROPN
ejde-637	199	29	σy	σy	NOUN
ejde-637	199	30	s	s	NOUN
ejde-637	199	31	and	and	CCONJ
ejde-637	199	32	f+	f+	NUM
ejde-637	199	33	1	1	NUM
ejde-637	199	34	(	(	PUNCT
ejde-637	199	35	0	0	NUM
ejde-637	199	36	,	,	PUNCT
ejde-637	199	37	y∗)f−	y∗)f−	PROPN
ejde-637	199	38	2	2	NUM
ejde-637	199	39	(	(	PUNCT
ejde-637	199	40	0	0	NUM
ejde-637	199	41	,	,	PUNCT
ejde-637	199	42	y∗)−	y∗)−	ADJ
ejde-637	199	43	f−	f−	PROPN
ejde-637	199	44	1	1	NUM
ejde-637	199	45	(	(	PUNCT
ejde-637	199	46	0	0	NUM
ejde-637	199	47	,	,	PUNCT
ejde-637	199	48	y∗)f+	y∗)f+	PROPN
ejde-637	199	49	2	2	NUM
ejde-637	199	50	(	(	PUNCT
ejde-637	199	51	0	0	NUM
ejde-637	199	52	,	,	PUNCT
ejde-637	199	53	y∗	y∗	PROPN
ejde-637	199	54	)	)	PUNCT
ejde-637	199	55	=	=	PUNCT
ejde-637	199	56	−det(a	−det(a	PROPN
ejde-637	199	57	)	)	PUNCT
ejde-637	199	58	[	[	PUNCT
ejde-637	199	59	(	(	PUNCT
ejde-637	199	60	x+	x+	X
ejde-637	199	61	e	e	NOUN
ejde-637	199	62	−	−	PROPN
ejde-637	199	63	x−	x−	PROPN
ejde-637	199	64	e	e	PROPN
ejde-637	199	65	)	)	PUNCT
ejde-637	199	66	y	y	PROPN
ejde-637	199	67	∗	∗	NOUN
ejde-637	199	68	+	+	CCONJ
ejde-637	199	69	(	(	PUNCT
ejde-637	199	70	x+	x+	X
ejde-637	199	71	e	e	X
ejde-637	199	72	+	+	CCONJ
ejde-637	199	73	x−	x−	PROPN
ejde-637	199	74	e	e	PROPN
ejde-637	199	75	)	)	PUNCT
ejde-637	199	76	y	y	PROPN
ejde-637	200	1	+	+	NUM
ejde-637	200	2	e	e	X
ejde-637	200	3	]	]	X
ejde-637	200	4	=	=	PUNCT
ejde-637	200	5	0	0	X
ejde-637	200	6	.	.	PUNCT
ejde-637	200	7	(	(	PUNCT
ejde-637	200	8	3.12	3.12	NUM
ejde-637	200	9	)	)	PUNCT
ejde-637	200	10	8	8	NUM
ejde-637	200	11	q.-q	q.-q	PROPN
ejde-637	200	12	.	.	PUNCT
ejde-637	201	1	han	han	PROPN
ejde-637	201	2	,	,	PUNCT
ejde-637	201	3	s.-m	s.-m	PROPN
ejde-637	201	4	.	.	PUNCT
ejde-637	202	1	huan	huan	PROPN
ejde-637	202	2	ejde-2024/57	ejde-2024/57	PROPN
ejde-637	202	3	then	then	ADV
ejde-637	202	4	we	we	PRON
ejde-637	202	5	obtain	obtain	VERB
ejde-637	202	6	x∗	x∗	PROPN
ejde-637	202	7	=	=	SYM
ejde-637	203	1	x−	x−	PROPN
ejde-637	203	2	e	e	X
ejde-637	203	3	+	+	PROPN
ejde-637	203	4	x+	x+	ADJ
ejde-637	203	5	e	e	X
ejde-637	203	6	2	2	NUM
ejde-637	203	7	and	and	CCONJ
ejde-637	203	8	y∗	y∗	PROPN
ejde-637	203	9	=	=	SYM
ejde-637	203	10	x−	x−	PROPN
ejde-637	203	11	e	e	X
ejde-637	203	12	+	+	PROPN
ejde-637	203	13	x+	x+	PROPN
ejde-637	203	14	e	e	X
ejde-637	203	15	x−	x−	PROPN
ejde-637	203	16	e	e	X
ejde-637	203	17	−x+	−x+	NOUN
ejde-637	203	18	e	e	NOUN
ejde-637	203	19	y+e	y+e	NOUN
ejde-637	203	20	directly	directly	ADV
ejde-637	203	21	from	from	ADP
ejde-637	203	22	(	(	PUNCT
ejde-637	203	23	3.11	3.11	NUM
ejde-637	203	24	)	)	PUNCT
ejde-637	203	25	and	and	CCONJ
ejde-637	203	26	(	(	PUNCT
ejde-637	203	27	3.12	3.12	NUM
ejde-637	203	28	)	)	PUNCT
ejde-637	203	29	.	.	PUNCT
ejde-637	204	1	in	in	ADP
ejde-637	204	2	addition	addition	NOUN
ejde-637	204	3	to	to	ADP
ejde-637	204	4	this	this	PRON
ejde-637	204	5	,	,	PUNCT
ejde-637	204	6	we	we	PRON
ejde-637	204	7	have	have	VERB
ejde-637	204	8	x∗	x∗	NOUN
ejde-637	204	9	=	=	SYM
ejde-637	204	10	x+	x+	PROPN
ejde-637	205	1	t	t	PROPN
ejde-637	205	2	+	+	NUM
ejde-637	205	3	x−	x−	PROPN
ejde-637	205	4	t	t	PROPN
ejde-637	205	5	2	2	NUM
ejde-637	205	6	=	=	SYM
ejde-637	205	7	x+	x+	X
ejde-637	205	8	m1	m1	PROPN
ejde-637	205	9	+	+	CCONJ
ejde-637	205	10	x−	x−	PROPN
ejde-637	205	11	m1	m1	PROPN
ejde-637	205	12	2	2	NUM
ejde-637	205	13	=	=	SYM
ejde-637	205	14	x+	x+	PROPN
ejde-637	205	15	m2	m2	PROPN
ejde-637	205	16	+	+	PROPN
ejde-637	205	17	x−	x−	PROPN
ejde-637	205	18	m2	m2	PROPN
ejde-637	205	19	2	2	NUM
ejde-637	205	20	,	,	PUNCT
ejde-637	205	21	which	which	PRON
ejde-637	205	22	means	mean	VERB
ejde-637	205	23	that	that	SCONJ
ejde-637	205	24	pex	pex	PROPN
ejde-637	205	25	is	be	AUX
ejde-637	205	26	the	the	DET
ejde-637	205	27	midpoint	midpoint	NOUN
ejde-637	205	28	of	of	ADP
ejde-637	205	29	x±	x±	PROPN
ejde-637	205	30	e	e	PROPN
ejde-637	205	31	,	,	PUNCT
ejde-637	205	32	x	x	PROPN
ejde-637	205	33	±	±	NUM
ejde-637	205	34	t	t	NOUN
ejde-637	205	35	,	,	PUNCT
ejde-637	205	36	x	x	PROPN
ejde-637	205	37	±	±	NUM
ejde-637	205	38	m1	m1	PROPN
ejde-637	205	39	and	and	CCONJ
ejde-637	205	40	x±	x±	PROPN
ejde-637	205	41	m2	m2	PROPN
ejde-637	205	42	at	at	ADP
ejde-637	205	43	the	the	DET
ejde-637	205	44	same	same	ADJ
ejde-637	205	45	time	time	NOUN
ejde-637	205	46	.	.	PUNCT
ejde-637	206	1	and	and	CCONJ
ejde-637	206	2	lim	lim	PROPN
ejde-637	206	3	x−	x−	PROPN
ejde-637	207	1	e	e	PROPN
ejde-637	207	2	→−∞	→−∞	PROPN
ejde-637	207	3	y∗	y∗	PROPN
ejde-637	207	4	=	=	SYM
ejde-637	207	5	y+e	y+e	NOUN
ejde-637	207	6	,	,	PUNCT
ejde-637	207	7	lim	lim	PROPN
ejde-637	207	8	x−	x−	PROPN
ejde-637	208	1	e	e	PROPN
ejde-637	208	2	→(x+	→(x+	PROPN
ejde-637	208	3	e	e	X
ejde-637	208	4	)	)	PUNCT
ejde-637	208	5	−	−	PROPN
ejde-637	208	6	y∗	y∗	PROPN
ejde-637	208	7	=	=	SYM
ejde-637	208	8	−∞	−∞	PROPN
ejde-637	208	9	,	,	PUNCT
ejde-637	208	10	lim	lim	PROPN
ejde-637	208	11	x−	x−	PROPN
ejde-637	209	1	e	e	PROPN
ejde-637	209	2	→(x+	→(x+	NOUN
ejde-637	209	3	e	e	X
ejde-637	209	4	)	)	PUNCT
ejde-637	210	1	+	+	CCONJ
ejde-637	210	2	y∗	y∗	PROPN
ejde-637	210	3	=	=	PUNCT
ejde-637	211	1	+	+	NUM
ejde-637	211	2	∞	∞	PROPN
ejde-637	211	3	,	,	PUNCT
ejde-637	211	4	lim	lim	PROPN
ejde-637	211	5	x−	x−	PROPN
ejde-637	211	6	e	e	PROPN
ejde-637	211	7	→+∞	→+∞	ADV
ejde-637	211	8	y∗	y∗	PROPN
ejde-637	211	9	=	=	SYM
ejde-637	211	10	y+e	y+e	NOUN
ejde-637	211	11	,	,	PUNCT
ejde-637	211	12	this	this	PRON
ejde-637	211	13	implies	imply	VERB
ejde-637	211	14	that	that	SCONJ
ejde-637	211	15	y∗	y∗	PROPN
ejde-637	211	16	decreases	decrease	VERB
ejde-637	211	17	with	with	ADP
ejde-637	211	18	respect	respect	NOUN
ejde-637	211	19	to	to	ADP
ejde-637	211	20	x−	x−	PROPN
ejde-637	211	21	e	e	PROPN
ejde-637	211	22	,	,	PUNCT
ejde-637	211	23	which	which	PRON
ejde-637	211	24	is	be	AUX
ejde-637	211	25	illustrated	illustrate	VERB
ejde-637	211	26	in	in	ADP
ejde-637	211	27	figure	figure	NOUN
ejde-637	211	28	1	1	NUM
ejde-637	211	29	.	.	PUNCT
ejde-637	212	1	-x	-x	X
ejde-637	213	1	e	e	X
ejde-637	213	2	+	+	CCONJ
ejde-637	213	3	y	y	PROPN
ejde-637	213	4	e	e	PROPN
ejde-637	213	5	+	+	CCONJ
ejde-637	213	6	x	x	SYM
ejde-637	213	7	e	e	SYM
ejde-637	213	8	y	y	PROPN
ejde-637	213	9	*	*	PUNCT
ejde-637	213	10	x	x	X
ejde-637	213	11	e	e	X
ejde-637	213	12	+	+	NUM
ejde-637	213	13	figure	figure	NOUN
ejde-637	213	14	1	1	NUM
ejde-637	213	15	.	.	PUNCT
ejde-637	214	1	the	the	DET
ejde-637	214	2	changing	changing	NOUN
ejde-637	214	3	of	of	ADP
ejde-637	214	4	y∗	y∗	ADV
ejde-637	214	5	with	with	ADP
ejde-637	214	6	respect	respect	NOUN
ejde-637	214	7	to	to	ADP
ejde-637	214	8	x−	x−	PROPN
ejde-637	214	9	e	e	PROPN
ejde-637	214	10	on	on	ADP
ejde-637	214	11	the	the	DET
ejde-637	214	12	one	one	NUM
ejde-637	214	13	hand	hand	NOUN
ejde-637	214	14	,	,	PUNCT
ejde-637	214	15	it	it	PRON
ejde-637	214	16	is	be	AUX
ejde-637	214	17	easy	easy	ADJ
ejde-637	214	18	to	to	PART
ejde-637	214	19	see	see	VERB
ejde-637	214	20	that	that	SCONJ
ejde-637	214	21	x∗	x∗	PROPN
ejde-637	214	22	≥	≥	X
ejde-637	214	23	0	0	PUNCT
ejde-637	215	1	when	when	SCONJ
ejde-637	215	2	x−	x−	PROPN
ejde-637	215	3	e	e	PROPN
ejde-637	215	4	≥	≥	X
ejde-637	215	5	−x+	−x+	X
ejde-637	215	6	e	e	NOUN
ejde-637	215	7	,	,	PUNCT
ejde-637	215	8	and	and	CCONJ
ejde-637	215	9	x∗	x∗	PROPN
ejde-637	215	10	=	=	SYM
ejde-637	215	11	0	0	PUNCT
ejde-637	215	12	if	if	SCONJ
ejde-637	215	13	and	and	CCONJ
ejde-637	215	14	only	only	ADV
ejde-637	215	15	if	if	SCONJ
ejde-637	215	16	x−	x−	PROPN
ejde-637	215	17	e	e	NOUN
ejde-637	215	18	=	=	PUNCT
ejde-637	215	19	−x+	−x+	X
ejde-637	215	20	e	e	NOUN
ejde-637	215	21	.	.	PUNCT
ejde-637	216	1	since	since	SCONJ
ejde-637	216	2	x−	x−	PROPN
ejde-637	216	3	e	e	PROPN
ejde-637	216	4	=	=	PUNCT
ejde-637	216	5	−x+	−x+	X
ejde-637	216	6	e	e	NOUN
ejde-637	216	7	<	<	X
ejde-637	216	8	0	0	PUNCT
ejde-637	216	9	<	<	X
ejde-637	216	10	µ1	µ1	PROPN
ejde-637	216	11	,	,	PUNCT
ejde-637	216	12	which	which	PRON
ejde-637	216	13	means	mean	VERB
ejde-637	216	14	that	that	SCONJ
ejde-637	216	15	pex	pex	PROPN
ejde-637	216	16	=	=	SYM
ejde-637	216	17	(	(	PUNCT
ejde-637	216	18	0	0	NUM
ejde-637	216	19	,	,	PUNCT
ejde-637	216	20	0	0	NUM
ejde-637	216	21	)	)	PUNCT
ejde-637	216	22	∈	∈	NOUN
ejde-637	216	23	σx	σx	ADP
ejde-637	216	24	s	s	NOUN
ejde-637	216	25	is	be	AUX
ejde-637	216	26	a	a	DET
ejde-637	216	27	pseudo	pseudo	NOUN
ejde-637	216	28	-	-	NOUN
ejde-637	216	29	equilibrium	equilibrium	NOUN
ejde-637	216	30	point	point	NOUN
ejde-637	216	31	by	by	ADP
ejde-637	216	32	(	(	PUNCT
ejde-637	216	33	3.2	3.2	NUM
ejde-637	216	34	)	)	PUNCT
ejde-637	216	35	.	.	PUNCT
ejde-637	217	1	furthermore	furthermore	ADV
ejde-637	217	2	,	,	PUNCT
ejde-637	217	3	to	to	PART
ejde-637	217	4	prove	prove	VERB
ejde-637	217	5	whether	whether	SCONJ
ejde-637	217	6	pex	pex	PROPN
ejde-637	217	7	=	=	SYM
ejde-637	217	8	(	(	PUNCT
ejde-637	217	9	x∗	x∗	PROPN
ejde-637	217	10	,	,	PUNCT
ejde-637	217	11	0	0	NUM
ejde-637	217	12	)	)	PUNCT
ejde-637	217	13	∈	∈	NOUN
ejde-637	217	14	σx	σx	NOUN
ejde-637	217	15	s	s	NOUN
ejde-637	217	16	as	as	ADP
ejde-637	217	17	x∗	x∗	PROPN
ejde-637	217	18	>	>	X
ejde-637	217	19	0	0	NUM
ejde-637	217	20	,	,	PUNCT
ejde-637	217	21	we	we	PRON
ejde-637	217	22	need	need	VERB
ejde-637	217	23	the	the	DET
ejde-637	217	24	following	follow	VERB
ejde-637	217	25	calculations	calculation	NOUN
ejde-637	217	26	:	:	PUNCT
ejde-637	217	27	x∗	x∗	PROPN
ejde-637	217	28	−	−	PROPN
ejde-637	217	29	x−	x−	PROPN
ejde-637	217	30	t	t	PROPN
ejde-637	217	31	=	=	SYM
ejde-637	217	32	1	1	NUM
ejde-637	217	33	2	2	NUM
ejde-637	217	34	(	(	PUNCT
ejde-637	217	35	x+	x+	X
ejde-637	217	36	e	e	X
ejde-637	217	37	+	+	NOUN
ejde-637	217	38	2µ1	2µ1	NUM
ejde-637	217	39	−	−	NOUN
ejde-637	217	40	x−	x−	PROPN
ejde-637	217	41	e	e	PROPN
ejde-637	217	42	)	)	PUNCT
ejde-637	217	43	,	,	PUNCT
ejde-637	217	44	x∗	x∗	PROPN
ejde-637	217	45	−	−	PROPN
ejde-637	218	1	x+	x+	PROPN
ejde-637	218	2	t	t	NOUN
ejde-637	218	3	=	=	SYM
ejde-637	218	4	1	1	NUM
ejde-637	218	5	2	2	NUM
ejde-637	218	6	(	(	PUNCT
ejde-637	218	7	x−	x−	PROPN
ejde-637	218	8	e	e	PROPN
ejde-637	218	9	−	−	PROPN
ejde-637	218	10	2µ1	2µ1	NUM
ejde-637	218	11	−	−	NUM
ejde-637	218	12	x+	x+	X
ejde-637	218	13	e	e	X
ejde-637	218	14	)	)	PUNCT
ejde-637	218	15	,	,	PUNCT
ejde-637	218	16	which	which	PRON
ejde-637	218	17	implies	imply	VERB
ejde-637	218	18	that	that	SCONJ
ejde-637	218	19	x−	x−	PROPN
ejde-637	218	20	t	t	PROPN
ejde-637	218	21	<	<	X
ejde-637	218	22	x∗	x∗	PROPN
ejde-637	218	23	<	<	X
ejde-637	218	24	x+	x+	PROPN
ejde-637	218	25	t	t	X
ejde-637	218	26	,	,	PUNCT
ejde-637	219	1	if	if	SCONJ
ejde-637	219	2	x−	x−	PROPN
ejde-637	219	3	e	e	PROPN
ejde-637	219	4	<	<	X
ejde-637	219	5	x+	x+	X
ejde-637	219	6	e	e	X
ejde-637	219	7	+	+	NOUN
ejde-637	219	8	2µ1	2µ1	NUM
ejde-637	219	9	;	;	PUNCT
ejde-637	219	10	x+	x+	NUM
ejde-637	219	11	t	t	X
ejde-637	219	12	<	<	X
ejde-637	219	13	x∗	x∗	PROPN
ejde-637	219	14	<	<	X
ejde-637	219	15	x−	x−	PROPN
ejde-637	219	16	t	t	PROPN
ejde-637	219	17	,	,	PUNCT
ejde-637	219	18	if	if	SCONJ
ejde-637	219	19	x−	x−	PROPN
ejde-637	219	20	e	e	PROPN
ejde-637	219	21	>	>	X
ejde-637	219	22	x+	x+	X
ejde-637	219	23	e	e	X
ejde-637	219	24	+	+	NOUN
ejde-637	219	25	2µ1	2µ1	NUM
ejde-637	219	26	.	.	PUNCT
ejde-637	220	1	then	then	ADV
ejde-637	220	2	by	by	ADP
ejde-637	220	3	(	(	PUNCT
ejde-637	220	4	3.2	3.2	NUM
ejde-637	220	5	)	)	PUNCT
ejde-637	220	6	,	,	PUNCT
ejde-637	220	7	we	we	PRON
ejde-637	220	8	obtain	obtain	VERB
ejde-637	220	9	pex	pex	NOUN
ejde-637	220	10	=	=	PUNCT
ejde-637	220	11	(	(	PUNCT
ejde-637	220	12	x∗	x∗	PROPN
ejde-637	220	13	,	,	PUNCT
ejde-637	220	14	0	0	NUM
ejde-637	220	15	)	)	PUNCT
ejde-637	220	16	∈	∈	PROPN
ejde-637	220	17	σx	σx	NOUN
ejde-637	220	18	s	s	PRON
ejde-637	220	19	,	,	PUNCT
ejde-637	220	20	that	that	ADV
ejde-637	220	21	is	be	AUX
ejde-637	220	22	pex	pex	PROPN
ejde-637	220	23	=	=	PUNCT
ejde-637	220	24	(	(	PUNCT
ejde-637	220	25	x∗	x∗	PROPN
ejde-637	220	26	,	,	PUNCT
ejde-637	220	27	0	0	NUM
ejde-637	220	28	)	)	PUNCT
ejde-637	220	29	is	be	AUX
ejde-637	220	30	a	a	DET
ejde-637	220	31	pseudoequilibrium	pseudoequilibrium	NOUN
ejde-637	220	32	point	point	NOUN
ejde-637	220	33	of	of	ADP
ejde-637	220	34	system	system	NOUN
ejde-637	220	35	(	(	PUNCT
ejde-637	220	36	1.1	1.1	NUM
ejde-637	220	37	)	)	PUNCT
ejde-637	220	38	only	only	ADV
ejde-637	220	39	as	as	ADP
ejde-637	220	40	x−	x−	PROPN
ejde-637	220	41	e	e	PROPN
ejde-637	220	42	>	>	PUNCT
ejde-637	220	43	−x+	−x+	X
ejde-637	220	44	e	e	NOUN
ejde-637	220	45	and	and	CCONJ
ejde-637	220	46	x−	x−	PROPN
ejde-637	220	47	e	e	PROPN
ejde-637	220	48	̸=	̸=	PROPN
ejde-637	220	49	x+	x+	PUNCT
ejde-637	220	50	e	e	X
ejde-637	220	51	+	+	NOUN
ejde-637	220	52	2µ1	2µ1	NUM
ejde-637	220	53	.	.	PUNCT
ejde-637	221	1	on	on	ADP
ejde-637	221	2	the	the	DET
ejde-637	221	3	other	other	ADJ
ejde-637	221	4	hand	hand	NOUN
ejde-637	221	5	,	,	PUNCT
ejde-637	221	6	according	accord	VERB
ejde-637	221	7	to	to	PART
ejde-637	221	8	figure	figure	NOUN
ejde-637	221	9	1	1	NUM
ejde-637	221	10	,	,	PUNCT
ejde-637	221	11	it	it	PRON
ejde-637	221	12	is	be	AUX
ejde-637	221	13	easy	easy	ADJ
ejde-637	221	14	to	to	PART
ejde-637	221	15	see	see	VERB
ejde-637	221	16	that	that	PRON
ejde-637	221	17	y∗	y∗	PROPN
ejde-637	221	18	>	>	X
ejde-637	221	19	0	0	PUNCT
ejde-637	221	20	when	when	SCONJ
ejde-637	221	21	x−	x−	PROPN
ejde-637	221	22	e	e	PROPN
ejde-637	221	23	∈	∈	PROPN
ejde-637	221	24	(	(	PUNCT
ejde-637	221	25	−∞,−x+	−∞,−x+	NOUN
ejde-637	221	26	e	e	NOUN
ejde-637	221	27	)	)	PUNCT
ejde-637	221	28	∪	∪	VERB
ejde-637	221	29	(	(	PUNCT
ejde-637	221	30	x+	x+	ADJ
ejde-637	221	31	e	e	X
ejde-637	221	32	,	,	PUNCT
ejde-637	221	33	+	+	NOUN
ejde-637	221	34	∞	∞	NOUN
ejde-637	221	35	)	)	PUNCT
ejde-637	221	36	,	,	PUNCT
ejde-637	221	37	and	and	CCONJ
ejde-637	221	38	y∗	y∗	ADV
ejde-637	221	39	=	=	SYM
ejde-637	221	40	0	0	PUNCT
ejde-637	222	1	if	if	SCONJ
ejde-637	222	2	and	and	CCONJ
ejde-637	222	3	only	only	ADV
ejde-637	222	4	if	if	SCONJ
ejde-637	222	5	x−	x−	PROPN
ejde-637	222	6	e	e	NOUN
ejde-637	222	7	=	=	PUNCT
ejde-637	222	8	−x+	−x+	X
ejde-637	222	9	e	e	NOUN
ejde-637	222	10	.	.	PUNCT
ejde-637	223	1	firstly	firstly	ADV
ejde-637	223	2	,	,	PUNCT
ejde-637	223	3	when	when	SCONJ
ejde-637	223	4	x−	x−	PROPN
ejde-637	223	5	e	e	PROPN
ejde-637	223	6	=	=	PUNCT
ejde-637	223	7	−x+	−x+	NUM
ejde-637	223	8	e	e	NOUN
ejde-637	223	9	,	,	PUNCT
ejde-637	223	10	simple	simple	ADJ
ejde-637	223	11	computation	computation	NOUN
ejde-637	223	12	shows	show	VERB
ejde-637	223	13	that	that	SCONJ
ejde-637	223	14	x−	x−	PROPN
ejde-637	223	15	e	e	PROPN
ejde-637	223	16	−	−	PROPN
ejde-637	223	17	µ2	µ2	PROPN
ejde-637	223	18	=	=	PROPN
ejde-637	223	19	−x+	−x+	NOUN
ejde-637	223	20	e	e	NOUN
ejde-637	223	21	−	−	PROPN
ejde-637	223	22	µ2	µ2	PROPN
ejde-637	223	23	=	=	SYM
ejde-637	223	24	−a12	−a12	PROPN
ejde-637	223	25	a11	a11	PROPN
ejde-637	223	26	y+t	y+t	PROPN
ejde-637	223	27	.	.	PUNCT
ejde-637	224	1	then	then	ADV
ejde-637	224	2	we	we	PRON
ejde-637	224	3	obtain	obtain	VERB
ejde-637	224	4	that	that	DET
ejde-637	224	5	pey	pey	NOUN
ejde-637	224	6	=	=	SYM
ejde-637	224	7	(	(	PUNCT
ejde-637	224	8	0	0	NUM
ejde-637	224	9	,	,	PUNCT
ejde-637	224	10	0	0	NUM
ejde-637	224	11	)	)	PUNCT
ejde-637	224	12	∈	∈	NOUN
ejde-637	224	13	σy	σy	NOUN
ejde-637	224	14	s	s	X
ejde-637	224	15	as	as	ADV
ejde-637	224	16	long	long	ADV
ejde-637	224	17	as	as	ADP
ejde-637	224	18	x+	x+	X
ejde-637	224	19	e	e	X
ejde-637	224	20	+	+	NOUN
ejde-637	224	21	µ2	µ2	PROPN
ejde-637	224	22	̸=	̸=	PROPN
ejde-637	224	23	0	0	NUM
ejde-637	224	24	by	by	ADP
ejde-637	224	25	(	(	PUNCT
ejde-637	224	26	3.4)-(3.6	3.4)-(3.6	NUM
ejde-637	224	27	)	)	PUNCT
ejde-637	224	28	.	.	PUNCT
ejde-637	225	1	furthermore	furthermore	ADV
ejde-637	225	2	,	,	PUNCT
ejde-637	225	3	ejde-2024/57	ejde-2024/57	NOUN
ejde-637	225	4	planar	planar	ADJ
ejde-637	225	5	sector	sector	NOUN
ejde-637	225	6	-	-	PUNCT
ejde-637	225	7	wise	wise	ADJ
ejde-637	225	8	linear	linear	NOUN
ejde-637	225	9	systems	system	NOUN
ejde-637	225	10	9	9	NUM
ejde-637	225	11	to	to	PART
ejde-637	225	12	prove	prove	VERB
ejde-637	225	13	whether	whether	SCONJ
ejde-637	225	14	pey	pey	NOUN
ejde-637	225	15	=	=	SYM
ejde-637	225	16	(	(	PUNCT
ejde-637	225	17	0	0	NUM
ejde-637	225	18	,	,	PUNCT
ejde-637	225	19	y∗	y∗	PROPN
ejde-637	225	20	)	)	PUNCT
ejde-637	225	21	∈	∈	PROPN
ejde-637	225	22	σy	σy	NOUN
ejde-637	225	23	s	s	NOUN
ejde-637	225	24	as	as	ADP
ejde-637	225	25	x−	x−	PROPN
ejde-637	225	26	e	e	PROPN
ejde-637	225	27	∈	∈	PROPN
ejde-637	225	28	(	(	PUNCT
ejde-637	225	29	−∞,−x+	−∞,−x+	NOUN
ejde-637	225	30	e	e	NOUN
ejde-637	225	31	)	)	PUNCT
ejde-637	225	32	∪	∪	VERB
ejde-637	225	33	(	(	PUNCT
ejde-637	225	34	x+	x+	ADJ
ejde-637	225	35	e	e	X
ejde-637	225	36	,	,	PUNCT
ejde-637	225	37	+	+	NOUN
ejde-637	225	38	∞	∞	NOUN
ejde-637	225	39	)	)	PUNCT
ejde-637	225	40	,	,	PUNCT
ejde-637	225	41	we	we	PRON
ejde-637	225	42	need	need	VERB
ejde-637	225	43	the	the	DET
ejde-637	225	44	following	follow	VERB
ejde-637	225	45	statements	statement	NOUN
ejde-637	225	46	:	:	PUNCT
ejde-637	225	47	y∗	y∗	PROPN
ejde-637	225	48	−	−	ADP
ejde-637	225	49	y−t	y−t	VERB
ejde-637	225	50	=	=	PUNCT
ejde-637	225	51	x−	x−	PROPN
ejde-637	225	52	e	e	PROPN
ejde-637	225	53	x−	x−	PROPN
ejde-637	225	54	e	e	PROPN
ejde-637	225	55	−	−	PROPN
ejde-637	225	56	x+	x+	PROPN
ejde-637	225	57	e	e	PROPN
ejde-637	225	58	a11	a11	PROPN
ejde-637	225	59	a12	a12	PROPN
ejde-637	225	60	(	(	PUNCT
ejde-637	225	61	x+	x+	X
ejde-637	225	62	e	e	X
ejde-637	225	63	+	+	PROPN
ejde-637	225	64	2µ2	2µ2	NUM
ejde-637	225	65	−	−	NOUN
ejde-637	225	66	x−	x−	PROPN
ejde-637	225	67	e	e	PROPN
ejde-637	225	68	)	)	PUNCT
ejde-637	225	69	,	,	PUNCT
ejde-637	225	70	y∗	y∗	PROPN
ejde-637	225	71	−	−	PROPN
ejde-637	225	72	y+t	y+t	X
ejde-637	226	1	=	=	PUNCT
ejde-637	227	1	x+	x+	PUNCT
ejde-637	227	2	e	e	X
ejde-637	227	3	x−	x−	PROPN
ejde-637	227	4	e	e	PROPN
ejde-637	227	5	−	−	PROPN
ejde-637	227	6	x+	x+	PROPN
ejde-637	227	7	e	e	PROPN
ejde-637	227	8	a11	a11	PROPN
ejde-637	227	9	a12	a12	PROPN
ejde-637	227	10	(	(	PUNCT
ejde-637	227	11	x+	x+	X
ejde-637	227	12	e	e	X
ejde-637	227	13	+	+	PROPN
ejde-637	227	14	2µ2	2µ2	NUM
ejde-637	227	15	−	−	NOUN
ejde-637	227	16	x−	x−	PROPN
ejde-637	227	17	e	e	PROPN
ejde-637	227	18	)	)	PUNCT
ejde-637	227	19	,	,	PUNCT
ejde-637	227	20	x+	x+	X
ejde-637	227	21	e	e	X
ejde-637	227	22	+	+	CCONJ
ejde-637	227	23	2µ2	2µ2	NUM
ejde-637	227	24	>	>	SYM
ejde-637	227	25	0	0	NUM
ejde-637	227	26	,	,	PUNCT
ejde-637	227	27	if	if	SCONJ
ejde-637	227	28	a	a	DET
ejde-637	227	29	∈	∈	PROPN
ejde-637	227	30	ω1	ω1	PROPN
ejde-637	227	31	,	,	PUNCT
ejde-637	227	32	x+	x+	ADJ
ejde-637	227	33	e	e	X
ejde-637	227	34	+	+	NOUN
ejde-637	227	35	2µ2	2µ2	NUM
ejde-637	227	36	<	<	X
ejde-637	227	37	0	0	NUM
ejde-637	227	38	,	,	PUNCT
ejde-637	227	39	if	if	SCONJ
ejde-637	227	40	a	a	DET
ejde-637	227	41	∈	∈	PROPN
ejde-637	227	42	ω2	ω2	NOUN
ejde-637	227	43	,	,	PUNCT
ejde-637	227	44	which	which	PRON
ejde-637	227	45	implies	imply	VERB
ejde-637	227	46	that	that	SCONJ
ejde-637	227	47	as	as	ADP
ejde-637	227	48	a	a	DET
ejde-637	227	49	∈	∈	PROPN
ejde-637	227	50	ω1	ω1	PROPN
ejde-637	227	51	and	and	CCONJ
ejde-637	227	52	x−	x−	PROPN
ejde-637	227	53	e	e	PROPN
ejde-637	227	54	<	<	X
ejde-637	227	55	x+	x+	PROPN
ejde-637	227	56	e	e	X
ejde-637	227	57	(	(	PUNCT
ejde-637	227	58	a	a	DET
ejde-637	227	59	∈	∈	PROPN
ejde-637	227	60	ω2	ω2	ADJ
ejde-637	227	61	and	and	CCONJ
ejde-637	227	62	x−	x−	PROPN
ejde-637	227	63	e	e	PROPN
ejde-637	227	64	>	>	PUNCT
ejde-637	227	65	x+	x+	X
ejde-637	227	66	e	e	X
ejde-637	227	67	)	)	PUNCT
ejde-637	227	68	,	,	PUNCT
ejde-637	227	69	we	we	PRON
ejde-637	227	70	have	have	VERB
ejde-637	227	71	x−	x−	PROPN
ejde-637	227	72	e	e	PROPN
ejde-637	227	73	<	<	X
ejde-637	227	74	x+	x+	X
ejde-637	227	75	e	e	X
ejde-637	227	76	+	+	NUM
ejde-637	227	77	2µ2	2µ2	NUM
ejde-637	227	78	(	(	PUNCT
ejde-637	227	79	x−	x−	PROPN
ejde-637	227	80	e	e	PROPN
ejde-637	227	81	>	>	X
ejde-637	227	82	x+	x+	X
ejde-637	227	83	e	e	X
ejde-637	227	84	+	+	NOUN
ejde-637	227	85	2µ2	2µ2	NUM
ejde-637	227	86	)	)	PUNCT
ejde-637	227	87	,	,	PUNCT
ejde-637	227	88	then	then	ADV
ejde-637	227	89	we	we	PRON
ejde-637	227	90	obtain	obtain	VERB
ejde-637	227	91	that	that	SCONJ
ejde-637	227	92	y−t	y−t	VERB
ejde-637	227	93	<	<	X
ejde-637	227	94	y∗	y∗	ADV
ejde-637	227	95	<	<	X
ejde-637	227	96	y+t	y+t	PROPN
ejde-637	227	97	(	(	PUNCT
ejde-637	227	98	y∗	y∗	ADV
ejde-637	227	99	>	>	X
ejde-637	227	100	max{y−t	max{y−t	PROPN
ejde-637	227	101	,	,	PUNCT
ejde-637	227	102	y+t	y+t	PROPN
ejde-637	227	103	}	}	PUNCT
ejde-637	227	104	)	)	PUNCT
ejde-637	227	105	.	.	PUNCT
ejde-637	228	1	as	as	ADP
ejde-637	228	2	a	a	DET
ejde-637	228	3	∈	∈	PROPN
ejde-637	228	4	ω1	ω1	PROPN
ejde-637	228	5	and	and	CCONJ
ejde-637	228	6	x−	x−	PROPN
ejde-637	228	7	e	e	PROPN
ejde-637	228	8	>	>	PUNCT
ejde-637	228	9	x+	x+	PROPN
ejde-637	228	10	e	e	X
ejde-637	228	11	(	(	PUNCT
ejde-637	228	12	a	a	DET
ejde-637	228	13	∈	∈	PROPN
ejde-637	228	14	ω2	ω2	NOUN
ejde-637	228	15	and	and	CCONJ
ejde-637	228	16	x−	x−	PROPN
ejde-637	228	17	e	e	PROPN
ejde-637	228	18	<	<	X
ejde-637	228	19	−x+	−x+	X
ejde-637	228	20	e	e	NOUN
ejde-637	228	21	)	)	PUNCT
ejde-637	228	22	,	,	PUNCT
ejde-637	228	23	we	we	PRON
ejde-637	228	24	obtain	obtain	VERB
ejde-637	228	25	that	that	SCONJ
ejde-637	228	26	y∗	y∗	ADV
ejde-637	228	27	<	<	X
ejde-637	228	28	min{y−t	min{y−t	NOUN
ejde-637	228	29	,	,	PUNCT
ejde-637	228	30	y+t	y+t	NUM
ejde-637	228	31	}	}	PUNCT
ejde-637	228	32	(	(	PUNCT
ejde-637	228	33	y−t	y−t	NOUN
ejde-637	228	34	<	<	X
ejde-637	228	35	y∗	y∗	ADV
ejde-637	228	36	<	<	X
ejde-637	228	37	y+t	y+t	PROPN
ejde-637	228	38	)	)	PUNCT
ejde-637	228	39	,	,	PUNCT
ejde-637	228	40	if	if	SCONJ
ejde-637	228	41	x−	x−	PROPN
ejde-637	228	42	e	e	PROPN
ejde-637	228	43	>	>	X
ejde-637	228	44	x+	x+	X
ejde-637	228	45	e	e	X
ejde-637	228	46	+	+	PROPN
ejde-637	228	47	2µ2	2µ2	NUM
ejde-637	228	48	;	;	PUNCT
ejde-637	228	49	y∗	y∗	ADV
ejde-637	228	50	>	>	X
ejde-637	228	51	max{y−t	max{y−t	PROPN
ejde-637	228	52	,	,	PUNCT
ejde-637	228	53	y+t	y+t	PROPN
ejde-637	228	54	}	}	PUNCT
ejde-637	228	55	(	(	PUNCT
ejde-637	228	56	y+t	y+t	X
ejde-637	228	57	<	<	X
ejde-637	228	58	y∗	y∗	ADV
ejde-637	228	59	<	<	X
ejde-637	228	60	y−t	y−t	PROPN
ejde-637	228	61	)	)	PUNCT
ejde-637	228	62	,	,	PUNCT
ejde-637	228	63	if	if	SCONJ
ejde-637	228	64	x−	x−	PROPN
ejde-637	228	65	e	e	PROPN
ejde-637	228	66	<	<	X
ejde-637	228	67	x+	x+	X
ejde-637	228	68	e	e	X
ejde-637	228	69	+	+	NOUN
ejde-637	228	70	2µ2	2µ2	NUM
ejde-637	228	71	.	.	PUNCT
ejde-637	229	1	then	then	ADV
ejde-637	229	2	by	by	ADP
ejde-637	229	3	(	(	PUNCT
ejde-637	229	4	3.4)-(3.6	3.4)-(3.6	NUM
ejde-637	229	5	)	)	PUNCT
ejde-637	229	6	,	,	PUNCT
ejde-637	229	7	it	it	PRON
ejde-637	229	8	follows	follow	VERB
ejde-637	229	9	that	that	SCONJ
ejde-637	229	10	pey	pey	NOUN
ejde-637	229	11	=	=	SYM
ejde-637	229	12	(	(	PUNCT
ejde-637	229	13	0	0	NUM
ejde-637	229	14	,	,	PUNCT
ejde-637	229	15	y∗	y∗	PROPN
ejde-637	229	16	)	)	PUNCT
ejde-637	229	17	∈	∈	PROPN
ejde-637	229	18	σy	σy	NOUN
ejde-637	229	19	s	s	NOUN
ejde-637	229	20	,	,	PUNCT
ejde-637	229	21	that	that	PRON
ejde-637	229	22	is	be	AUX
ejde-637	229	23	pey	pey	NOUN
ejde-637	229	24	=	=	SYM
ejde-637	229	25	(	(	PUNCT
ejde-637	229	26	0	0	NUM
ejde-637	229	27	,	,	PUNCT
ejde-637	229	28	y∗	y∗	PROPN
ejde-637	229	29	)	)	PUNCT
ejde-637	229	30	is	be	AUX
ejde-637	229	31	a	a	DET
ejde-637	229	32	pseudo	pseudo	NOUN
ejde-637	229	33	-	-	NOUN
ejde-637	229	34	equilibrium	equilibrium	NOUN
ejde-637	229	35	point	point	NOUN
ejde-637	229	36	of	of	ADP
ejde-637	229	37	system	system	NOUN
ejde-637	229	38	(	(	PUNCT
ejde-637	229	39	1.1	1.1	NUM
ejde-637	229	40	)	)	PUNCT
ejde-637	229	41	only	only	ADV
ejde-637	229	42	as	as	ADP
ejde-637	229	43	x−	x−	PROPN
ejde-637	229	44	e	e	PROPN
ejde-637	229	45	<	<	X
ejde-637	229	46	−x+	−x+	X
ejde-637	229	47	e	e	NOUN
ejde-637	229	48	and	and	CCONJ
ejde-637	229	49	x−	x−	PROPN
ejde-637	229	50	e	e	PROPN
ejde-637	229	51	̸=	̸=	PROPN
ejde-637	229	52	x+	x+	PUNCT
ejde-637	229	53	e	e	X
ejde-637	229	54	+	+	NOUN
ejde-637	229	55	2µ2	2µ2	NUM
ejde-637	229	56	.	.	PUNCT
ejde-637	230	1	finally	finally	ADV
ejde-637	230	2	,	,	PUNCT
ejde-637	230	3	we	we	PRON
ejde-637	230	4	discuss	discuss	VERB
ejde-637	230	5	the	the	DET
ejde-637	230	6	stability	stability	NOUN
ejde-637	230	7	of	of	ADP
ejde-637	230	8	pex	pex	PROPN
ejde-637	230	9	and	and	CCONJ
ejde-637	230	10	pey	pey	PROPN
ejde-637	230	11	.	.	PUNCT
ejde-637	231	1	let	let	VERB
ejde-637	231	2	f(x	f(x	PROPN
ejde-637	231	3	)	)	PUNCT
ejde-637	232	1	=	=	SYM
ejde-637	232	2	2	2	NUM
ejde-637	232	3	det(a	det(a	NOUN
ejde-637	232	4	)	)	PUNCT
ejde-637	232	5	·	·	PUNCT
ejde-637	233	1	y+e	y+e	NOUN
ejde-637	233	2	·	·	PUNCT
ejde-637	233	3	(	(	PUNCT
ejde-637	233	4	x−	x−	PROPN
ejde-637	233	5	x−	x−	PROPN
ejde-637	233	6	e	e	PROPN
ejde-637	234	1	+	+	PROPN
ejde-637	234	2	x+	x+	ADJ
ejde-637	234	3	e	e	X
ejde-637	234	4	2	2	NUM
ejde-637	234	5	)	)	PUNCT
ejde-637	234	6	and	and	CCONJ
ejde-637	234	7	g(x	g(x	NOUN
ejde-637	234	8	)	)	PUNCT
ejde-637	234	9	=	=	SYM
ejde-637	234	10	det(a	det(a	PROPN
ejde-637	234	11	)	)	PUNCT
ejde-637	234	12	·	·	PUNCT
ejde-637	235	1	[	[	X
ejde-637	235	2	(	(	PUNCT
ejde-637	235	3	x+	x+	X
ejde-637	235	4	e	e	NOUN
ejde-637	235	5	−	−	PROPN
ejde-637	235	6	x−	x−	PROPN
ejde-637	235	7	e	e	PROPN
ejde-637	235	8	)	)	PUNCT
ejde-637	235	9	y	y	PROPN
ejde-637	236	1	+	+	CCONJ
ejde-637	236	2	(	(	PUNCT
ejde-637	236	3	x+	x+	X
ejde-637	236	4	e	e	X
ejde-637	236	5	+	+	CCONJ
ejde-637	236	6	x−	x−	PROPN
ejde-637	236	7	e	e	PROPN
ejde-637	236	8	)	)	PUNCT
ejde-637	236	9	y	y	PROPN
ejde-637	236	10	+	+	NUM
ejde-637	236	11	e	e	X
ejde-637	236	12	]	]	PUNCT
ejde-637	236	13	.	.	PUNCT
ejde-637	237	1	then	then	ADV
ejde-637	237	2	x∗	x∗	PROPN
ejde-637	237	3	and	and	CCONJ
ejde-637	237	4	y∗	y∗	PROPN
ejde-637	237	5	are	be	AUX
ejde-637	237	6	the	the	DET
ejde-637	237	7	isolated	isolated	ADJ
ejde-637	237	8	root	root	NOUN
ejde-637	237	9	of	of	ADP
ejde-637	237	10	the	the	DET
ejde-637	237	11	equation	equation	NOUN
ejde-637	237	12	f(x	f(x	PROPN
ejde-637	237	13	)	)	PUNCT
ejde-637	238	1	=	=	SYM
ejde-637	238	2	0	0	NUM
ejde-637	238	3	and	and	CCONJ
ejde-637	238	4	g(x	g(x	NOUN
ejde-637	238	5	)	)	PUNCT
ejde-637	239	1	=	=	SYM
ejde-637	239	2	0	0	NUM
ejde-637	239	3	,	,	PUNCT
ejde-637	239	4	respectively	respectively	ADV
ejde-637	239	5	.	.	PUNCT
ejde-637	240	1	we	we	PRON
ejde-637	240	2	first	first	ADV
ejde-637	240	3	discuss	discuss	VERB
ejde-637	240	4	the	the	DET
ejde-637	240	5	stability	stability	NOUN
ejde-637	240	6	of	of	ADP
ejde-637	240	7	pex	pex	PROPN
ejde-637	240	8	.	.	PUNCT
ejde-637	241	1	by	by	ADP
ejde-637	241	2	definition	definition	NOUN
ejde-637	241	3	2.3	2.3	NUM
ejde-637	241	4	,	,	PUNCT
ejde-637	241	5	on	on	ADP
ejde-637	241	6	the	the	DET
ejde-637	241	7	one	one	NUM
ejde-637	241	8	hand	hand	NOUN
ejde-637	241	9	,	,	PUNCT
ejde-637	241	10	σx	σx	ADP
ejde-637	241	11	s	s	NOUN
ejde-637	241	12	=	=	X
ejde-637	241	13	{	{	PUNCT
ejde-637	241	14	(	(	PUNCT
ejde-637	241	15	x	x	NOUN
ejde-637	241	16	,	,	PUNCT
ejde-637	241	17	0	0	NUM
ejde-637	241	18	)	)	PUNCT
ejde-637	241	19	:	:	PUNCT
ejde-637	241	20	f+	f+	PROPN
ejde-637	241	21	2	2	NUM
ejde-637	241	22	(	(	PUNCT
ejde-637	241	23	x	x	NOUN
ejde-637	241	24	,	,	PUNCT
ejde-637	241	25	0	0	NUM
ejde-637	241	26	)	)	PUNCT
ejde-637	241	27	·	·	PUNCT
ejde-637	242	1	f−	f−	NOUN
ejde-637	242	2	2	2	NUM
ejde-637	242	3	(	(	PUNCT
ejde-637	242	4	x	x	NOUN
ejde-637	242	5	,	,	PUNCT
ejde-637	242	6	0	0	NUM
ejde-637	242	7	)	)	PUNCT
ejde-637	242	8	<	<	X
ejde-637	242	9	0	0	NUM
ejde-637	242	10	}	}	PUNCT
ejde-637	242	11	.	.	PUNCT
ejde-637	243	1	so	so	ADV
ejde-637	243	2	the	the	DET
ejde-637	243	3	sliding	slide	VERB
ejde-637	243	4	set	set	NOUN
ejde-637	243	5	σx	σx	ADP
ejde-637	243	6	s	s	PROPN
ejde-637	243	7	is	be	AUX
ejde-637	243	8	escaping	escape	VERB
ejde-637	243	9	if	if	SCONJ
ejde-637	243	10	f−	f−	PROPN
ejde-637	243	11	2	2	NUM
ejde-637	243	12	(	(	PUNCT
ejde-637	243	13	x	x	NOUN
ejde-637	243	14	,	,	PUNCT
ejde-637	243	15	0	0	NUM
ejde-637	243	16	)	)	PUNCT
ejde-637	243	17	<	<	X
ejde-637	243	18	0	0	PUNCT
ejde-637	243	19	and	and	CCONJ
ejde-637	243	20	attracting	attract	VERB
ejde-637	243	21	if	if	SCONJ
ejde-637	243	22	f−	f−	PROPN
ejde-637	243	23	2	2	NUM
ejde-637	243	24	(	(	PUNCT
ejde-637	243	25	x	x	NOUN
ejde-637	243	26	,	,	PUNCT
ejde-637	243	27	0	0	NUM
ejde-637	243	28	)	)	PUNCT
ejde-637	243	29	>	>	X
ejde-637	244	1	0	0	X
ejde-637	244	2	.	.	PUNCT
ejde-637	245	1	on	on	ADP
ejde-637	245	2	the	the	DET
ejde-637	245	3	other	other	ADJ
ejde-637	245	4	hand	hand	NOUN
ejde-637	245	5	,	,	PUNCT
ejde-637	245	6	the	the	DET
ejde-637	245	7	sliding	slide	VERB
ejde-637	245	8	field	field	NOUN
ejde-637	245	9	(	(	PUNCT
ejde-637	245	10	3.10	3.10	NUM
ejde-637	245	11	)	)	PUNCT
ejde-637	245	12	at	at	ADP
ejde-637	245	13	(	(	PUNCT
ejde-637	245	14	x	x	NOUN
ejde-637	245	15	,	,	PUNCT
ejde-637	245	16	0	0	NUM
ejde-637	245	17	)	)	PUNCT
ejde-637	245	18	∈	∈	NOUN
ejde-637	245	19	σx	σx	ADP
ejde-637	245	20	s	s	NOUN
ejde-637	245	21	is	be	AUX
ejde-637	245	22	fsx(x	fsx(x	NOUN
ejde-637	245	23	,	,	PUNCT
ejde-637	245	24	0	0	NUM
ejde-637	245	25	)	)	PUNCT
ejde-637	245	26	=	=	SYM
ejde-637	246	1	(	(	PUNCT
ejde-637	246	2	f	f	NOUN
ejde-637	246	3	1	1	NUM
ejde-637	246	4	sx(x	sx(x	ADJ
ejde-637	246	5	,	,	PUNCT
ejde-637	246	6	0	0	NUM
ejde-637	246	7	)	)	PUNCT
ejde-637	246	8	0	0	NUM
ejde-637	246	9	)	)	PUNCT
ejde-637	246	10	,	,	PUNCT
ejde-637	246	11	f	f	PROPN
ejde-637	246	12	1	1	NUM
ejde-637	246	13	sx(x	sx(x	ADJ
ejde-637	246	14	,	,	PUNCT
ejde-637	246	15	0	0	NUM
ejde-637	246	16	)	)	PUNCT
ejde-637	246	17	=	=	SYM
ejde-637	246	18	f(x	f(x	PROPN
ejde-637	246	19	)	)	PUNCT
ejde-637	246	20	f−	f−	NOUN
ejde-637	246	21	2	2	NUM
ejde-637	246	22	(	(	PUNCT
ejde-637	246	23	x	x	NOUN
ejde-637	246	24	,	,	PUNCT
ejde-637	246	25	0)−	0)−	NUM
ejde-637	246	26	f+	f+	PROPN
ejde-637	246	27	2	2	NUM
ejde-637	246	28	(	(	PUNCT
ejde-637	246	29	x	x	NOUN
ejde-637	246	30	,	,	PUNCT
ejde-637	246	31	0	0	NUM
ejde-637	246	32	)	)	PUNCT
ejde-637	246	33	.	.	PUNCT
ejde-637	247	1	(	(	PUNCT
ejde-637	247	2	3.13	3.13	NUM
ejde-637	247	3	)	)	PUNCT
ejde-637	247	4	then	then	ADV
ejde-637	247	5	from	from	ADP
ejde-637	247	6	(	(	PUNCT
ejde-637	247	7	3.13	3.13	NUM
ejde-637	247	8	)	)	PUNCT
ejde-637	247	9	and	and	CCONJ
ejde-637	247	10	the	the	DET
ejde-637	247	11	fact	fact	NOUN
ejde-637	247	12	that	that	SCONJ
ejde-637	247	13	f+	f+	ADJ
ejde-637	247	14	2	2	NUM
ejde-637	247	15	(	(	PUNCT
ejde-637	247	16	x	x	NOUN
ejde-637	247	17	,	,	PUNCT
ejde-637	247	18	0	0	NUM
ejde-637	247	19	)	)	PUNCT
ejde-637	247	20	·	·	PUNCT
ejde-637	248	1	f−	f−	NOUN
ejde-637	248	2	2	2	NUM
ejde-637	248	3	(	(	PUNCT
ejde-637	248	4	x	x	NOUN
ejde-637	248	5	,	,	PUNCT
ejde-637	248	6	0	0	NUM
ejde-637	248	7	)	)	PUNCT
ejde-637	248	8	<	<	X
ejde-637	248	9	0	0	NUM
ejde-637	248	10	,	,	PUNCT
ejde-637	248	11	we	we	PRON
ejde-637	248	12	have	have	VERB
ejde-637	248	13	sign(f	sign(f	VERB
ejde-637	248	14	1	1	NUM
ejde-637	248	15	sx(x	sx(x	ADJ
ejde-637	248	16	,	,	PUNCT
ejde-637	248	17	0	0	NUM
ejde-637	248	18	)	)	PUNCT
ejde-637	248	19	)	)	PUNCT
ejde-637	249	1	=	=	SYM
ejde-637	249	2	sign(f−	sign(f−	NOUN
ejde-637	249	3	2	2	NUM
ejde-637	249	4	(	(	PUNCT
ejde-637	249	5	x	x	NOUN
ejde-637	249	6	,	,	PUNCT
ejde-637	249	7	0)f(x	0)f(x	PROPN
ejde-637	249	8	)	)	PUNCT
ejde-637	249	9	)	)	PUNCT
ejde-637	249	10	.	.	PUNCT
ejde-637	250	1	(	(	PUNCT
ejde-637	250	2	3.14	3.14	NUM
ejde-637	250	3	)	)	PUNCT
ejde-637	250	4	and	and	CCONJ
ejde-637	250	5	it	it	PRON
ejde-637	250	6	is	be	AUX
ejde-637	250	7	easy	easy	ADJ
ejde-637	250	8	to	to	PART
ejde-637	250	9	see	see	VERB
ejde-637	250	10	f	f	PROPN
ejde-637	250	11	′(x∗	′(x∗	PROPN
ejde-637	250	12	)	)	PUNCT
ejde-637	250	13	=	=	SYM
ejde-637	250	14	2	2	NUM
ejde-637	250	15	det(a	det(a	NOUN
ejde-637	250	16	)	)	PUNCT
ejde-637	250	17	·	·	PUNCT
ejde-637	251	1	y+e	y+e	NOUN
ejde-637	251	2	<	<	X
ejde-637	251	3	0	0	X
ejde-637	251	4	.	.	PUNCT
ejde-637	252	1	so	so	ADV
ejde-637	252	2	we	we	PRON
ejde-637	252	3	must	must	AUX
ejde-637	252	4	have	have	VERB
ejde-637	252	5	f(x	f(x	PROPN
ejde-637	252	6	)	)	PUNCT
ejde-637	252	7	>	>	X
ejde-637	252	8	0	0	PUNCT
ejde-637	253	1	on	on	ADP
ejde-637	253	2	(	(	PUNCT
ejde-637	253	3	x∗	x∗	PROPN
ejde-637	253	4	−	−	PROPN
ejde-637	253	5	ε	ε	PROPN
ejde-637	253	6	,	,	PUNCT
ejde-637	253	7	x∗	x∗	PROPN
ejde-637	253	8	)	)	PUNCT
ejde-637	253	9	and	and	CCONJ
ejde-637	253	10	f(x	f(x	PROPN
ejde-637	253	11	)	)	PUNCT
ejde-637	253	12	<	<	X
ejde-637	253	13	0	0	PUNCT
ejde-637	253	14	on	on	ADP
ejde-637	253	15	(	(	PUNCT
ejde-637	253	16	x∗	x∗	PROPN
ejde-637	253	17	,	,	PUNCT
ejde-637	253	18	x∗	x∗	PROPN
ejde-637	253	19	+	+	CCONJ
ejde-637	253	20	ε	ε	PROPN
ejde-637	253	21	)	)	PUNCT
ejde-637	253	22	for	for	ADP
ejde-637	253	23	some	some	DET
ejde-637	253	24	small	small	ADJ
ejde-637	253	25	ε	ε	PROPN
ejde-637	253	26	>	>	X
ejde-637	253	27	0	0	PROPN
ejde-637	253	28	.	.	PUNCT
ejde-637	254	1	from	from	ADP
ejde-637	254	2	(	(	PUNCT
ejde-637	254	3	3.14	3.14	NUM
ejde-637	254	4	)	)	PUNCT
ejde-637	254	5	,	,	PUNCT
ejde-637	254	6	if	if	SCONJ
ejde-637	254	7	the	the	DET
ejde-637	254	8	sliding	slide	VERB
ejde-637	254	9	set	set	NOUN
ejde-637	254	10	is	be	AUX
ejde-637	254	11	attracting	attract	VERB
ejde-637	254	12	(	(	PUNCT
ejde-637	254	13	escaping	escaping	NOUN
ejde-637	254	14	)	)	PUNCT
ejde-637	254	15	,	,	PUNCT
ejde-637	254	16	i.e.	i.e.	X
ejde-637	254	17	,	,	PUNCT
ejde-637	254	18	f−	f−	PROPN
ejde-637	254	19	2	2	NUM
ejde-637	254	20	(	(	PUNCT
ejde-637	254	21	x	x	NOUN
ejde-637	254	22	,	,	PUNCT
ejde-637	254	23	0	0	NUM
ejde-637	254	24	)	)	PUNCT
ejde-637	254	25	>	>	X
ejde-637	255	1	0	0	PUNCT
ejde-637	255	2	(	(	PUNCT
ejde-637	255	3	<	<	NOUN
ejde-637	255	4	0	0	NUM
ejde-637	255	5	)	)	PUNCT
ejde-637	255	6	,	,	PUNCT
ejde-637	255	7	pex	pex	PROPN
ejde-637	255	8	will	will	AUX
ejde-637	255	9	be	be	AUX
ejde-637	255	10	stable	stable	ADJ
ejde-637	255	11	(	(	PUNCT
ejde-637	255	12	unstable	unstable	ADJ
ejde-637	255	13	)	)	PUNCT
ejde-637	255	14	.	.	PUNCT
ejde-637	256	1	that	that	PRON
ejde-637	256	2	is	be	AUX
ejde-637	256	3	pex	pex	PROPN
ejde-637	256	4	will	will	AUX
ejde-637	256	5	always	always	ADV
ejde-637	256	6	be	be	AUX
ejde-637	256	7	a	a	DET
ejde-637	256	8	pseudo	pseudo	NOUN
ejde-637	256	9	-	-	NOUN
ejde-637	256	10	node	node	NOUN
ejde-637	256	11	of	of	ADP
ejde-637	256	12	system	system	NOUN
ejde-637	256	13	(	(	PUNCT
ejde-637	256	14	1.1	1.1	NUM
ejde-637	256	15	)	)	PUNCT
ejde-637	256	16	with	with	ADP
ejde-637	256	17	a	a	DET
ejde-637	256	18	∈	∈	PROPN
ejde-637	256	19	ω1∪ω2	ω1∪ω2	PROPN
ejde-637	256	20	,	,	PUNCT
ejde-637	256	21	which	which	PRON
ejde-637	256	22	is	be	AUX
ejde-637	256	23	a	a	DET
ejde-637	256	24	stable	stable	ADJ
ejde-637	256	25	(	(	PUNCT
ejde-637	256	26	an	an	DET
ejde-637	256	27	unstable	unstable	ADJ
ejde-637	256	28	)	)	PUNCT
ejde-637	256	29	pseudo	pseudo	NOUN
ejde-637	256	30	-	-	NOUN
ejde-637	256	31	node	node	ADJ
ejde-637	256	32	when	when	SCONJ
ejde-637	256	33	x−	x−	PROPN
ejde-637	256	34	e	e	PROPN
ejde-637	256	35	<	<	X
ejde-637	256	36	x+	x+	X
ejde-637	257	1	e	e	X
ejde-637	257	2	+2µ1(x	+2µ1(x	NOUN
ejde-637	257	3	−	−	NOUN
ejde-637	257	4	e	e	X
ejde-637	257	5	>	>	X
ejde-637	257	6	x+	x+	X
ejde-637	257	7	e	e	X
ejde-637	257	8	+2µ1	+2µ1	NUM
ejde-637	257	9	)	)	PUNCT
ejde-637	257	10	.	.	PUNCT
ejde-637	258	1	similarly	similarly	ADV
ejde-637	258	2	,	,	PUNCT
ejde-637	258	3	we	we	PRON
ejde-637	258	4	can	can	AUX
ejde-637	258	5	also	also	ADV
ejde-637	258	6	get	get	VERB
ejde-637	258	7	the	the	DET
ejde-637	258	8	stability	stability	NOUN
ejde-637	258	9	of	of	ADP
ejde-637	258	10	pey	pey	NOUN
ejde-637	258	11	.	.	PUNCT
ejde-637	259	1	the	the	DET
ejde-637	259	2	proof	proof	NOUN
ejde-637	259	3	is	be	AUX
ejde-637	259	4	complete	complete	ADJ
ejde-637	259	5	.	.	PUNCT
ejde-637	260	1	□	□	PUNCT
ejde-637	260	2	next	next	ADV
ejde-637	260	3	,	,	PUNCT
ejde-637	260	4	we	we	PRON
ejde-637	260	5	give	give	VERB
ejde-637	260	6	the	the	DET
ejde-637	260	7	properties	property	NOUN
ejde-637	260	8	of	of	ADP
ejde-637	260	9	the	the	DET
ejde-637	260	10	non	non	ADJ
ejde-637	260	11	-	-	ADJ
ejde-637	260	12	regular	regular	ADJ
ejde-637	260	13	point	point	NOUN
ejde-637	260	14	p0	p0	NOUN
ejde-637	260	15	.	.	PUNCT
ejde-637	261	1	proposition	proposition	NOUN
ejde-637	261	2	3.3	3.3	NUM
ejde-637	261	3	.	.	PUNCT
ejde-637	261	4	suppose	suppose	VERB
ejde-637	261	5	that	that	SCONJ
ejde-637	261	6	condition	condition	NOUN
ejde-637	261	7	(	(	PUNCT
ejde-637	261	8	3.1	3.1	NUM
ejde-637	261	9	)	)	PUNCT
ejde-637	261	10	holds	hold	NOUN
ejde-637	261	11	and	and	CCONJ
ejde-637	261	12	a	a	DET
ejde-637	261	13	∈	∈	PROPN
ejde-637	261	14	ω1	ω1	PROPN
ejde-637	261	15	∪	∪	X
ejde-637	261	16	ω2	ω2	PROPN
ejde-637	261	17	.	.	PUNCT
ejde-637	262	1	we	we	PRON
ejde-637	262	2	have	have	VERB
ejde-637	262	3	the	the	DET
ejde-637	262	4	following	follow	VERB
ejde-637	262	5	statements	statement	NOUN
ejde-637	262	6	about	about	ADP
ejde-637	262	7	the	the	DET
ejde-637	262	8	non	non	ADJ
ejde-637	262	9	-	-	ADJ
ejde-637	262	10	regular	regular	ADJ
ejde-637	262	11	point	point	NOUN
ejde-637	262	12	p0	p0	NOUN
ejde-637	262	13	.	.	PUNCT
ejde-637	263	1	(	(	PUNCT
ejde-637	263	2	a	a	X
ejde-637	263	3	)	)	PUNCT
ejde-637	263	4	when	when	SCONJ
ejde-637	263	5	a	a	DET
ejde-637	263	6	∈	∈	PROPN
ejde-637	263	7	ω1	ω1	PROPN
ejde-637	263	8	,	,	PUNCT
ejde-637	263	9	about	about	ADP
ejde-637	263	10	the	the	DET
ejde-637	263	11	non	non	ADJ
ejde-637	263	12	-	-	ADJ
ejde-637	263	13	regular	regular	ADJ
ejde-637	263	14	point	point	NOUN
ejde-637	263	15	p0	p0	NOUN
ejde-637	263	16	,	,	PUNCT
ejde-637	263	17	we	we	PRON
ejde-637	263	18	have	have	VERB
ejde-637	263	19	(	(	PUNCT
ejde-637	263	20	a1	a1	PROPN
ejde-637	263	21	)	)	PUNCT
ejde-637	263	22	as	as	ADP
ejde-637	263	23	x−	x−	PROPN
ejde-637	263	24	e	e	PROPN
ejde-637	263	25	=	=	PROPN
ejde-637	263	26	µ1	µ1	PROPN
ejde-637	263	27	or	or	CCONJ
ejde-637	263	28	x−	x−	PROPN
ejde-637	263	29	e	e	PROPN
ejde-637	263	30	=	=	PROPN
ejde-637	263	31	µ2	µ2	PROPN
ejde-637	263	32	,	,	PUNCT
ejde-637	263	33	p0	p0	NOUN
ejde-637	263	34	is	be	AUX
ejde-637	263	35	a	a	DET
ejde-637	263	36	boundary	boundary	ADJ
ejde-637	263	37	equilibrium	equilibrium	NOUN
ejde-637	263	38	point	point	NOUN
ejde-637	263	39	;	;	PUNCT
ejde-637	263	40	(	(	PUNCT
ejde-637	263	41	a2	a2	PROPN
ejde-637	263	42	)	)	PUNCT
ejde-637	263	43	as	as	ADP
ejde-637	263	44	min{µ1	min{µ1	NOUN
ejde-637	263	45	,	,	PUNCT
ejde-637	263	46	µ2	µ2	PROPN
ejde-637	263	47	}	}	PUNCT
ejde-637	263	48	<	<	X
ejde-637	263	49	x−	x−	PROPN
ejde-637	263	50	e	e	X
ejde-637	263	51	<	<	X
ejde-637	263	52	max{µ1	max{µ1	PROPN
ejde-637	263	53	,	,	PUNCT
ejde-637	263	54	µ2	µ2	PROPN
ejde-637	263	55	}	}	PUNCT
ejde-637	263	56	,	,	PUNCT
ejde-637	263	57	p0	p0	NOUN
ejde-637	263	58	is	be	AUX
ejde-637	263	59	a	a	DET
ejde-637	263	60	sliding	slide	VERB
ejde-637	263	61	boundary	boundary	ADJ
ejde-637	263	62	point	point	NOUN
ejde-637	263	63	;	;	PUNCT
ejde-637	263	64	(	(	PUNCT
ejde-637	263	65	a3	a3	NOUN
ejde-637	263	66	)	)	PUNCT
ejde-637	263	67	as	as	ADP
ejde-637	263	68	x−	x−	PROPN
ejde-637	263	69	e	e	PROPN
ejde-637	263	70	>	>	X
ejde-637	263	71	max{µ1	max{µ1	PROPN
ejde-637	263	72	,	,	PUNCT
ejde-637	263	73	µ2	µ2	PROPN
ejde-637	263	74	}	}	PUNCT
ejde-637	263	75	,	,	PUNCT
ejde-637	263	76	p0	p0	NOUN
ejde-637	263	77	is	be	AUX
ejde-637	263	78	a	a	DET
ejde-637	263	79	crossing	crossing	NOUN
ejde-637	263	80	point	point	NOUN
ejde-637	263	81	;	;	PUNCT
ejde-637	263	82	10	10	NUM
ejde-637	263	83	q.-q	q.-q	PROPN
ejde-637	263	84	.	.	PUNCT
ejde-637	264	1	han	han	PROPN
ejde-637	264	2	,	,	PUNCT
ejde-637	264	3	s.-m	s.-m	PROPN
ejde-637	264	4	.	.	PUNCT
ejde-637	265	1	huan	huan	PROPN
ejde-637	265	2	ejde-2024/57	ejde-2024/57	PROPN
ejde-637	265	3	(	(	PUNCT
ejde-637	265	4	a4	a4	NOUN
ejde-637	265	5	)	)	PUNCT
ejde-637	265	6	when	when	SCONJ
ejde-637	265	7	a12	a12	PROPN
ejde-637	265	8	>	>	X
ejde-637	265	9	0	0	PUNCT
ejde-637	266	1	(	(	PUNCT
ejde-637	266	2	a12	a12	NOUN
ejde-637	266	3	<	<	X
ejde-637	266	4	0	0	NUM
ejde-637	266	5	)	)	PUNCT
ejde-637	266	6	,	,	PUNCT
ejde-637	266	7	p0	p0	PROPN
ejde-637	266	8	is	be	AUX
ejde-637	266	9	a	a	DET
ejde-637	266	10	non	non	ADJ
ejde-637	266	11	-	-	ADJ
ejde-637	266	12	regular	regular	ADJ
ejde-637	266	13	boundary	boundary	ADJ
ejde-637	266	14	saddle	saddle	NOUN
ejde-637	266	15	(	(	PUNCT
ejde-637	266	16	a	a	DET
ejde-637	266	17	non	non	ADJ
ejde-637	266	18	-	-	ADJ
ejde-637	266	19	regular	regular	ADJ
ejde-637	266	20	boundary	boundary	ADJ
ejde-637	266	21	sink	sink	NOUN
ejde-637	266	22	)	)	PUNCT
ejde-637	266	23	,	,	PUNCT
ejde-637	266	24	a	a	DET
ejde-637	266	25	stable	stable	ADJ
ejde-637	266	26	pseudo	pseudo	NOUN
ejde-637	266	27	-	-	NOUN
ejde-637	266	28	node	node	ADJ
ejde-637	266	29	(	(	PUNCT
ejde-637	266	30	a	a	DET
ejde-637	266	31	pseudo	pseudo	NOUN
ejde-637	266	32	-	-	ADJ
ejde-637	266	33	saddle	saddle	NOUN
ejde-637	266	34	-	-	PUNCT
ejde-637	266	35	node	node	NOUN
ejde-637	266	36	)	)	PUNCT
ejde-637	266	37	,	,	PUNCT
ejde-637	266	38	a	a	DET
ejde-637	266	39	non	non	ADJ
ejde-637	266	40	-	-	ADJ
ejde-637	266	41	regular	regular	ADJ
ejde-637	266	42	boundary	boundary	ADJ
ejde-637	266	43	saddle	saddle	NOUN
ejde-637	266	44	(	(	PUNCT
ejde-637	266	45	a	a	DET
ejde-637	266	46	non	non	ADJ
ejde-637	266	47	-	-	ADJ
ejde-637	266	48	regular	regular	ADJ
ejde-637	266	49	boundary	boundary	ADJ
ejde-637	266	50	source	source	NOUN
ejde-637	266	51	)	)	PUNCT
ejde-637	266	52	for	for	ADP
ejde-637	266	53	x−	x−	PROPN
ejde-637	266	54	e	e	PROPN
ejde-637	266	55	<	<	X
ejde-637	266	56	−x+	−x+	X
ejde-637	266	57	e	e	NOUN
ejde-637	266	58	,	,	PUNCT
ejde-637	266	59	x	x	X
ejde-637	267	1	−	−	NOUN
ejde-637	267	2	e	e	NOUN
ejde-637	267	3	=	=	SYM
ejde-637	267	4	−x+	−x+	NOUN
ejde-637	267	5	e	e	NOUN
ejde-637	267	6	and	and	CCONJ
ejde-637	267	7	−x+	−x+	NOUN
ejde-637	267	8	e	e	NOUN
ejde-637	267	9	<	<	X
ejde-637	267	10	x−	x−	PROPN
ejde-637	267	11	e	e	X
ejde-637	267	12	<	<	X
ejde-637	267	13	min{µ1	min{µ1	PROPN
ejde-637	267	14	,	,	PUNCT
ejde-637	267	15	µ2	µ2	PROPN
ejde-637	267	16	}	}	PUNCT
ejde-637	267	17	,	,	PUNCT
ejde-637	267	18	respectively	respectively	ADV
ejde-637	267	19	.	.	PUNCT
ejde-637	268	1	(	(	PUNCT
ejde-637	268	2	b	b	X
ejde-637	268	3	)	)	PUNCT
ejde-637	268	4	when	when	SCONJ
ejde-637	268	5	a	a	DET
ejde-637	268	6	∈	∈	PROPN
ejde-637	268	7	ω2	ω2	NOUN
ejde-637	268	8	,	,	PUNCT
ejde-637	268	9	about	about	ADP
ejde-637	268	10	the	the	DET
ejde-637	268	11	non	non	ADJ
ejde-637	268	12	-	-	ADJ
ejde-637	268	13	regular	regular	ADJ
ejde-637	268	14	point	point	NOUN
ejde-637	268	15	p0	p0	NOUN
ejde-637	268	16	,	,	PUNCT
ejde-637	268	17	we	we	PRON
ejde-637	268	18	have	have	VERB
ejde-637	268	19	(	(	PUNCT
ejde-637	268	20	b1	b1	NOUN
ejde-637	268	21	)	)	PUNCT
ejde-637	268	22	as	as	ADP
ejde-637	268	23	x−	x−	PROPN
ejde-637	268	24	e	e	PROPN
ejde-637	268	25	=	=	PROPN
ejde-637	268	26	µ1	µ1	PROPN
ejde-637	268	27	or	or	CCONJ
ejde-637	268	28	x−	x−	PROPN
ejde-637	268	29	e	e	PROPN
ejde-637	269	1	=	=	PROPN
ejde-637	269	2	µ2	µ2	PROPN
ejde-637	269	3	,	,	PUNCT
ejde-637	269	4	p0	p0	NOUN
ejde-637	269	5	is	be	AUX
ejde-637	269	6	a	a	DET
ejde-637	269	7	boundary	boundary	ADJ
ejde-637	269	8	equilibrium	equilibrium	NOUN
ejde-637	269	9	point	point	NOUN
ejde-637	269	10	;	;	PUNCT
ejde-637	269	11	(	(	PUNCT
ejde-637	269	12	b2	b2	NOUN
ejde-637	269	13	)	)	PUNCT
ejde-637	269	14	as	as	ADP
ejde-637	269	15	x−	x−	PROPN
ejde-637	269	16	e	e	PROPN
ejde-637	269	17	>	>	X
ejde-637	269	18	µ1	µ1	PROPN
ejde-637	269	19	,	,	PUNCT
ejde-637	269	20	p0	p0	NOUN
ejde-637	269	21	is	be	AUX
ejde-637	269	22	a	a	DET
ejde-637	269	23	crossing	crossing	NOUN
ejde-637	269	24	point	point	NOUN
ejde-637	269	25	;	;	PUNCT
ejde-637	269	26	(	(	PUNCT
ejde-637	269	27	b3	b3	PROPN
ejde-637	269	28	)	)	PUNCT
ejde-637	269	29	when	when	SCONJ
ejde-637	269	30	x+	x+	X
ejde-637	269	31	e	e	NOUN
ejde-637	269	32	+	+	CCONJ
ejde-637	269	33	µ2	µ2	PROPN
ejde-637	269	34	>	>	X
ejde-637	269	35	0	0	PUNCT
ejde-637	270	1	(	(	PUNCT
ejde-637	270	2	x+	x+	X
ejde-637	270	3	e	e	X
ejde-637	270	4	+	+	NOUN
ejde-637	270	5	µ2	µ2	PROPN
ejde-637	270	6	<	<	X
ejde-637	270	7	0	0	NUM
ejde-637	270	8	)	)	PUNCT
ejde-637	270	9	,	,	PUNCT
ejde-637	270	10	p0	p0	PROPN
ejde-637	270	11	is	be	AUX
ejde-637	270	12	a	a	DET
ejde-637	270	13	non	non	ADJ
ejde-637	270	14	-	-	ADJ
ejde-637	270	15	regular	regular	ADJ
ejde-637	270	16	boundary	boundary	ADJ
ejde-637	270	17	sink	sink	NOUN
ejde-637	270	18	(	(	PUNCT
ejde-637	270	19	a	a	DET
ejde-637	270	20	sliding	slide	VERB
ejde-637	270	21	boundary	boundary	ADJ
ejde-637	270	22	point	point	NOUN
ejde-637	270	23	)	)	PUNCT
ejde-637	270	24	,	,	PUNCT
ejde-637	270	25	a	a	DET
ejde-637	270	26	pseudo	pseudo	NOUN
ejde-637	270	27	-	-	ADJ
ejde-637	270	28	saddle	saddle	NOUN
ejde-637	270	29	-	-	PUNCT
ejde-637	270	30	node	node	NOUN
ejde-637	270	31	(	(	PUNCT
ejde-637	270	32	a	a	DET
ejde-637	270	33	stable	stable	ADJ
ejde-637	270	34	pseudo	pseudo	NOUN
ejde-637	270	35	-	-	NOUN
ejde-637	270	36	node	node	NOUN
ejde-637	270	37	)	)	PUNCT
ejde-637	270	38	,	,	PUNCT
ejde-637	270	39	a	a	DET
ejde-637	270	40	non	non	ADJ
ejde-637	270	41	-	-	ADJ
ejde-637	270	42	regular	regular	ADJ
ejde-637	270	43	boundary	boundary	ADJ
ejde-637	270	44	source	source	NOUN
ejde-637	270	45	(	(	PUNCT
ejde-637	270	46	a	a	DET
ejde-637	270	47	non	non	ADJ
ejde-637	270	48	-	-	ADJ
ejde-637	270	49	regular	regular	ADJ
ejde-637	270	50	boundary	boundary	ADJ
ejde-637	270	51	saddle	saddle	NOUN
ejde-637	270	52	)	)	PUNCT
ejde-637	270	53	,	,	PUNCT
ejde-637	270	54	a	a	DET
ejde-637	270	55	sliding	slide	VERB
ejde-637	270	56	boundary	boundary	ADJ
ejde-637	270	57	point	point	NOUN
ejde-637	270	58	(	(	PUNCT
ejde-637	270	59	a	a	DET
ejde-637	270	60	non	non	ADJ
ejde-637	270	61	-	-	ADJ
ejde-637	270	62	regular	regular	ADJ
ejde-637	270	63	boundary	boundary	ADJ
ejde-637	270	64	saddle	saddle	NOUN
ejde-637	270	65	)	)	PUNCT
ejde-637	270	66	for	for	ADP
ejde-637	270	67	x−	x−	PROPN
ejde-637	270	68	e	e	PROPN
ejde-637	270	69	<	<	X
ejde-637	270	70	min{−x+	min{−x+	PROPN
ejde-637	270	71	e	e	NOUN
ejde-637	270	72	,	,	PUNCT
ejde-637	270	73	µ2	µ2	PROPN
ejde-637	270	74	}	}	PUNCT
ejde-637	270	75	,	,	PUNCT
ejde-637	270	76	x−	x−	PROPN
ejde-637	270	77	e	e	NOUN
ejde-637	270	78	=	=	PUNCT
ejde-637	270	79	−x+	−x+	NUM
ejde-637	270	80	e	e	NOUN
ejde-637	270	81	,	,	PUNCT
ejde-637	270	82	min{−x+	min{−x+	PROPN
ejde-637	270	83	e	e	NOUN
ejde-637	270	84	,	,	PUNCT
ejde-637	270	85	µ2	µ2	PROPN
ejde-637	270	86	}	}	PUNCT
ejde-637	270	87	<	<	X
ejde-637	270	88	x−	x−	PROPN
ejde-637	270	89	e	e	X
ejde-637	270	90	<	<	X
ejde-637	270	91	max{−x+	max{−x+	PROPN
ejde-637	270	92	e	e	PROPN
ejde-637	270	93	,	,	PUNCT
ejde-637	270	94	µ2	µ2	PROPN
ejde-637	270	95	}	}	PUNCT
ejde-637	270	96	and	and	CCONJ
ejde-637	270	97	max{−x+	max{−x+	PROPN
ejde-637	270	98	e	e	PROPN
ejde-637	270	99	,	,	PUNCT
ejde-637	270	100	µ2	µ2	PROPN
ejde-637	270	101	}	}	PUNCT
ejde-637	270	102	<	<	X
ejde-637	270	103	x−	x−	PROPN
ejde-637	270	104	e	e	X
ejde-637	270	105	<	<	X
ejde-637	270	106	µ1	µ1	PROPN
ejde-637	270	107	,	,	PUNCT
ejde-637	270	108	respectively	respectively	ADV
ejde-637	270	109	.	.	PUNCT
ejde-637	271	1	proof	proof	NOUN
ejde-637	271	2	.	.	PUNCT
ejde-637	272	1	to	to	PART
ejde-637	272	2	discuss	discuss	VERB
ejde-637	272	3	the	the	DET
ejde-637	272	4	non	non	ADJ
ejde-637	272	5	-	-	ADJ
ejde-637	272	6	regular	regular	ADJ
ejde-637	272	7	point	point	NOUN
ejde-637	272	8	p0	p0	NOUN
ejde-637	272	9	,	,	PUNCT
ejde-637	272	10	we	we	PRON
ejde-637	272	11	need	need	VERB
ejde-637	272	12	the	the	DET
ejde-637	272	13	following	follow	VERB
ejde-637	272	14	statements	statement	NOUN
ejde-637	272	15	:	:	PUNCT
ejde-637	272	16	µ2	µ2	PROPN
ejde-637	272	17	−	−	PROPN
ejde-637	272	18	µ1	µ1	PROPN
ejde-637	272	19	=	=	SYM
ejde-637	272	20	−det(a	−det(a	PROPN
ejde-637	272	21	)	)	PUNCT
ejde-637	272	22	a11a21	a11a21	PROPN
ejde-637	272	23	y+e	y+e	NUM
ejde-637	272	24	,	,	PUNCT
ejde-637	272	25	µ2	µ2	PROPN
ejde-637	272	26	−	−	PROPN
ejde-637	272	27	(	(	PUNCT
ejde-637	272	28	−x+	−x+	NOUN
ejde-637	272	29	e	e	NOUN
ejde-637	272	30	)	)	PUNCT
ejde-637	273	1	=	=	SYM
ejde-637	273	2	a12	a12	PROPN
ejde-637	273	3	a11	a11	PROPN
ejde-637	273	4	y+t	y+t	PROPN
ejde-637	273	5	,	,	PUNCT
ejde-637	273	6	µ1	µ1	PROPN
ejde-637	273	7	−	−	PROPN
ejde-637	273	8	(	(	PUNCT
ejde-637	273	9	−x+	−x+	NOUN
ejde-637	273	10	e	e	NOUN
ejde-637	273	11	)	)	PUNCT
ejde-637	274	1	=	=	PUNCT
ejde-637	274	2	x+	x+	PROPN
ejde-637	274	3	t	t	X
ejde-637	274	4	>	>	X
ejde-637	274	5	0	0	X
ejde-637	274	6	.	.	PUNCT
ejde-637	275	1	then	then	ADV
ejde-637	275	2	it	it	PRON
ejde-637	275	3	is	be	AUX
ejde-637	275	4	easy	easy	ADJ
ejde-637	275	5	to	to	PART
ejde-637	275	6	see	see	VERB
ejde-637	275	7	that	that	SCONJ
ejde-637	275	8	when	when	SCONJ
ejde-637	275	9	a	a	DET
ejde-637	275	10	∈	∈	PROPN
ejde-637	275	11	ω1	ω1	PROPN
ejde-637	275	12	,	,	PUNCT
ejde-637	275	13	we	we	PRON
ejde-637	275	14	obtain	obtain	VERB
ejde-637	275	15	−x+	−x+	NOUN
ejde-637	275	16	e	e	X
ejde-637	275	17	<	<	X
ejde-637	275	18	0	0	PUNCT
ejde-637	275	19	<	<	X
ejde-637	275	20	µ1	µ1	PROPN
ejde-637	275	21	<	<	X
ejde-637	275	22	µ2	µ2	PROPN
ejde-637	275	23	,	,	PUNCT
ejde-637	275	24	for	for	ADP
ejde-637	275	25	a12	a12	PROPN
ejde-637	275	26	>	>	X
ejde-637	275	27	0	0	NUM
ejde-637	275	28	;	;	PUNCT
ejde-637	276	1	−x+	−x+	X
ejde-637	276	2	e	e	X
ejde-637	276	3	<	<	X
ejde-637	276	4	0	0	PUNCT
ejde-637	276	5	<	<	X
ejde-637	276	6	µ2	µ2	PROPN
ejde-637	276	7	<	<	X
ejde-637	276	8	µ1	µ1	PROPN
ejde-637	276	9	,	,	PUNCT
ejde-637	276	10	for	for	ADP
ejde-637	276	11	a12	a12	NOUN
ejde-637	276	12	<	<	X
ejde-637	276	13	0	0	NUM
ejde-637	276	14	.	.	PUNCT
ejde-637	277	1	and	and	CCONJ
ejde-637	277	2	when	when	SCONJ
ejde-637	277	3	a	a	DET
ejde-637	277	4	∈	∈	PROPN
ejde-637	277	5	ω2	ω2	NOUN
ejde-637	277	6	,	,	PUNCT
ejde-637	277	7	we	we	PRON
ejde-637	277	8	obtain	obtain	VERB
ejde-637	277	9	−x+	−x+	NOUN
ejde-637	277	10	e	e	NOUN
ejde-637	277	11	<	<	X
ejde-637	277	12	µ2	µ2	PROPN
ejde-637	277	13	<	<	X
ejde-637	277	14	0	0	PUNCT
ejde-637	277	15	<	<	X
ejde-637	277	16	µ1	µ1	PROPN
ejde-637	277	17	,	,	PUNCT
ejde-637	277	18	for	for	ADP
ejde-637	277	19	x+	x+	ADJ
ejde-637	277	20	e	e	PROPN
ejde-637	277	21	+	+	CCONJ
ejde-637	277	22	µ2	µ2	PROPN
ejde-637	277	23	>	>	X
ejde-637	277	24	0	0	NUM
ejde-637	277	25	;	;	PUNCT
ejde-637	277	26	(	(	PUNCT
ejde-637	277	27	3.15	3.15	NUM
ejde-637	277	28	)	)	PUNCT
ejde-637	277	29	µ2	µ2	NOUN
ejde-637	277	30	<	<	X
ejde-637	277	31	−x+	−x+	X
ejde-637	277	32	e	e	X
ejde-637	277	33	<	<	X
ejde-637	277	34	0	0	PUNCT
ejde-637	277	35	<	<	X
ejde-637	277	36	µ1	µ1	PROPN
ejde-637	277	37	,	,	PUNCT
ejde-637	277	38	for	for	ADP
ejde-637	277	39	x+	x+	ADJ
ejde-637	277	40	e	e	PROPN
ejde-637	278	1	+	+	CCONJ
ejde-637	278	2	µ2	µ2	VERB
ejde-637	278	3	≤	≤	PROPN
ejde-637	278	4	0	0	NUM
ejde-637	278	5	.	.	PUNCT
ejde-637	279	1	(	(	PUNCT
ejde-637	279	2	3.16	3.16	NUM
ejde-637	279	3	)	)	PUNCT
ejde-637	279	4	and	and	CCONJ
ejde-637	279	5	for	for	ADP
ejde-637	279	6	x−	x−	PROPN
ejde-637	279	7	e	e	PROPN
ejde-637	279	8	=	=	PUNCT
ejde-637	279	9	−x+	−x+	X
ejde-637	279	10	e	e	NOUN
ejde-637	279	11	,	,	PUNCT
ejde-637	279	12	it	it	PRON
ejde-637	279	13	is	be	AUX
ejde-637	279	14	easy	easy	ADJ
ejde-637	279	15	to	to	PART
ejde-637	279	16	see	see	VERB
ejde-637	279	17	pex	pex	NOUN
ejde-637	279	18	=	=	PROPN
ejde-637	279	19	pey	pey	PROPN
ejde-637	279	20	=	=	NOUN
ejde-637	279	21	p0	p0	NOUN
ejde-637	279	22	.	.	PUNCT
ejde-637	280	1	thus	thus	ADV
ejde-637	280	2	by	by	ADP
ejde-637	280	3	proposition	proposition	NOUN
ejde-637	280	4	3.1	3.1	NUM
ejde-637	280	5	and	and	CCONJ
ejde-637	280	6	proposition	proposition	NOUN
ejde-637	280	7	3.2	3.2	NUM
ejde-637	280	8	,	,	PUNCT
ejde-637	280	9	the	the	DET
ejde-637	280	10	statements	statement	NOUN
ejde-637	280	11	in	in	ADP
ejde-637	280	12	this	this	DET
ejde-637	280	13	proposition	proposition	NOUN
ejde-637	280	14	can	can	AUX
ejde-637	280	15	be	be	AUX
ejde-637	280	16	obtained	obtain	VERB
ejde-637	280	17	directly	directly	ADV
ejde-637	280	18	.	.	PUNCT
ejde-637	281	1	□	□	PUNCT
ejde-637	281	2	before	before	SCONJ
ejde-637	281	3	we	we	PRON
ejde-637	281	4	give	give	VERB
ejde-637	281	5	the	the	DET
ejde-637	281	6	global	global	ADJ
ejde-637	281	7	qualitative	qualitative	ADJ
ejde-637	281	8	dynamics	dynamic	NOUN
ejde-637	281	9	of	of	ADP
ejde-637	281	10	system	system	NOUN
ejde-637	281	11	(	(	PUNCT
ejde-637	281	12	1.1	1.1	NUM
ejde-637	281	13	)	)	PUNCT
ejde-637	281	14	,	,	PUNCT
ejde-637	281	15	we	we	PRON
ejde-637	281	16	denote	denote	VERB
ejde-637	281	17	µ3	µ3	NOUN
ejde-637	281	18	:	:	PUNCT
ejde-637	281	19	=	=	SYM
ejde-637	281	20	x+	x+	SYM
ejde-637	282	1	e	e	X
ejde-637	282	2	+	+	CCONJ
ejde-637	282	3	a22	a22	PROPN
ejde-637	282	4	−	−	PROPN
ejde-637	282	5	a11	a11	PROPN
ejde-637	282	6	a21	a21	PROPN
ejde-637	282	7	y+e	y+e	PROPN
ejde-637	282	8	,	,	PUNCT
ejde-637	282	9	µ4	µ4	PROPN
ejde-637	282	10	:	:	PUNCT
ejde-637	282	11	=	=	SYM
ejde-637	282	12	x+	x+	SYM
ejde-637	282	13	e	e	X
ejde-637	282	14	+	+	CCONJ
ejde-637	282	15	a22(λ2	a22(λ2	PROPN
ejde-637	282	16	−	−	PROPN
ejde-637	282	17	a11)−	a11)−	ADJ
ejde-637	282	18	a12a21	a12a21	ADJ
ejde-637	282	19	a21(λ2	a21(λ2	PROPN
ejde-637	282	20	−	−	PROPN
ejde-637	282	21	a11	a11	PROPN
ejde-637	282	22	)	)	PUNCT
ejde-637	282	23	y+e	y+e	NOUN
ejde-637	282	24	,	,	PUNCT
ejde-637	282	25	µ5	µ5	PROPN
ejde-637	282	26	:	:	PUNCT
ejde-637	282	27	=	=	SYM
ejde-637	282	28	x+	x+	PUNCT
ejde-637	282	29	e	e	NOUN
ejde-637	282	30	−	−	NOUN
ejde-637	282	31	2a12	2a12	NUM
ejde-637	282	32	λ2	λ2	NOUN
ejde-637	282	33	−	−	PROPN
ejde-637	282	34	a11	a11	PROPN
ejde-637	282	35	y+e	y+e	NUM
ejde-637	282	36	,	,	PUNCT
ejde-637	282	37	µ6	µ6	NOUN
ejde-637	282	38	:	:	PUNCT
ejde-637	282	39	=	=	SYM
ejde-637	282	40	(	(	PUNCT
ejde-637	282	41	λ2	λ2	NOUN
ejde-637	282	42	−	−	NOUN
ejde-637	282	43	a11)x	a11)x	NOUN
ejde-637	282	44	+	+	CCONJ
ejde-637	282	45	e	e	NOUN
ejde-637	282	46	−	−	PROPN
ejde-637	282	47	2a12y	2a12y	NOUN
ejde-637	283	1	+	+	CCONJ
ejde-637	283	2	e	e	X
ejde-637	283	3	λ1	λ1	PROPN
ejde-637	283	4	−	−	PROPN
ejde-637	283	5	a11	a11	PROPN
ejde-637	283	6	,	,	PUNCT
ejde-637	283	7	µ7	µ7	PROPN
ejde-637	283	8	:	:	PUNCT
ejde-637	283	9	=	=	NOUN
ejde-637	283	10	−a11x	−a11x	NOUN
ejde-637	284	1	+	+	CCONJ
ejde-637	284	2	e	e	X
ejde-637	284	3	+	+	NOUN
ejde-637	284	4	2a12y	2a12y	NUM
ejde-637	285	1	+	+	CCONJ
ejde-637	285	2	e	e	X
ejde-637	285	3	λ1	λ1	PROPN
ejde-637	285	4	−	−	PROPN
ejde-637	285	5	a11	a11	PROPN
ejde-637	285	6	,	,	PUNCT
ejde-637	285	7	µ8	µ8	PROPN
ejde-637	285	8	:	:	PUNCT
ejde-637	285	9	=	=	SYM
ejde-637	285	10	2a12y	2a12y	NUM
ejde-637	286	1	+	+	CCONJ
ejde-637	286	2	e	e	X
ejde-637	286	3	−	−	PROPN
ejde-637	286	4	(	(	PUNCT
ejde-637	286	5	λ2	λ2	PROPN
ejde-637	286	6	−	−	PROPN
ejde-637	286	7	a11	a11	PROPN
ejde-637	286	8	)	)	PUNCT
ejde-637	286	9	a11	a11	PROPN
ejde-637	286	10	,	,	PUNCT
ejde-637	286	11	µ9	µ9	NOUN
ejde-637	286	12	:	:	PUNCT
ejde-637	286	13	=	=	SYM
ejde-637	287	1	−	−	PROPN
ejde-637	287	2	a12	a12	NOUN
ejde-637	287	3	λ1	λ1	PROPN
ejde-637	287	4	−	−	PROPN
ejde-637	287	5	a11	a11	PROPN
ejde-637	287	6	y+e	y+e	NUM
ejde-637	287	7	.	.	PUNCT
ejde-637	288	1	(	(	PUNCT
ejde-637	288	2	3.17	3.17	NUM
ejde-637	288	3	)	)	PUNCT
ejde-637	288	4	and	and	CCONJ
ejde-637	288	5	by	by	ADP
ejde-637	288	6	simple	simple	ADJ
ejde-637	288	7	computations	computation	NOUN
ejde-637	288	8	,	,	PUNCT
ejde-637	288	9	it	it	PRON
ejde-637	288	10	follows	follow	VERB
ejde-637	288	11	that	that	SCONJ
ejde-637	288	12	x−	x−	PROPN
ejde-637	288	13	e	e	PROPN
ejde-637	288	14	=	=	PROPN
ejde-637	288	15	µ3	µ3	PROPN
ejde-637	288	16	⇔	⇔	X
ejde-637	288	17	x+	x+	PROPN
ejde-637	288	18	m2	m2	PROPN
ejde-637	288	19	=	=	PROPN
ejde-637	288	20	x−	x−	PROPN
ejde-637	288	21	m1	m1	PROPN
ejde-637	288	22	,	,	PUNCT
ejde-637	288	23	x−	x−	PROPN
ejde-637	288	24	e	e	PROPN
ejde-637	288	25	=	=	PROPN
ejde-637	288	26	µ4	µ4	PROPN
ejde-637	288	27	⇔	⇔	PROPN
ejde-637	288	28	x+	x+	PROPN
ejde-637	288	29	m2	m2	PROPN
ejde-637	288	30	=	=	PROPN
ejde-637	288	31	x−	x−	PROPN
ejde-637	288	32	t	t	PROPN
ejde-637	288	33	,	,	PUNCT
ejde-637	288	34	x−	x−	PROPN
ejde-637	288	35	e	e	PROPN
ejde-637	288	36	=	=	PROPN
ejde-637	288	37	µ5	µ5	PROPN
ejde-637	288	38	⇔	⇔	PROPN
ejde-637	288	39	x+	x+	PROPN
ejde-637	288	40	m2	m2	PROPN
ejde-637	288	41	=	=	PROPN
ejde-637	288	42	x−	x−	PROPN
ejde-637	288	43	m2	m2	PROPN
ejde-637	288	44	,	,	PUNCT
ejde-637	289	1	x−	x−	PROPN
ejde-637	289	2	e	e	PROPN
ejde-637	289	3	=	=	PROPN
ejde-637	289	4	µ6	µ6	PROPN
ejde-637	289	5	⇔	⇔	PROPN
ejde-637	289	6	y−m1	y−m1	PROPN
ejde-637	289	7	=	=	SYM
ejde-637	289	8	y+m2	y+m2	PROPN
ejde-637	289	9	,	,	PUNCT
ejde-637	289	10	x−	x−	PROPN
ejde-637	289	11	e	e	PROPN
ejde-637	289	12	=	=	PROPN
ejde-637	289	13	µ7	µ7	PROPN
ejde-637	289	14	⇔	⇔	PROPN
ejde-637	289	15	y−m1	y−m1	X
ejde-637	289	16	=	=	SYM
ejde-637	289	17	y+t	y+t	PROPN
ejde-637	289	18	,	,	PUNCT
ejde-637	290	1	x−	x−	PROPN
ejde-637	290	2	e	e	PROPN
ejde-637	290	3	=	=	PROPN
ejde-637	290	4	µ8	µ8	PROPN
ejde-637	290	5	⇔	⇔	PROPN
ejde-637	290	6	y−t	y−t	PROPN
ejde-637	290	7	=	=	SYM
ejde-637	290	8	y+m2	y+m2	PROPN
ejde-637	290	9	,	,	PUNCT
ejde-637	290	10	x−	x−	PROPN
ejde-637	290	11	e	e	NOUN
ejde-637	290	12	=	=	PROPN
ejde-637	290	13	µ9	µ9	PROPN
ejde-637	290	14	⇔	⇔	NOUN
ejde-637	290	15	y−m1	y−m1	X
ejde-637	290	16	=	=	SYM
ejde-637	290	17	0	0	PROPN
ejde-637	290	18	.	.	PUNCT
ejde-637	291	1	(	(	PUNCT
ejde-637	291	2	3.18	3.18	NUM
ejde-637	291	3	)	)	PUNCT
ejde-637	291	4	ejde-2024/57	ejde-2024/57	NOUN
ejde-637	291	5	planar	planar	ADJ
ejde-637	291	6	sector	sector	NOUN
ejde-637	291	7	-	-	PUNCT
ejde-637	291	8	wise	wise	ADJ
ejde-637	291	9	linear	linear	ADJ
ejde-637	291	10	systems	system	NOUN
ejde-637	291	11	11	11	NUM
ejde-637	291	12	secondly	secondly	ADV
ejde-637	291	13	,	,	PUNCT
ejde-637	291	14	to	to	PART
ejde-637	291	15	make	make	VERB
ejde-637	291	16	our	our	PRON
ejde-637	291	17	analysis	analysis	NOUN
ejde-637	291	18	of	of	ADP
ejde-637	291	19	the	the	DET
ejde-637	291	20	dynamics	dynamic	NOUN
ejde-637	291	21	more	more	ADV
ejde-637	291	22	concrete	concrete	ADJ
ejde-637	291	23	,	,	PUNCT
ejde-637	291	24	without	without	ADP
ejde-637	291	25	loss	loss	NOUN
ejde-637	291	26	of	of	ADP
ejde-637	291	27	generality	generality	NOUN
ejde-637	291	28	,	,	PUNCT
ejde-637	291	29	we	we	PRON
ejde-637	291	30	assume	assume	VERB
ejde-637	291	31	that	that	SCONJ
ejde-637	291	32	x+	x+	PROPN
ejde-637	291	33	m1	m1	PROPN
ejde-637	291	34	>	>	X
ejde-637	291	35	0	0	NUM
ejde-637	292	1	⇔	⇔	X
ejde-637	292	2	0	0	PUNCT
ejde-637	292	3	<	<	X
ejde-637	292	4	y+e	y+e	NUM
ejde-637	292	5	<	<	X
ejde-637	292	6	λ1	λ1	PROPN
ejde-637	292	7	−	−	PROPN
ejde-637	292	8	a11	a11	PROPN
ejde-637	292	9	a12	a12	NOUN
ejde-637	292	10	x+	x+	PROPN
ejde-637	292	11	e	e	X
ejde-637	292	12	.	.	PUNCT
ejde-637	293	1	(	(	PUNCT
ejde-637	293	2	3.19	3.19	NUM
ejde-637	293	3	)	)	PUNCT
ejde-637	293	4	since	since	SCONJ
ejde-637	293	5	the	the	DET
ejde-637	293	6	discussion	discussion	NOUN
ejde-637	293	7	with	with	ADP
ejde-637	293	8	x+	x+	ADJ
ejde-637	293	9	m1	m1	PROPN
ejde-637	293	10	≤	≤	NOUN
ejde-637	293	11	0	0	NUM
ejde-637	293	12	is	be	AUX
ejde-637	293	13	similar	similar	ADJ
ejde-637	293	14	,	,	PUNCT
ejde-637	293	15	so	so	ADV
ejde-637	293	16	we	we	PRON
ejde-637	293	17	omit	omit	VERB
ejde-637	293	18	it	it	PRON
ejde-637	293	19	.	.	PUNCT
ejde-637	294	1	theorem	theorem	VERB
ejde-637	294	2	3.4	3.4	NUM
ejde-637	294	3	.	.	PUNCT
ejde-637	295	1	suppose	suppose	VERB
ejde-637	295	2	that	that	SCONJ
ejde-637	295	3	condition	condition	NOUN
ejde-637	295	4	(	(	PUNCT
ejde-637	295	5	3.1	3.1	NUM
ejde-637	295	6	)	)	PUNCT
ejde-637	295	7	holds	hold	NOUN
ejde-637	295	8	and	and	CCONJ
ejde-637	295	9	a	a	DET
ejde-637	295	10	∈	∈	PROPN
ejde-637	295	11	ω1	ω1	PROPN
ejde-637	295	12	∪	∪	X
ejde-637	295	13	ω2	ω2	PROPN
ejde-637	295	14	.	.	PUNCT
ejde-637	296	1	we	we	PRON
ejde-637	296	2	have	have	VERB
ejde-637	296	3	max{2µ1	max{2µ1	PROPN
ejde-637	296	4	+	+	CCONJ
ejde-637	296	5	x+	x+	PROPN
ejde-637	296	6	e	e	X
ejde-637	296	7	,	,	PUNCT
ejde-637	296	8	µ3	µ3	NUM
ejde-637	296	9	}	}	PUNCT
ejde-637	296	10	<	<	X
ejde-637	296	11	µ4	µ4	PROPN
ejde-637	296	12	<	<	X
ejde-637	296	13	µ5	µ5	PROPN
ejde-637	296	14	and	and	CCONJ
ejde-637	296	15	the	the	DET
ejde-637	296	16	following	following	ADJ
ejde-637	296	17	statements	statement	NOUN
ejde-637	296	18	hold	hold	VERB
ejde-637	296	19	.	.	PUNCT
ejde-637	297	1	(	(	PUNCT
ejde-637	297	2	a	a	X
ejde-637	297	3	)	)	PUNCT
ejde-637	297	4	when	when	SCONJ
ejde-637	297	5	x−	x−	PROPN
ejde-637	297	6	e	e	PROPN
ejde-637	297	7	=	=	NOUN
ejde-637	297	8	µ3	µ3	NUM
ejde-637	297	9	,	,	PUNCT
ejde-637	297	10	there	there	PRON
ejde-637	297	11	exists	exist	VERB
ejde-637	297	12	one	one	NUM
ejde-637	297	13	heteroclinic	heteroclinic	ADJ
ejde-637	297	14	cycle	cycle	NOUN
ejde-637	297	15	;	;	PUNCT
ejde-637	297	16	(	(	PUNCT
ejde-637	297	17	b	b	X
ejde-637	297	18	)	)	PUNCT
ejde-637	297	19	when	when	SCONJ
ejde-637	297	20	min{2µ1+x+	min{2µ1+x+	PROPN
ejde-637	297	21	e	e	PROPN
ejde-637	297	22	,	,	PUNCT
ejde-637	297	23	µ3	µ3	NUM
ejde-637	297	24	}	}	PUNCT
ejde-637	297	25	<	<	X
ejde-637	297	26	x−	x−	PROPN
ejde-637	297	27	e	e	PROPN
ejde-637	297	28	<	<	X
ejde-637	297	29	max{2µ1+x+	max{2µ1+x+	PROPN
ejde-637	297	30	e	e	NOUN
ejde-637	297	31	,	,	PUNCT
ejde-637	297	32	µ3	µ3	PROPN
ejde-637	297	33	}	}	PUNCT
ejde-637	297	34	,	,	PUNCT
ejde-637	297	35	there	there	PRON
ejde-637	297	36	exists	exist	VERB
ejde-637	297	37	one	one	NUM
ejde-637	297	38	limit	limit	NOUN
ejde-637	297	39	cycle	cycle	NOUN
ejde-637	297	40	,	,	PUNCT
ejde-637	297	41	which	which	PRON
ejde-637	297	42	is	be	AUX
ejde-637	297	43	repulsive	repulsive	ADJ
ejde-637	297	44	(	(	PUNCT
ejde-637	297	45	attractive	attractive	ADJ
ejde-637	297	46	)	)	PUNCT
ejde-637	297	47	if	if	SCONJ
ejde-637	297	48	µ3	µ3	NOUN
ejde-637	297	49	<	<	X
ejde-637	297	50	2µ1	2µ1	NUM
ejde-637	298	1	+	+	CCONJ
ejde-637	298	2	x+	x+	ADJ
ejde-637	298	3	e	e	X
ejde-637	298	4	(	(	PUNCT
ejde-637	298	5	µ3	µ3	NOUN
ejde-637	298	6	>	>	X
ejde-637	298	7	2µ1	2µ1	NUM
ejde-637	298	8	+	+	CCONJ
ejde-637	298	9	x+	x+	ADJ
ejde-637	298	10	e	e	NOUN
ejde-637	298	11	)	)	PUNCT
ejde-637	298	12	;	;	PUNCT
ejde-637	298	13	(	(	PUNCT
ejde-637	298	14	c	c	X
ejde-637	298	15	)	)	PUNCT
ejde-637	298	16	when	when	SCONJ
ejde-637	298	17	x−	x−	PROPN
ejde-637	298	18	e	e	PROPN
ejde-637	298	19	=	=	PROPN
ejde-637	298	20	µ4	µ4	PROPN
ejde-637	298	21	and	and	CCONJ
ejde-637	298	22	x−	x−	PROPN
ejde-637	298	23	e	e	PROPN
ejde-637	298	24	=	=	PROPN
ejde-637	298	25	µ5	µ5	PROPN
ejde-637	298	26	,	,	PUNCT
ejde-637	298	27	there	there	PRON
ejde-637	298	28	both	both	PRON
ejde-637	298	29	exist	exist	VERB
ejde-637	298	30	two	two	NUM
ejde-637	298	31	sliding	slide	VERB
ejde-637	298	32	heteroclinic	heteroclinic	ADJ
ejde-637	298	33	orbits	orbit	NOUN
ejde-637	298	34	.	.	PUNCT
ejde-637	299	1	theorem	theorem	VERB
ejde-637	299	2	3.5	3.5	NUM
ejde-637	299	3	.	.	PUNCT
ejde-637	300	1	suppose	suppose	VERB
ejde-637	300	2	that	that	SCONJ
ejde-637	300	3	condition	condition	NOUN
ejde-637	300	4	(	(	PUNCT
ejde-637	300	5	3.1	3.1	NUM
ejde-637	300	6	)	)	PUNCT
ejde-637	300	7	holds	hold	NOUN
ejde-637	300	8	and	and	CCONJ
ejde-637	300	9	a	a	DET
ejde-637	300	10	∈	∈	PROPN
ejde-637	300	11	ω1	ω1	PROPN
ejde-637	300	12	,	,	PUNCT
ejde-637	300	13	the	the	DET
ejde-637	300	14	following	following	ADJ
ejde-637	300	15	statements	statement	NOUN
ejde-637	300	16	are	be	AUX
ejde-637	300	17	true	true	ADJ
ejde-637	300	18	.	.	PUNCT
ejde-637	301	1	(	(	PUNCT
ejde-637	301	2	a	a	X
ejde-637	301	3	)	)	PUNCT
ejde-637	301	4	when	when	SCONJ
ejde-637	301	5	a11	a11	PROPN
ejde-637	301	6	>	>	X
ejde-637	301	7	0	0	PROPN
ejde-637	301	8	,	,	PUNCT
ejde-637	301	9	we	we	PRON
ejde-637	301	10	have	have	VERB
ejde-637	301	11	µ6	µ6	PROPN
ejde-637	301	12	<	<	X
ejde-637	301	13	µ7	µ7	PROPN
ejde-637	301	14	<	<	X
ejde-637	301	15	0	0	PUNCT
ejde-637	301	16	<	<	X
ejde-637	301	17	µ1	µ1	PROPN
ejde-637	301	18	<	<	X
ejde-637	301	19	µ3	µ3	PROPN
ejde-637	301	20	<	<	X
ejde-637	301	21	2µ1	2µ1	NUM
ejde-637	301	22	+	+	CCONJ
ejde-637	301	23	x+	x+	ADJ
ejde-637	301	24	e	e	X
ejde-637	301	25	<	<	X
ejde-637	301	26	µ4	µ4	PROPN
ejde-637	301	27	<	<	X
ejde-637	301	28	µ5	µ5	PROPN
ejde-637	301	29	and	and	CCONJ
ejde-637	301	30	the	the	DET
ejde-637	301	31	following	following	ADJ
ejde-637	301	32	statements	statement	NOUN
ejde-637	301	33	hold	hold	VERB
ejde-637	301	34	.	.	PUNCT
ejde-637	302	1	(	(	PUNCT
ejde-637	302	2	a1	a1	NOUN
ejde-637	302	3	)	)	PUNCT
ejde-637	302	4	when	when	SCONJ
ejde-637	302	5	x−	x−	PROPN
ejde-637	302	6	e	e	PROPN
ejde-637	302	7	<	<	X
ejde-637	302	8	min{−x+	min{−x+	PROPN
ejde-637	302	9	e	e	NOUN
ejde-637	302	10	,	,	PUNCT
ejde-637	302	11	µ6	µ6	PROPN
ejde-637	302	12	}	}	PUNCT
ejde-637	302	13	,	,	PUNCT
ejde-637	302	14	there	there	PRON
ejde-637	302	15	exists	exist	VERB
ejde-637	302	16	one	one	NUM
ejde-637	302	17	sliding	slide	VERB
ejde-637	302	18	heteroclinic	heteroclinic	ADJ
ejde-637	302	19	orbit	orbit	NOUN
ejde-637	302	20	;	;	PUNCT
ejde-637	302	21	(	(	PUNCT
ejde-637	302	22	a2	a2	PROPN
ejde-637	302	23	)	)	PUNCT
ejde-637	302	24	when	when	SCONJ
ejde-637	302	25	x−	x−	PROPN
ejde-637	302	26	e	e	PROPN
ejde-637	302	27	=	=	PROPN
ejde-637	302	28	µ6	µ6	PROPN
ejde-637	302	29	,	,	PUNCT
ejde-637	302	30	there	there	PRON
ejde-637	302	31	exist	exist	VERB
ejde-637	302	32	one	one	NUM
ejde-637	302	33	heteroclinic	heteroclinic	ADJ
ejde-637	302	34	orbit	orbit	NOUN
ejde-637	302	35	and	and	CCONJ
ejde-637	302	36	one	one	NUM
ejde-637	302	37	sliding	slide	VERB
ejde-637	302	38	heteroclinic	heteroclinic	ADJ
ejde-637	302	39	orbit	orbit	NOUN
ejde-637	302	40	;	;	PUNCT
ejde-637	302	41	(	(	PUNCT
ejde-637	302	42	a3	a3	NOUN
ejde-637	302	43	)	)	PUNCT
ejde-637	303	1	when	when	SCONJ
ejde-637	303	2	x−	x−	PROPN
ejde-637	303	3	e	e	PROPN
ejde-637	303	4	=	=	PUNCT
ejde-637	303	5	−x+	−x+	X
ejde-637	303	6	e	e	NOUN
ejde-637	303	7	,	,	PUNCT
ejde-637	303	8	if	if	SCONJ
ejde-637	303	9	x	x	PRON
ejde-637	303	10	−	−	X
ejde-637	303	11	e	e	X
ejde-637	303	12	<	<	X
ejde-637	303	13	µ6	µ6	PROPN
ejde-637	303	14	,	,	PUNCT
ejde-637	303	15	there	there	PRON
ejde-637	303	16	exists	exist	VERB
ejde-637	303	17	one	one	NUM
ejde-637	303	18	sliding	slide	VERB
ejde-637	303	19	heteroclinic	heteroclinic	ADJ
ejde-637	303	20	orbit	orbit	NOUN
ejde-637	303	21	;	;	PUNCT
ejde-637	303	22	or	or	CCONJ
ejde-637	303	23	there	there	PRON
ejde-637	303	24	exist	exist	VERB
ejde-637	303	25	two	two	NUM
ejde-637	303	26	sliding	slide	VERB
ejde-637	303	27	heteroclinic	heteroclinic	ADJ
ejde-637	303	28	orbits	orbit	NOUN
ejde-637	303	29	;	;	PUNCT
ejde-637	303	30	(	(	PUNCT
ejde-637	303	31	a4	a4	NOUN
ejde-637	303	32	)	)	PUNCT
ejde-637	303	33	when	when	SCONJ
ejde-637	303	34	min{−x+	min{−x+	NOUN
ejde-637	303	35	e	e	NOUN
ejde-637	303	36	,	,	PUNCT
ejde-637	303	37	µ6	µ6	PROPN
ejde-637	303	38	}	}	PUNCT
ejde-637	303	39	<	<	X
ejde-637	303	40	x−	x−	PROPN
ejde-637	303	41	e	e	X
ejde-637	303	42	<	<	X
ejde-637	303	43	µ3	µ3	NOUN
ejde-637	303	44	,	,	PUNCT
ejde-637	303	45	there	there	PRON
ejde-637	303	46	exist	exist	VERB
ejde-637	303	47	two	two	NUM
ejde-637	303	48	sliding	slide	VERB
ejde-637	303	49	heteroclinic	heteroclinic	ADJ
ejde-637	303	50	orbits	orbit	NOUN
ejde-637	303	51	.	.	PUNCT
ejde-637	304	1	(	(	PUNCT
ejde-637	304	2	b	b	X
ejde-637	304	3	)	)	PUNCT
ejde-637	304	4	when	when	SCONJ
ejde-637	304	5	a11	a11	PROPN
ejde-637	304	6	<	<	X
ejde-637	304	7	0	0	PROPN
ejde-637	304	8	,	,	PUNCT
ejde-637	304	9	we	we	PRON
ejde-637	304	10	have	have	VERB
ejde-637	304	11	−x+	−x+	NOUN
ejde-637	304	12	e	e	NOUN
ejde-637	304	13	<	<	X
ejde-637	304	14	0	0	PUNCT
ejde-637	304	15	<	<	X
ejde-637	304	16	µ9	µ9	PROPN
ejde-637	304	17	<	<	X
ejde-637	304	18	min{2µ1	min{2µ1	NOUN
ejde-637	304	19	+	+	CCONJ
ejde-637	304	20	x+	x+	PROPN
ejde-637	304	21	e	e	X
ejde-637	304	22	,	,	PUNCT
ejde-637	304	23	µ3	µ3	NUM
ejde-637	304	24	}	}	PUNCT
ejde-637	304	25	<	<	X
ejde-637	304	26	max{2µ1	max{2µ1	PROPN
ejde-637	304	27	+	+	CCONJ
ejde-637	304	28	x+	x+	PROPN
ejde-637	304	29	e	e	X
ejde-637	304	30	,	,	PUNCT
ejde-637	304	31	µ3	µ3	NUM
ejde-637	304	32	}	}	PUNCT
ejde-637	304	33	<	<	X
ejde-637	304	34	µ4	µ4	PROPN
ejde-637	304	35	<	<	X
ejde-637	304	36	µ5	µ5	PROPN
ejde-637	304	37	and	and	CCONJ
ejde-637	304	38	the	the	DET
ejde-637	304	39	following	following	ADJ
ejde-637	304	40	statements	statement	NOUN
ejde-637	304	41	.	.	PUNCT
ejde-637	305	1	(	(	PUNCT
ejde-637	305	2	b1	b1	NOUN
ejde-637	305	3	)	)	PUNCT
ejde-637	305	4	when	when	SCONJ
ejde-637	305	5	x−	x−	PROPN
ejde-637	305	6	e	e	PROPN
ejde-637	305	7	<	<	X
ejde-637	305	8	−x+	−x+	X
ejde-637	305	9	e	e	NOUN
ejde-637	305	10	,	,	PUNCT
ejde-637	305	11	there	there	PRON
ejde-637	305	12	exists	exist	VERB
ejde-637	305	13	one	one	NUM
ejde-637	305	14	sliding	slide	VERB
ejde-637	305	15	orbit	orbit	NOUN
ejde-637	305	16	containing	contain	VERB
ejde-637	305	17	pey	pey	NOUN
ejde-637	305	18	,	,	PUNCT
ejde-637	305	19	p0	p0	NOUN
ejde-637	305	20	and	and	CCONJ
ejde-637	305	21	x+	x+	ADJ
ejde-637	305	22	e	e	X
ejde-637	305	23	;	;	PUNCT
ejde-637	305	24	(	(	PUNCT
ejde-637	305	25	b2	b2	NOUN
ejde-637	305	26	)	)	PUNCT
ejde-637	305	27	when	when	SCONJ
ejde-637	305	28	−x+	−x+	X
ejde-637	305	29	e	e	NOUN
ejde-637	305	30	≤	≤	NUM
ejde-637	305	31	x−	x−	PROPN
ejde-637	306	1	e	e	PROPN
ejde-637	306	2	<	<	X
ejde-637	306	3	µ9	µ9	PROPN
ejde-637	306	4	,	,	PUNCT
ejde-637	306	5	there	there	PRON
ejde-637	306	6	exists	exist	VERB
ejde-637	306	7	one	one	NUM
ejde-637	306	8	sliding	slide	VERB
ejde-637	306	9	heteroclinic	heteroclinic	ADJ
ejde-637	306	10	orbit	orbit	NOUN
ejde-637	306	11	;	;	PUNCT
ejde-637	306	12	(	(	PUNCT
ejde-637	306	13	b3	b3	PROPN
ejde-637	306	14	)	)	PUNCT
ejde-637	306	15	when	when	SCONJ
ejde-637	306	16	µ9	µ9	PROPN
ejde-637	306	17	≤	≤	X
ejde-637	306	18	x−	x−	PROPN
ejde-637	306	19	e	e	PROPN
ejde-637	306	20	<	<	X
ejde-637	306	21	min{2µ1	min{2µ1	PROPN
ejde-637	306	22	+	+	CCONJ
ejde-637	306	23	x+	x+	PROPN
ejde-637	306	24	e	e	X
ejde-637	306	25	,	,	PUNCT
ejde-637	306	26	µ3	µ3	PROPN
ejde-637	306	27	}	}	PUNCT
ejde-637	306	28	,	,	PUNCT
ejde-637	306	29	there	there	PRON
ejde-637	306	30	exist	exist	VERB
ejde-637	306	31	two	two	NUM
ejde-637	306	32	sliding	slide	VERB
ejde-637	306	33	heteroclinic	heteroclinic	ADJ
ejde-637	306	34	orbits	orbit	NOUN
ejde-637	306	35	.	.	PUNCT
ejde-637	307	1	theorem	theorem	VERB
ejde-637	307	2	3.6	3.6	NUM
ejde-637	307	3	.	.	PUNCT
ejde-637	308	1	suppose	suppose	VERB
ejde-637	308	2	that	that	SCONJ
ejde-637	308	3	condition	condition	NOUN
ejde-637	308	4	(	(	PUNCT
ejde-637	308	5	3.1	3.1	NUM
ejde-637	308	6	)	)	PUNCT
ejde-637	308	7	holds	hold	NOUN
ejde-637	308	8	and	and	CCONJ
ejde-637	308	9	a	a	DET
ejde-637	308	10	∈	∈	PROPN
ejde-637	308	11	ω2	ω2	NOUN
ejde-637	308	12	,	,	PUNCT
ejde-637	308	13	the	the	DET
ejde-637	308	14	following	following	ADJ
ejde-637	308	15	statements	statement	NOUN
ejde-637	308	16	are	be	AUX
ejde-637	308	17	true	true	ADJ
ejde-637	308	18	.	.	PUNCT
ejde-637	309	1	(	(	PUNCT
ejde-637	309	2	a	a	X
ejde-637	309	3	)	)	PUNCT
ejde-637	309	4	when	when	SCONJ
ejde-637	309	5	a11	a11	PROPN
ejde-637	309	6	<	<	X
ejde-637	309	7	0	0	PROPN
ejde-637	309	8	and	and	CCONJ
ejde-637	309	9	0	0	NUM
ejde-637	309	10	<	<	X
ejde-637	309	11	y+e	y+e	NUM
ejde-637	309	12	<	<	X
ejde-637	309	13	−a11	−a11	PROPN
ejde-637	309	14	a12	a12	NOUN
ejde-637	309	15	x+	x+	PROPN
ejde-637	310	1	e	e	X
ejde-637	310	2	,	,	PUNCT
ejde-637	310	3	we	we	PRON
ejde-637	310	4	have	have	VERB
ejde-637	310	5	µ8	µ8	PROPN
ejde-637	310	6	<	<	X
ejde-637	310	7	min{µ6	min{µ6	NUM
ejde-637	310	8	,	,	PUNCT
ejde-637	310	9	µ2	µ2	ADJ
ejde-637	310	10	}	}	PUNCT
ejde-637	310	11	<	<	X
ejde-637	310	12	0	0	PUNCT
ejde-637	310	13	<	<	X
ejde-637	310	14	µ1	µ1	PROPN
ejde-637	310	15	<	<	X
ejde-637	310	16	max{2µ1	max{2µ1	PROPN
ejde-637	310	17	+	+	CCONJ
ejde-637	310	18	x+	x+	PROPN
ejde-637	310	19	e	e	X
ejde-637	310	20	,	,	PUNCT
ejde-637	310	21	µ3	µ3	NUM
ejde-637	310	22	}	}	PUNCT
ejde-637	310	23	<	<	X
ejde-637	310	24	µ4	µ4	PROPN
ejde-637	310	25	<	<	X
ejde-637	310	26	µ5	µ5	PROPN
ejde-637	310	27	and	and	CCONJ
ejde-637	310	28	the	the	DET
ejde-637	310	29	following	following	ADJ
ejde-637	310	30	statements	statement	NOUN
ejde-637	310	31	hold	hold	VERB
ejde-637	310	32	.	.	PUNCT
ejde-637	311	1	(	(	PUNCT
ejde-637	311	2	a1	a1	NOUN
ejde-637	311	3	)	)	PUNCT
ejde-637	311	4	when	when	SCONJ
ejde-637	311	5	x−	x−	PROPN
ejde-637	311	6	e	e	PROPN
ejde-637	311	7	<	<	X
ejde-637	311	8	min{µ8,−x+	min{µ8,−x+	X
ejde-637	311	9	e	e	NOUN
ejde-637	311	10	}	}	PUNCT
ejde-637	311	11	,	,	PUNCT
ejde-637	311	12	there	there	PRON
ejde-637	311	13	exists	exist	VERB
ejde-637	311	14	one	one	NUM
ejde-637	311	15	sliding	slide	VERB
ejde-637	311	16	orbit	orbit	NOUN
ejde-637	311	17	containing	contain	VERB
ejde-637	311	18	x+	x+	ADJ
ejde-637	311	19	e	e	PROPN
ejde-637	311	20	,	,	PUNCT
ejde-637	311	21	p0	p0	NOUN
ejde-637	311	22	and	and	CCONJ
ejde-637	311	23	pey	pey	NOUN
ejde-637	311	24	;	;	PUNCT
ejde-637	311	25	(	(	PUNCT
ejde-637	311	26	a2	a2	PROPN
ejde-637	311	27	)	)	PUNCT
ejde-637	311	28	when	when	SCONJ
ejde-637	311	29	x−	x−	PROPN
ejde-637	311	30	e	e	PROPN
ejde-637	311	31	=	=	PROPN
ejde-637	311	32	µ8	µ8	PROPN
ejde-637	311	33	,	,	PUNCT
ejde-637	311	34	there	there	PRON
ejde-637	311	35	exists	exist	VERB
ejde-637	311	36	one	one	NUM
ejde-637	311	37	sliding	slide	VERB
ejde-637	311	38	cycle	cycle	NOUN
ejde-637	311	39	;	;	PUNCT
ejde-637	311	40	(	(	PUNCT
ejde-637	311	41	a3	a3	NOUN
ejde-637	311	42	)	)	PUNCT
ejde-637	311	43	when	when	SCONJ
ejde-637	311	44	x−	x−	PROPN
ejde-637	311	45	e	e	PROPN
ejde-637	311	46	=	=	PROPN
ejde-637	311	47	µ6	µ6	PROPN
ejde-637	311	48	,	,	PUNCT
ejde-637	311	49	there	there	PRON
ejde-637	311	50	exists	exist	VERB
ejde-637	311	51	one	one	NUM
ejde-637	311	52	sliding	slide	VERB
ejde-637	311	53	heteroclinic	heteroclinic	ADJ
ejde-637	311	54	orbit	orbit	NOUN
ejde-637	311	55	;	;	PUNCT
ejde-637	311	56	(	(	PUNCT
ejde-637	311	57	a4	a4	INTJ
ejde-637	311	58	)	)	PUNCT
ejde-637	311	59	if	if	SCONJ
ejde-637	311	60	µ8	µ8	PROPN
ejde-637	311	61	<	<	X
ejde-637	311	62	−x+	−x+	X
ejde-637	311	63	e	e	NOUN
ejde-637	311	64	,	,	PUNCT
ejde-637	311	65	we	we	PRON
ejde-637	311	66	obtain	obtain	VERB
ejde-637	311	67	(	(	PUNCT
ejde-637	311	68	a41	a41	NOUN
ejde-637	311	69	)	)	PUNCT
ejde-637	311	70	when	when	SCONJ
ejde-637	311	71	µ8	µ8	PROPN
ejde-637	311	72	<	<	X
ejde-637	311	73	x−	x−	PROPN
ejde-637	311	74	e	e	X
ejde-637	311	75	<	<	X
ejde-637	311	76	−x+	−x+	X
ejde-637	311	77	e	e	NOUN
ejde-637	311	78	,	,	PUNCT
ejde-637	311	79	there	there	PRON
ejde-637	311	80	exists	exist	VERB
ejde-637	311	81	one	one	NUM
ejde-637	311	82	sliding	slide	VERB
ejde-637	311	83	cycle	cycle	NOUN
ejde-637	311	84	;	;	PUNCT
ejde-637	311	85	(	(	PUNCT
ejde-637	311	86	a42	a42	NOUN
ejde-637	311	87	)	)	PUNCT
ejde-637	311	88	when	when	SCONJ
ejde-637	311	89	x−	x−	PROPN
ejde-637	311	90	e	e	PROPN
ejde-637	311	91	=	=	PUNCT
ejde-637	311	92	−x+	−x+	NOUN
ejde-637	311	93	e	e	NOUN
ejde-637	311	94	,	,	PUNCT
ejde-637	311	95	there	there	PRON
ejde-637	311	96	exist	exist	VERB
ejde-637	311	97	one	one	NUM
ejde-637	311	98	sliding	slide	VERB
ejde-637	311	99	homoclinic	homoclinic	ADJ
ejde-637	311	100	cycle	cycle	NOUN
ejde-637	311	101	and	and	CCONJ
ejde-637	311	102	one	one	NUM
ejde-637	311	103	sliding	slide	VERB
ejde-637	311	104	heteroclinic	heteroclinic	ADJ
ejde-637	311	105	orbit	orbit	NOUN
ejde-637	311	106	;	;	PUNCT
ejde-637	311	107	12	12	NUM
ejde-637	311	108	q.-q	q.-q	PROPN
ejde-637	311	109	.	.	PUNCT
ejde-637	312	1	han	han	PROPN
ejde-637	312	2	,	,	PUNCT
ejde-637	312	3	s.-m	s.-m	PROPN
ejde-637	312	4	.	.	PUNCT
ejde-637	313	1	huan	huan	PROPN
ejde-637	313	2	ejde-2024/57	ejde-2024/57	PROPN
ejde-637	313	3	(	(	PUNCT
ejde-637	313	4	a5	a5	PROPN
ejde-637	313	5	)	)	PUNCT
ejde-637	313	6	when	when	SCONJ
ejde-637	313	7	min{−x+	min{−x+	NOUN
ejde-637	313	8	e	e	NOUN
ejde-637	313	9	,	,	PUNCT
ejde-637	313	10	µ6	µ6	PROPN
ejde-637	313	11	,	,	PUNCT
ejde-637	313	12	µ2	µ2	PROPN
ejde-637	313	13	}	}	PUNCT
ejde-637	313	14	<	<	X
ejde-637	313	15	x−	x−	PROPN
ejde-637	313	16	e	e	X
ejde-637	313	17	<	<	X
ejde-637	313	18	min{2µ1+x+	min{2µ1+x+	PROPN
ejde-637	313	19	e	e	NOUN
ejde-637	313	20	,	,	PUNCT
ejde-637	313	21	µ3	µ3	PROPN
ejde-637	313	22	}	}	PUNCT
ejde-637	313	23	,	,	PUNCT
ejde-637	313	24	there	there	PRON
ejde-637	313	25	exist	exist	VERB
ejde-637	313	26	two	two	NUM
ejde-637	313	27	sliding	slide	VERB
ejde-637	313	28	heteroclinic	heteroclinic	ADJ
ejde-637	313	29	orbits	orbit	NOUN
ejde-637	313	30	and	and	CCONJ
ejde-637	313	31	at	at	ADP
ejde-637	313	32	most	most	ADV
ejde-637	313	33	one	one	NUM
ejde-637	313	34	sliding	slide	VERB
ejde-637	313	35	cycle	cycle	NOUN
ejde-637	313	36	.	.	PUNCT
ejde-637	314	1	(	(	PUNCT
ejde-637	314	2	b	b	X
ejde-637	314	3	)	)	PUNCT
ejde-637	314	4	when	when	SCONJ
ejde-637	314	5	a11	a11	PROPN
ejde-637	314	6	<	<	X
ejde-637	314	7	0	0	PROPN
ejde-637	314	8	and	and	CCONJ
ejde-637	314	9	−a11	−a11	PROPN
ejde-637	314	10	a12	a12	NOUN
ejde-637	314	11	x+	x+	PUNCT
ejde-637	314	12	e	e	X
ejde-637	314	13	<	<	X
ejde-637	314	14	y+e	y+e	NUM
ejde-637	314	15	<	<	X
ejde-637	314	16	λ1−a11	λ1−a11	PROPN
ejde-637	314	17	a12	a12	X
ejde-637	314	18	x+	x+	PROPN
ejde-637	314	19	e	e	X
ejde-637	314	20	,	,	PUNCT
ejde-637	314	21	we	we	PRON
ejde-637	314	22	have	have	VERB
ejde-637	314	23	µ8	µ8	PROPN
ejde-637	314	24	<	<	X
ejde-637	314	25	µ6	µ6	PROPN
ejde-637	314	26	<	<	X
ejde-637	314	27	µ7	µ7	PROPN
ejde-637	314	28	,	,	PUNCT
ejde-637	314	29	µ8	µ8	NOUN
ejde-637	314	30	<	<	X
ejde-637	314	31	2µ2	2µ2	NUM
ejde-637	315	1	+	+	CCONJ
ejde-637	315	2	x+	x+	ADJ
ejde-637	315	3	e	e	X
ejde-637	315	4	<	<	X
ejde-637	315	5	µ2	µ2	PROPN
ejde-637	315	6	<	<	X
ejde-637	315	7	−x+	−x+	X
ejde-637	315	8	e	e	X
ejde-637	315	9	<	<	X
ejde-637	315	10	0	0	PUNCT
ejde-637	315	11	<	<	X
ejde-637	315	12	max{2µ1	max{2µ1	PROPN
ejde-637	315	13	+	+	CCONJ
ejde-637	315	14	x+	x+	PROPN
ejde-637	315	15	e	e	X
ejde-637	315	16	,	,	PUNCT
ejde-637	315	17	µ3	µ3	NUM
ejde-637	315	18	}	}	PUNCT
ejde-637	315	19	<	<	X
ejde-637	315	20	µ4	µ4	PROPN
ejde-637	315	21	<	<	X
ejde-637	315	22	µ5	µ5	PROPN
ejde-637	315	23	and	and	CCONJ
ejde-637	315	24	the	the	DET
ejde-637	315	25	following	following	ADJ
ejde-637	315	26	statements	statement	NOUN
ejde-637	315	27	hold	hold	VERB
ejde-637	315	28	.	.	PUNCT
ejde-637	316	1	(	(	PUNCT
ejde-637	316	2	b1	b1	NOUN
ejde-637	316	3	)	)	PUNCT
ejde-637	317	1	when	when	SCONJ
ejde-637	317	2	x−	x−	PROPN
ejde-637	317	3	e	e	PROPN
ejde-637	317	4	=	=	PROPN
ejde-637	317	5	µ8	µ8	PROPN
ejde-637	317	6	,	,	PUNCT
ejde-637	317	7	there	there	PRON
ejde-637	317	8	exists	exist	VERB
ejde-637	317	9	one	one	NUM
ejde-637	317	10	sliding	slide	VERB
ejde-637	317	11	heteroclinic	heteroclinic	ADJ
ejde-637	317	12	orbit	orbit	NOUN
ejde-637	317	13	;	;	PUNCT
ejde-637	317	14	(	(	PUNCT
ejde-637	317	15	b2	b2	NOUN
ejde-637	317	16	)	)	PUNCT
ejde-637	317	17	when	when	SCONJ
ejde-637	317	18	x−	x−	PROPN
ejde-637	317	19	e	e	PROPN
ejde-637	317	20	=	=	PROPN
ejde-637	317	21	µ6	µ6	PROPN
ejde-637	317	22	,	,	PUNCT
ejde-637	317	23	there	there	PRON
ejde-637	317	24	exists	exist	VERB
ejde-637	317	25	one	one	NUM
ejde-637	317	26	heteroclinic	heteroclinic	ADJ
ejde-637	317	27	orbit	orbit	NOUN
ejde-637	317	28	;	;	PUNCT
ejde-637	317	29	(	(	PUNCT
ejde-637	317	30	b3	b3	PROPN
ejde-637	317	31	)	)	PUNCT
ejde-637	318	1	if	if	SCONJ
ejde-637	318	2	2µ2	2µ2	NUM
ejde-637	318	3	+	+	CCONJ
ejde-637	318	4	x+	x+	ADJ
ejde-637	318	5	e	e	X
ejde-637	318	6	<	<	X
ejde-637	318	7	µ6	µ6	PROPN
ejde-637	318	8	<	<	X
ejde-637	318	9	µ2	µ2	PROPN
ejde-637	318	10	,	,	PUNCT
ejde-637	318	11	when	when	SCONJ
ejde-637	318	12	µ8	µ8	PROPN
ejde-637	318	13	<	<	X
ejde-637	318	14	x−	x−	PROPN
ejde-637	318	15	e	e	X
ejde-637	318	16	<	<	X
ejde-637	318	17	2µ2	2µ2	NUM
ejde-637	319	1	+	+	CCONJ
ejde-637	319	2	x+	x+	ADJ
ejde-637	319	3	e	e	X
ejde-637	319	4	,	,	PUNCT
ejde-637	319	5	there	there	PRON
ejde-637	319	6	exists	exist	VERB
ejde-637	319	7	one	one	NUM
ejde-637	319	8	sliding	slide	VERB
ejde-637	319	9	homoclinic	homoclinic	ADJ
ejde-637	319	10	cycle	cycle	NOUN
ejde-637	319	11	;	;	PUNCT
ejde-637	319	12	(	(	PUNCT
ejde-637	319	13	b4	b4	NOUN
ejde-637	319	14	)	)	PUNCT
ejde-637	319	15	if	if	SCONJ
ejde-637	319	16	µ6	µ6	PROPN
ejde-637	319	17	<	<	X
ejde-637	319	18	2µ2	2µ2	NUM
ejde-637	319	19	+	+	CCONJ
ejde-637	319	20	x+	x+	ADJ
ejde-637	319	21	e	e	NOUN
ejde-637	319	22	,	,	PUNCT
ejde-637	319	23	when	when	SCONJ
ejde-637	319	24	µ8	µ8	PROPN
ejde-637	319	25	<	<	X
ejde-637	319	26	x−	x−	PROPN
ejde-637	319	27	e	e	X
ejde-637	319	28	<	<	X
ejde-637	319	29	2µ2	2µ2	NUM
ejde-637	319	30	+	+	CCONJ
ejde-637	319	31	x+	x+	ADJ
ejde-637	319	32	e	e	X
ejde-637	319	33	,	,	PUNCT
ejde-637	319	34	there	there	PRON
ejde-637	319	35	exist	exist	VERB
ejde-637	319	36	a	a	DET
ejde-637	319	37	sliding	slide	VERB
ejde-637	319	38	cycle	cycle	NOUN
ejde-637	319	39	bifurcation	bifurcation	NOUN
ejde-637	319	40	and	and	CCONJ
ejde-637	319	41	a	a	DET
ejde-637	319	42	sliding	slide	VERB
ejde-637	319	43	homoclinic	homoclinic	ADJ
ejde-637	319	44	bifurcation	bifurcation	NOUN
ejde-637	319	45	;	;	PUNCT
ejde-637	319	46	(	(	PUNCT
ejde-637	319	47	b5	b5	PROPN
ejde-637	319	48	)	)	PUNCT
ejde-637	319	49	when	when	SCONJ
ejde-637	319	50	2µ2	2µ2	NUM
ejde-637	319	51	+	+	CCONJ
ejde-637	319	52	x+	x+	ADJ
ejde-637	319	53	e	e	X
ejde-637	319	54	<	<	X
ejde-637	319	55	x−	x−	PROPN
ejde-637	319	56	e	e	PROPN
ejde-637	319	57	<	<	X
ejde-637	319	58	min{2µ1	min{2µ1	PROPN
ejde-637	319	59	+	+	CCONJ
ejde-637	319	60	x+	x+	PROPN
ejde-637	319	61	e	e	X
ejde-637	319	62	,	,	PUNCT
ejde-637	319	63	µ3	µ3	PROPN
ejde-637	319	64	}	}	PUNCT
ejde-637	319	65	,	,	PUNCT
ejde-637	319	66	there	there	PRON
ejde-637	319	67	exist	exist	VERB
ejde-637	319	68	two	two	NUM
ejde-637	319	69	sliding	slide	VERB
ejde-637	319	70	heteroclinic	heteroclinic	ADJ
ejde-637	319	71	orbits	orbit	NOUN
ejde-637	319	72	.	.	PUNCT
ejde-637	320	1	there	there	PRON
ejde-637	320	2	is	be	VERB
ejde-637	320	3	no	no	DET
ejde-637	320	4	other	other	ADJ
ejde-637	320	5	separatrix	separatrix	NOUN
ejde-637	320	6	of	of	ADP
ejde-637	320	7	system	system	NOUN
ejde-637	320	8	(	(	PUNCT
ejde-637	320	9	1.1	1.1	NUM
ejde-637	320	10	)	)	PUNCT
ejde-637	320	11	except	except	SCONJ
ejde-637	320	12	for	for	ADP
ejde-637	320	13	the	the	DET
ejde-637	320	14	separatrixes	separatrix	NOUN
ejde-637	320	15	given	give	VERB
ejde-637	320	16	in	in	ADP
ejde-637	320	17	the	the	DET
ejde-637	320	18	above	above	ADJ
ejde-637	320	19	theorems	theorem	NOUN
ejde-637	320	20	.	.	PUNCT
ejde-637	321	1	4	4	X
ejde-637	321	2	.	.	X
ejde-637	321	3	proofs	proof	NOUN
ejde-637	321	4	of	of	ADP
ejde-637	321	5	main	main	ADJ
ejde-637	321	6	results	result	NOUN
ejde-637	321	7	proof	proof	NOUN
ejde-637	321	8	of	of	ADP
ejde-637	321	9	theorem	theorem	ADJ
ejde-637	321	10	3.4	3.4	NUM
ejde-637	321	11	.	.	PUNCT
ejde-637	321	12	by	by	ADP
ejde-637	321	13	(	(	PUNCT
ejde-637	321	14	2.5	2.5	NUM
ejde-637	321	15	)	)	PUNCT
ejde-637	321	16	and	and	CCONJ
ejde-637	321	17	(	(	PUNCT
ejde-637	321	18	2.6	2.6	NUM
ejde-637	321	19	)	)	PUNCT
ejde-637	321	20	,	,	PUNCT
ejde-637	321	21	it	it	PRON
ejde-637	321	22	is	be	AUX
ejde-637	321	23	easy	easy	ADJ
ejde-637	321	24	to	to	PART
ejde-637	321	25	see	see	VERB
ejde-637	321	26	that	that	PRON
ejde-637	321	27	x−	x−	PROPN
ejde-637	321	28	m1	m1	PROPN
ejde-637	321	29	x−	x−	PROPN
ejde-637	321	30	m2	m2	PROPN
ejde-637	321	31	and	and	CCONJ
ejde-637	321	32	x−	x−	PROPN
ejde-637	321	33	t	t	PROPN
ejde-637	321	34	increase	increase	NOUN
ejde-637	321	35	with	with	ADP
ejde-637	321	36	respect	respect	NOUN
ejde-637	321	37	to	to	ADP
ejde-637	321	38	x−	x−	PROPN
ejde-637	321	39	e	e	PROPN
ejde-637	321	40	.	.	PUNCT
ejde-637	322	1	and	and	CCONJ
ejde-637	322	2	by	by	ADP
ejde-637	322	3	(	(	PUNCT
ejde-637	322	4	3.19	3.19	NUM
ejde-637	322	5	)	)	PUNCT
ejde-637	322	6	and	and	CCONJ
ejde-637	322	7	simple	simple	ADJ
ejde-637	322	8	calculation	calculation	NOUN
ejde-637	322	9	,	,	PUNCT
ejde-637	322	10	it	it	PRON
ejde-637	322	11	follows	follow	VERB
ejde-637	322	12	that	that	SCONJ
ejde-637	322	13	for	for	ADP
ejde-637	322	14	a	a	DET
ejde-637	322	15	∈	∈	PROPN
ejde-637	322	16	ω1	ω1	PROPN
ejde-637	322	17	∪	∪	X
ejde-637	322	18	ω2	ω2	PROPN
ejde-637	322	19	,	,	PUNCT
ejde-637	322	20	we	we	PRON
ejde-637	322	21	have	have	VERB
ejde-637	322	22	x−	x−	PROPN
ejde-637	322	23	m2	m2	PROPN
ejde-637	322	24	<	<	PROPN
ejde-637	322	25	x−	x−	PROPN
ejde-637	322	26	t	t	PROPN
ejde-637	322	27	<	<	X
ejde-637	322	28	x−	x−	PROPN
ejde-637	322	29	m1	m1	PROPN
ejde-637	322	30	,	,	PUNCT
ejde-637	322	31	0	0	PUNCT
ejde-637	322	32	<	<	X
ejde-637	322	33	x+	x+	X
ejde-637	322	34	m1	m1	PROPN
ejde-637	322	35	<	<	X
ejde-637	322	36	x+	x+	PROPN
ejde-637	322	37	t	t	X
ejde-637	322	38	<	<	X
ejde-637	322	39	x+	x+	PROPN
ejde-637	322	40	m2	m2	PROPN
ejde-637	322	41	.	.	PUNCT
ejde-637	323	1	(	(	PUNCT
ejde-637	323	2	4.1	4.1	NUM
ejde-637	323	3	)	)	PUNCT
ejde-637	323	4	then	then	ADV
ejde-637	323	5	µ3	µ3	VERB
ejde-637	323	6	<	<	X
ejde-637	323	7	µ4	µ4	PROPN
ejde-637	323	8	<	<	X
ejde-637	323	9	µ5	µ5	PROPN
ejde-637	323	10	and	and	CCONJ
ejde-637	323	11	2µ1	2µ1	NUM
ejde-637	323	12	+	+	CCONJ
ejde-637	323	13	x+	x+	SYM
ejde-637	323	14	e	e	X
ejde-637	323	15	<	<	X
ejde-637	323	16	µ4	µ4	PROPN
ejde-637	323	17	can	can	AUX
ejde-637	323	18	be	be	AUX
ejde-637	323	19	obtained	obtain	VERB
ejde-637	323	20	directly	directly	ADV
ejde-637	323	21	since	since	SCONJ
ejde-637	323	22	(	(	PUNCT
ejde-637	323	23	3.7	3.7	NUM
ejde-637	323	24	)	)	PUNCT
ejde-637	323	25	and	and	CCONJ
ejde-637	323	26	(	(	PUNCT
ejde-637	323	27	3.18	3.18	NUM
ejde-637	323	28	)	)	PUNCT
ejde-637	323	29	,	,	PUNCT
ejde-637	323	30	which	which	PRON
ejde-637	323	31	means	mean	VERB
ejde-637	323	32	max{µ3	max{µ3	NOUN
ejde-637	323	33	,	,	PUNCT
ejde-637	323	34	2µ1	2µ1	NUM
ejde-637	324	1	+	+	CCONJ
ejde-637	324	2	x+	x+	ADJ
ejde-637	324	3	e	e	X
ejde-637	324	4	}	}	PUNCT
ejde-637	324	5	<	<	X
ejde-637	324	6	µ4	µ4	PROPN
ejde-637	324	7	<	<	X
ejde-637	324	8	µ5	µ5	PROPN
ejde-637	324	9	.	.	PUNCT
ejde-637	325	1	as	as	ADP
ejde-637	325	2	x−	x−	PROPN
ejde-637	325	3	e	e	PROPN
ejde-637	325	4	=	=	NOUN
ejde-637	325	5	µ3	µ3	PROPN
ejde-637	325	6	,	,	PUNCT
ejde-637	325	7	we	we	PRON
ejde-637	325	8	know	know	VERB
ejde-637	325	9	x∓	x∓	PROPN
ejde-637	325	10	m1	m1	PROPN
ejde-637	325	11	=	=	SYM
ejde-637	325	12	x±	x±	PROPN
ejde-637	325	13	m2	m2	PROPN
ejde-637	325	14	,	,	PUNCT
ejde-637	325	15	it	it	PRON
ejde-637	325	16	is	be	AUX
ejde-637	325	17	also	also	ADV
ejde-637	325	18	easy	easy	ADJ
ejde-637	325	19	to	to	PART
ejde-637	325	20	see	see	VERB
ejde-637	325	21	x+	x+	ADJ
ejde-637	325	22	m1	m1	PROPN
ejde-637	325	23	<	<	X
ejde-637	325	24	min{x+	min{x+	NOUN
ejde-637	325	25	t	t	NOUN
ejde-637	325	26	,	,	PUNCT
ejde-637	325	27	x	x	PROPN
ejde-637	325	28	−	−	PROPN
ejde-637	325	29	t	t	X
ejde-637	325	30	}	}	PUNCT
ejde-637	325	31	<	<	X
ejde-637	325	32	max{x+	max{x+	PROPN
ejde-637	325	33	t	t	PROPN
ejde-637	325	34	,	,	PUNCT
ejde-637	325	35	x	x	PROPN
ejde-637	325	36	−	−	PROPN
ejde-637	325	37	t	t	NOUN
ejde-637	325	38	}	}	PUNCT
ejde-637	325	39	<	<	X
ejde-637	325	40	x+	x+	PROPN
ejde-637	325	41	m2	m2	PROPN
ejde-637	325	42	by	by	ADP
ejde-637	325	43	(	(	PUNCT
ejde-637	325	44	3.19	3.19	NUM
ejde-637	325	45	)	)	PUNCT
ejde-637	325	46	.	.	PUNCT
ejde-637	326	1	so	so	ADV
ejde-637	326	2	there	there	PRON
ejde-637	326	3	is	be	VERB
ejde-637	326	4	a	a	DET
ejde-637	326	5	heteroclinic	heteroclinic	ADJ
ejde-637	326	6	cycle	cycle	NOUN
ejde-637	326	7	connecting	connect	VERB
ejde-637	326	8	x+	x+	ADJ
ejde-637	326	9	e	e	NOUN
ejde-637	326	10	with	with	ADP
ejde-637	326	11	x−	x−	PROPN
ejde-637	326	12	e	e	PROPN
ejde-637	326	13	.	.	PUNCT
ejde-637	327	1	in	in	ADP
ejde-637	327	2	addition	addition	NOUN
ejde-637	327	3	,	,	PUNCT
ejde-637	327	4	by	by	ADP
ejde-637	327	5	simple	simple	ADJ
ejde-637	327	6	calculation	calculation	NOUN
ejde-637	327	7	,	,	PUNCT
ejde-637	327	8	it	it	PRON
ejde-637	327	9	follows	follow	VERB
ejde-637	327	10	that	that	DET
ejde-637	327	11	µ3	µ3	NOUN
ejde-637	327	12	−	−	PROPN
ejde-637	328	1	(	(	PUNCT
ejde-637	328	2	2µ1	2µ1	NUM
ejde-637	328	3	+	+	CCONJ
ejde-637	328	4	x+	x+	ADJ
ejde-637	328	5	e	e	NOUN
ejde-637	328	6	)	)	PUNCT
ejde-637	328	7	=	=	SYM
ejde-637	328	8	−	−	PROPN
ejde-637	328	9	y+e	y+e	NUM
ejde-637	328	10	a21	a21	NOUN
ejde-637	328	11	(	(	PUNCT
ejde-637	328	12	a11	a11	PROPN
ejde-637	328	13	+	+	CCONJ
ejde-637	328	14	a22	a22	PROPN
ejde-637	328	15	)	)	PUNCT
ejde-637	328	16	.	.	PUNCT
ejde-637	329	1	then	then	ADV
ejde-637	329	2	for	for	ADP
ejde-637	329	3	a	a	DET
ejde-637	329	4	∈	∈	PROPN
ejde-637	329	5	ω1	ω1	PROPN
ejde-637	329	6	∪	∪	X
ejde-637	329	7	ω2	ω2	PROPN
ejde-637	329	8	,	,	PUNCT
ejde-637	329	9	we	we	PRON
ejde-637	329	10	obtain	obtain	VERB
ejde-637	329	11	that	that	DET
ejde-637	329	12	µ3	µ3	PROPN
ejde-637	329	13	>	>	X
ejde-637	329	14	2µ1	2µ1	NUM
ejde-637	330	1	+	+	CCONJ
ejde-637	330	2	x+	x+	ADJ
ejde-637	330	3	e	e	NOUN
ejde-637	330	4	,	,	PUNCT
ejde-637	330	5	if	if	SCONJ
ejde-637	330	6	a11	a11	PROPN
ejde-637	330	7	+	+	CCONJ
ejde-637	330	8	a22	a22	X
ejde-637	330	9	<	<	X
ejde-637	330	10	0	0	NUM
ejde-637	330	11	;	;	PUNCT
ejde-637	330	12	µ3	µ3	NOUN
ejde-637	330	13	<	<	X
ejde-637	330	14	2µ1	2µ1	NUM
ejde-637	330	15	+	+	CCONJ
ejde-637	330	16	x+	x+	ADJ
ejde-637	330	17	e	e	NOUN
ejde-637	330	18	,	,	PUNCT
ejde-637	330	19	if	if	SCONJ
ejde-637	330	20	a11	a11	PROPN
ejde-637	330	21	+	+	CCONJ
ejde-637	330	22	a22	a22	PROPN
ejde-637	330	23	>	>	X
ejde-637	330	24	0	0	PROPN
ejde-637	330	25	.	.	PUNCT
ejde-637	330	26	(	(	PUNCT
ejde-637	330	27	4.2	4.2	NUM
ejde-637	330	28	)	)	PUNCT
ejde-637	330	29	for	for	ADP
ejde-637	330	30	µ3	µ3	PROPN
ejde-637	330	31	<	<	X
ejde-637	330	32	x−	x−	PROPN
ejde-637	330	33	e	e	X
ejde-637	330	34	<	<	X
ejde-637	330	35	2µ1	2µ1	NUM
ejde-637	330	36	+	+	CCONJ
ejde-637	330	37	x+	x+	ADJ
ejde-637	330	38	e	e	X
ejde-637	330	39	,	,	PUNCT
ejde-637	330	40	we	we	PRON
ejde-637	330	41	have	have	VERB
ejde-637	330	42	x+	x+	ADJ
ejde-637	330	43	m1	m1	PROPN
ejde-637	330	44	<	<	X
ejde-637	330	45	x−	x−	PROPN
ejde-637	330	46	m2	m2	PROPN
ejde-637	330	47	<	<	PROPN
ejde-637	330	48	x−	x−	PROPN
ejde-637	330	49	t	t	PROPN
ejde-637	330	50	<	<	X
ejde-637	330	51	x+	x+	PROPN
ejde-637	330	52	t	t	X
ejde-637	330	53	<	<	X
ejde-637	330	54	x+	x+	PROPN
ejde-637	330	55	m2	m2	PROPN
ejde-637	330	56	<	<	X
ejde-637	330	57	x−	x−	PROPN
ejde-637	330	58	m1	m1	PROPN
ejde-637	330	59	.	.	PUNCT
ejde-637	331	1	and	and	CCONJ
ejde-637	331	2	by	by	ADP
ejde-637	331	3	proposition	proposition	NOUN
ejde-637	331	4	3.2	3.2	NUM
ejde-637	331	5	,	,	PUNCT
ejde-637	331	6	pex	pex	PROPN
ejde-637	331	7	∈	∈	PROPN
ejde-637	331	8	σx	σx	ADP
ejde-637	331	9	s	s	NOUN
ejde-637	331	10	is	be	AUX
ejde-637	331	11	stable	stable	ADJ
ejde-637	331	12	.	.	PUNCT
ejde-637	332	1	then	then	ADV
ejde-637	332	2	there	there	PRON
ejde-637	332	3	must	must	AUX
ejde-637	332	4	exist	exist	VERB
ejde-637	332	5	a	a	DET
ejde-637	332	6	repulsive	repulsive	ADJ
ejde-637	332	7	limit	limit	NOUN
ejde-637	332	8	cycle	cycle	NOUN
ejde-637	332	9	l1	l1	PROPN
ejde-637	332	10	.	.	PUNCT
ejde-637	333	1	to	to	PART
ejde-637	333	2	prove	prove	VERB
ejde-637	333	3	this	this	PRON
ejde-637	333	4	,	,	PUNCT
ejde-637	333	5	we	we	PRON
ejde-637	333	6	need	need	VERB
ejde-637	333	7	to	to	PART
ejde-637	333	8	construct	construct	VERB
ejde-637	333	9	the	the	DET
ejde-637	333	10	poincaré	poincaré	ADJ
ejde-637	333	11	map	map	NOUN
ejde-637	333	12	as	as	SCONJ
ejde-637	333	13	follows	follow	VERB
ejde-637	333	14	:	:	PUNCT
ejde-637	333	15	p1	p1	NOUN
ejde-637	333	16	:	:	PUNCT
ejde-637	333	17	dp1	dp1	PROPN
ejde-637	333	18	7→	7→	PROPN
ejde-637	334	1	dp1	dp1	PROPN
ejde-637	334	2	,	,	PUNCT
ejde-637	334	3	p1(x0	p1(x0	PROPN
ejde-637	334	4	,	,	PUNCT
ejde-637	334	5	0	0	NUM
ejde-637	334	6	)	)	PUNCT
ejde-637	334	7	=	=	SYM
ejde-637	334	8	(	(	PUNCT
ejde-637	334	9	x1	x1	PROPN
ejde-637	334	10	,	,	PUNCT
ejde-637	334	11	0	0	NUM
ejde-637	334	12	)	)	PUNCT
ejde-637	334	13	,	,	PUNCT
ejde-637	334	14	wheredp1	wheredp1	NOUN
ejde-637	334	15	=	=	PUNCT
ejde-637	334	16	{	{	PUNCT
ejde-637	334	17	(	(	PUNCT
ejde-637	334	18	x	x	NOUN
ejde-637	334	19	,	,	PUNCT
ejde-637	334	20	0	0	NUM
ejde-637	334	21	)	)	PUNCT
ejde-637	334	22	:	:	PUNCT
ejde-637	335	1	x	x	X
ejde-637	335	2	∈	∈	PROPN
ejde-637	335	3	[	[	X
ejde-637	335	4	x+	x+	X
ejde-637	335	5	t	t	PROPN
ejde-637	335	6	,	,	PUNCT
ejde-637	335	7	x	x	PROPN
ejde-637	335	8	+	+	NUM
ejde-637	335	9	m2	m2	PROPN
ejde-637	335	10	]	]	PUNCT
ejde-637	335	11	}	}	PUNCT
ejde-637	335	12	,	,	PUNCT
ejde-637	335	13	and	and	CCONJ
ejde-637	335	14	(	(	PUNCT
ejde-637	335	15	x1	x1	PROPN
ejde-637	335	16	,	,	PUNCT
ejde-637	335	17	0	0	NUM
ejde-637	335	18	)	)	PUNCT
ejde-637	335	19	is	be	AUX
ejde-637	335	20	the	the	DET
ejde-637	335	21	first	first	ADJ
ejde-637	335	22	arriving	arriving	NOUN
ejde-637	335	23	point	point	NOUN
ejde-637	335	24	atdp1	atdp1	NOUN
ejde-637	335	25	of	of	ADP
ejde-637	335	26	the	the	DET
ejde-637	335	27	orbit	orbit	NOUN
ejde-637	335	28	of	of	ADP
ejde-637	335	29	system	system	NOUN
ejde-637	335	30	(	(	PUNCT
ejde-637	335	31	1.1	1.1	NUM
ejde-637	335	32	)	)	PUNCT
ejde-637	335	33	with	with	ADP
ejde-637	335	34	the	the	DET
ejde-637	335	35	initial	initial	ADJ
ejde-637	335	36	point	point	NOUN
ejde-637	335	37	(	(	PUNCT
ejde-637	335	38	x0	x0	PROPN
ejde-637	335	39	,	,	PUNCT
ejde-637	335	40	0	0	NUM
ejde-637	335	41	)	)	PUNCT
ejde-637	335	42	∈	∈	PROPN
ejde-637	336	1	dp1	dp1	PROPN
ejde-637	336	2	.	.	PUNCT
ejde-637	337	1	since	since	SCONJ
ejde-637	337	2	x−	x−	PROPN
ejde-637	337	3	t	t	PROPN
ejde-637	337	4	<	<	X
ejde-637	337	5	x+	x+	PROPN
ejde-637	337	6	t	t	X
ejde-637	337	7	<	<	X
ejde-637	337	8	x+	x+	PROPN
ejde-637	337	9	m2	m2	PROPN
ejde-637	337	10	,	,	PUNCT
ejde-637	337	11	there	there	PRON
ejde-637	337	12	must	must	AUX
ejde-637	337	13	exist	exist	VERB
ejde-637	337	14	(	(	PUNCT
ejde-637	337	15	x⋆	x⋆	SYM
ejde-637	337	16	1	1	NUM
ejde-637	337	17	,	,	PUNCT
ejde-637	337	18	0	0	NUM
ejde-637	337	19	)	)	PUNCT
ejde-637	337	20	,	,	PUNCT
ejde-637	337	21	(	(	PUNCT
ejde-637	337	22	x	x	X
ejde-637	337	23	⋆	⋆	X
ejde-637	337	24	2	2	NUM
ejde-637	337	25	,	,	PUNCT
ejde-637	337	26	0	0	NUM
ejde-637	337	27	)	)	PUNCT
ejde-637	337	28	∈	∈	PROPN
ejde-637	337	29	dp1	dp1	PROPN
ejde-637	337	30	and	and	CCONJ
ejde-637	337	31	x+	x+	PROPN
ejde-637	337	32	t	t	X
ejde-637	337	33	<	<	X
ejde-637	337	34	x⋆	x⋆	X
ejde-637	337	35	2	2	NUM
ejde-637	337	36	<	<	X
ejde-637	337	37	x⋆	x⋆	X
ejde-637	337	38	1	1	NUM
ejde-637	337	39	<	<	X
ejde-637	337	40	x+	x+	PROPN
ejde-637	337	41	m2	m2	PROPN
ejde-637	337	42	,	,	PUNCT
ejde-637	337	43	such	such	ADJ
ejde-637	337	44	that	that	DET
ejde-637	337	45	p1(x	p1(x	NOUN
ejde-637	337	46	⋆	⋆	VERB
ejde-637	337	47	1	1	NUM
ejde-637	337	48	,	,	PUNCT
ejde-637	337	49	0	0	NUM
ejde-637	337	50	)	)	PUNCT
ejde-637	337	51	=	=	SYM
ejde-637	337	52	(	(	PUNCT
ejde-637	337	53	x+	x+	PROPN
ejde-637	337	54	m2	m2	PROPN
ejde-637	337	55	,	,	PUNCT
ejde-637	337	56	0	0	NUM
ejde-637	337	57	)	)	PUNCT
ejde-637	337	58	,	,	PUNCT
ejde-637	337	59	p1(x	p1(x	NOUN
ejde-637	337	60	⋆	⋆	VERB
ejde-637	337	61	2	2	NUM
ejde-637	337	62	,	,	PUNCT
ejde-637	337	63	0	0	NUM
ejde-637	337	64	)	)	PUNCT
ejde-637	337	65	=	=	SYM
ejde-637	338	1	(	(	PUNCT
ejde-637	338	2	x+	x+	PROPN
ejde-637	338	3	t	t	PROPN
ejde-637	338	4	,	,	PUNCT
ejde-637	338	5	0	0	NUM
ejde-637	338	6	)	)	PUNCT
ejde-637	338	7	.	.	PUNCT
ejde-637	339	1	this	this	PRON
ejde-637	339	2	means	mean	VERB
ejde-637	339	3	there	there	PRON
ejde-637	339	4	must	must	AUX
ejde-637	339	5	be	be	AUX
ejde-637	339	6	(	(	PUNCT
ejde-637	339	7	x⋆	x⋆	ADJ
ejde-637	339	8	,	,	PUNCT
ejde-637	339	9	0	0	X
ejde-637	339	10	)	)	PUNCT
ejde-637	339	11	∈	∈	PROPN
ejde-637	339	12	dp1	dp1	PROPN
ejde-637	339	13	,	,	PUNCT
ejde-637	339	14	such	such	ADJ
ejde-637	339	15	that	that	DET
ejde-637	339	16	p1(x	p1(x	NOUN
ejde-637	339	17	⋆	⋆	NOUN
ejde-637	339	18	,	,	PUNCT
ejde-637	339	19	0	0	NUM
ejde-637	339	20	)	)	PUNCT
ejde-637	339	21	=	=	NOUN
ejde-637	339	22	(	(	PUNCT
ejde-637	339	23	x⋆	x⋆	ADJ
ejde-637	339	24	,	,	PUNCT
ejde-637	339	25	0	0	NUM
ejde-637	339	26	)	)	PUNCT
ejde-637	339	27	,	,	PUNCT
ejde-637	339	28	ejde-2024/57	ejde-2024/57	NOUN
ejde-637	339	29	planar	planar	ADJ
ejde-637	339	30	sector	sector	NOUN
ejde-637	339	31	-	-	PUNCT
ejde-637	339	32	wise	wise	ADJ
ejde-637	339	33	linear	linear	PROPN
ejde-637	339	34	systems	system	NOUN
ejde-637	339	35	13	13	NUM
ejde-637	339	36	which	which	PRON
ejde-637	339	37	implies	imply	VERB
ejde-637	339	38	the	the	DET
ejde-637	339	39	existence	existence	NOUN
ejde-637	339	40	of	of	ADP
ejde-637	339	41	the	the	DET
ejde-637	339	42	repulsive	repulsive	ADJ
ejde-637	339	43	limit	limit	NOUN
ejde-637	339	44	cycle	cycle	NOUN
ejde-637	339	45	l1	l1	PROPN
ejde-637	339	46	.	.	PUNCT
ejde-637	340	1	similarly	similarly	ADV
ejde-637	340	2	,	,	PUNCT
ejde-637	340	3	for	for	ADP
ejde-637	340	4	µ3	µ3	PROPN
ejde-637	340	5	<	<	X
ejde-637	340	6	x−	x−	PROPN
ejde-637	340	7	e	e	X
ejde-637	340	8	<	<	X
ejde-637	340	9	2µ1	2µ1	NUM
ejde-637	340	10	+	+	CCONJ
ejde-637	340	11	x+	x+	ADJ
ejde-637	340	12	e	e	X
ejde-637	340	13	,	,	PUNCT
ejde-637	340	14	we	we	PRON
ejde-637	340	15	can	can	AUX
ejde-637	340	16	prove	prove	VERB
ejde-637	340	17	the	the	DET
ejde-637	340	18	existence	existence	NOUN
ejde-637	340	19	of	of	ADP
ejde-637	340	20	an	an	DET
ejde-637	340	21	attractive	attractive	ADJ
ejde-637	340	22	limit	limit	NOUN
ejde-637	340	23	cycle	cycle	NOUN
ejde-637	340	24	l2	l2	NOUN
ejde-637	340	25	.	.	PUNCT
ejde-637	341	1	as	as	ADP
ejde-637	341	2	x−	x−	PROPN
ejde-637	341	3	e	e	PROPN
ejde-637	341	4	>	>	X
ejde-637	341	5	max{2µ1+x+	max{2µ1+x+	PROPN
ejde-637	341	6	e	e	NOUN
ejde-637	341	7	,	,	PUNCT
ejde-637	341	8	µ3	µ3	PROPN
ejde-637	341	9	}	}	PUNCT
ejde-637	341	10	,	,	PUNCT
ejde-637	341	11	we	we	PRON
ejde-637	341	12	have	have	VERB
ejde-637	341	13	x+	x+	PROPN
ejde-637	341	14	t	t	PROPN
ejde-637	341	15	<	<	X
ejde-637	341	16	x−	x−	PROPN
ejde-637	341	17	t	t	PROPN
ejde-637	341	18	and	and	CCONJ
ejde-637	341	19	x−	x−	PROPN
ejde-637	341	20	m1	m1	PROPN
ejde-637	341	21	>	>	X
ejde-637	341	22	x+	x+	PROPN
ejde-637	341	23	m2	m2	PROPN
ejde-637	341	24	.	.	PUNCT
ejde-637	342	1	then	then	ADV
ejde-637	342	2	according	accord	VERB
ejde-637	342	3	to	to	ADP
ejde-637	342	4	proposition	proposition	NOUN
ejde-637	342	5	3.1	3.1	NUM
ejde-637	342	6	and	and	CCONJ
ejde-637	342	7	proposition	proposition	NOUN
ejde-637	342	8	3.2	3.2	NUM
ejde-637	342	9	,	,	PUNCT
ejde-637	342	10	it	it	PRON
ejde-637	342	11	follows	follow	VERB
ejde-637	342	12	that	that	SCONJ
ejde-637	342	13	σx	σx	PROPN
ejde-637	342	14	s	s	NOUN
ejde-637	342	15	=	=	X
ejde-637	342	16	{	{	PUNCT
ejde-637	342	17	(	(	PUNCT
ejde-637	342	18	x	x	NOUN
ejde-637	342	19	,	,	PUNCT
ejde-637	342	20	0	0	NUM
ejde-637	342	21	)	)	PUNCT
ejde-637	342	22	:	:	PUNCT
ejde-637	342	23	x+	x+	PROPN
ejde-637	342	24	t	t	X
ejde-637	342	25	<	<	X
ejde-637	342	26	x	x	X
ejde-637	342	27	<	<	X
ejde-637	342	28	x−	x−	PROPN
ejde-637	342	29	t	t	PROPN
ejde-637	342	30	}	}	PUNCT
ejde-637	342	31	is	be	AUX
ejde-637	342	32	repulsive	repulsive	ADJ
ejde-637	342	33	and	and	CCONJ
ejde-637	342	34	pex	pex	PROPN
ejde-637	342	35	is	be	AUX
ejde-637	342	36	unstable	unstable	ADJ
ejde-637	342	37	.	.	PUNCT
ejde-637	343	1	so	so	ADV
ejde-637	343	2	there	there	PRON
ejde-637	343	3	is	be	VERB
ejde-637	343	4	no	no	DET
ejde-637	343	5	other	other	ADJ
ejde-637	343	6	special	special	ADJ
ejde-637	343	7	dynamics	dynamic	NOUN
ejde-637	343	8	expect	expect	VERB
ejde-637	343	9	for	for	ADP
ejde-637	343	10	two	two	NUM
ejde-637	343	11	sliding	slide	VERB
ejde-637	343	12	heteroclinic	heteroclinic	ADJ
ejde-637	343	13	orbits	orbit	NOUN
ejde-637	343	14	l3	l3	PROPN
ejde-637	343	15	and	and	CCONJ
ejde-637	343	16	l4	l4	PROPN
ejde-637	343	17	,	,	PUNCT
ejde-637	343	18	both	both	PRON
ejde-637	343	19	of	of	ADP
ejde-637	343	20	which	which	PRON
ejde-637	343	21	connect	connect	VERB
ejde-637	343	22	x±	x±	PROPN
ejde-637	343	23	e	e	PROPN
ejde-637	343	24	and	and	CCONJ
ejde-637	343	25	pex	pex	PROPN
ejde-637	343	26	as	as	ADP
ejde-637	343	27	x−	x−	PROPN
ejde-637	343	28	e	e	PROPN
ejde-637	343	29	=	=	PROPN
ejde-637	343	30	µ4	µ4	PROPN
ejde-637	343	31	and	and	CCONJ
ejde-637	343	32	x−	x−	PROPN
ejde-637	343	33	e	e	PROPN
ejde-637	343	34	=	=	PROPN
ejde-637	343	35	µ5	µ5	PROPN
ejde-637	343	36	,	,	PUNCT
ejde-637	343	37	respectively	respectively	ADV
ejde-637	343	38	.	.	PUNCT
ejde-637	344	1	the	the	DET
ejde-637	344	2	proof	proof	NOUN
ejde-637	344	3	is	be	AUX
ejde-637	344	4	complete	complete	ADJ
ejde-637	344	5	.	.	PUNCT
ejde-637	345	1	□	□	PUNCT
ejde-637	345	2	proof	proof	NOUN
ejde-637	345	3	of	of	ADP
ejde-637	345	4	theorem	theorem	ADJ
ejde-637	345	5	3.5	3.5	NUM
ejde-637	345	6	.	.	PUNCT
ejde-637	346	1	(	(	PUNCT
ejde-637	346	2	a	a	X
ejde-637	346	3	)	)	PUNCT
ejde-637	346	4	in	in	ADP
ejde-637	346	5	this	this	DET
ejde-637	346	6	case	case	NOUN
ejde-637	346	7	,	,	PUNCT
ejde-637	346	8	since	since	SCONJ
ejde-637	346	9	a11	a11	PROPN
ejde-637	346	10	>	>	X
ejde-637	346	11	0	0	PROPN
ejde-637	347	1	and	and	CCONJ
ejde-637	347	2	(	(	PUNCT
ejde-637	347	3	3.19	3.19	NUM
ejde-637	347	4	)	)	PUNCT
ejde-637	347	5	,	,	PUNCT
ejde-637	347	6	we	we	PRON
ejde-637	347	7	obtain	obtain	VERB
ejde-637	347	8	that	that	PRON
ejde-637	347	9	y+m2	y+m2	AUX
ejde-637	347	10	>	>	X
ejde-637	347	11	y+t	y+t	PROPN
ejde-637	347	12	>	>	X
ejde-637	347	13	y+e	y+e	X
ejde-637	347	14	>	>	X
ejde-637	347	15	0	0	PUNCT
ejde-637	347	16	>	>	X
ejde-637	347	17	y+m1	y+m1	PROPN
ejde-637	347	18	,	,	PUNCT
ejde-637	347	19	0	0	PUNCT
ejde-637	347	20	<	<	X
ejde-637	347	21	x+	x+	X
ejde-637	347	22	m1	m1	PROPN
ejde-637	347	23	<	<	X
ejde-637	347	24	x+	x+	X
ejde-637	347	25	e	e	X
ejde-637	347	26	<	<	X
ejde-637	347	27	x+	x+	PROPN
ejde-637	347	28	t	t	X
ejde-637	347	29	<	<	X
ejde-637	347	30	x+	x+	PROPN
ejde-637	347	31	m2	m2	PROPN
ejde-637	347	32	.	.	PUNCT
ejde-637	348	1	by	by	ADP
ejde-637	348	2	(	(	PUNCT
ejde-637	348	3	2.6	2.6	NUM
ejde-637	348	4	)	)	PUNCT
ejde-637	348	5	,	,	PUNCT
ejde-637	348	6	it	it	PRON
ejde-637	348	7	is	be	AUX
ejde-637	348	8	obvious	obvious	ADJ
ejde-637	348	9	that	that	SCONJ
ejde-637	348	10	y−m1	y−m1	NOUN
ejde-637	348	11	decreases	decrease	VERB
ejde-637	348	12	with	with	ADP
ejde-637	348	13	respect	respect	NOUN
ejde-637	348	14	to	to	ADP
ejde-637	348	15	x−	x−	PROPN
ejde-637	348	16	e	e	PROPN
ejde-637	348	17	.	.	PUNCT
ejde-637	349	1	so	so	ADV
ejde-637	349	2	we	we	PRON
ejde-637	349	3	obtain	obtain	VERB
ejde-637	349	4	µ6	µ6	PROPN
ejde-637	349	5	<	<	X
ejde-637	349	6	µ7	µ7	PROPN
ejde-637	349	7	<	<	X
ejde-637	349	8	0	0	PUNCT
ejde-637	350	1	directly	directly	ADV
ejde-637	350	2	because	because	SCONJ
ejde-637	350	3	of	of	ADP
ejde-637	350	4	(	(	PUNCT
ejde-637	350	5	3.18	3.18	NUM
ejde-637	350	6	)	)	PUNCT
ejde-637	350	7	.	.	PUNCT
ejde-637	351	1	moreover	moreover	ADV
ejde-637	351	2	,	,	PUNCT
ejde-637	351	3	when	when	SCONJ
ejde-637	351	4	x−	x−	PROPN
ejde-637	351	5	e	e	PROPN
ejde-637	351	6	=	=	PROPN
ejde-637	351	7	µ5	µ5	PROPN
ejde-637	351	8	,	,	PUNCT
ejde-637	351	9	we	we	PRON
ejde-637	351	10	have	have	VERB
ejde-637	351	11	x∓	x∓	PROPN
ejde-637	351	12	m1	m1	PROPN
ejde-637	351	13	=	=	SYM
ejde-637	351	14	x±	x±	PROPN
ejde-637	351	15	m2	m2	PROPN
ejde-637	351	16	,	,	PUNCT
ejde-637	351	17	which	which	PRON
ejde-637	351	18	means	mean	VERB
ejde-637	351	19	x−	x−	PROPN
ejde-637	351	20	t	t	PROPN
ejde-637	351	21	>	>	X
ejde-637	351	22	0	0	PROPN
ejde-637	351	23	.	.	PUNCT
ejde-637	352	1	so	so	ADV
ejde-637	352	2	we	we	PRON
ejde-637	352	3	obtain	obtain	VERB
ejde-637	352	4	that	that	DET
ejde-637	352	5	0	0	NUM
ejde-637	352	6	<	<	X
ejde-637	352	7	µ1	µ1	PROPN
ejde-637	352	8	<	<	X
ejde-637	352	9	µ3	µ3	NOUN
ejde-637	352	10	.	.	PUNCT
ejde-637	353	1	since	since	SCONJ
ejde-637	353	2	(	(	PUNCT
ejde-637	353	3	4.2	4.2	NUM
ejde-637	353	4	)	)	PUNCT
ejde-637	353	5	,	,	PUNCT
ejde-637	353	6	it	it	PRON
ejde-637	353	7	is	be	AUX
ejde-637	353	8	easy	easy	ADJ
ejde-637	353	9	to	to	PART
ejde-637	353	10	see	see	VERB
ejde-637	353	11	µ3	µ3	PROPN
ejde-637	353	12	<	<	X
ejde-637	353	13	2µ1	2µ1	NUM
ejde-637	353	14	+	+	CCONJ
ejde-637	353	15	x+	x+	ADJ
ejde-637	353	16	e	e	X
ejde-637	353	17	.	.	PUNCT
ejde-637	354	1	then	then	ADV
ejde-637	354	2	by	by	ADP
ejde-637	354	3	theorem	theorem	NOUN
ejde-637	354	4	3.4	3.4	NUM
ejde-637	354	5	,	,	PUNCT
ejde-637	354	6	we	we	PRON
ejde-637	354	7	obtain	obtain	VERB
ejde-637	354	8	that	that	DET
ejde-637	354	9	µ6	µ6	PROPN
ejde-637	354	10	<	<	X
ejde-637	354	11	µ7	µ7	PROPN
ejde-637	354	12	<	<	X
ejde-637	354	13	0	0	PUNCT
ejde-637	354	14	<	<	X
ejde-637	354	15	µ1	µ1	PROPN
ejde-637	354	16	<	<	X
ejde-637	354	17	µ3	µ3	PROPN
ejde-637	354	18	<	<	X
ejde-637	354	19	2µ1	2µ1	NUM
ejde-637	354	20	+	+	CCONJ
ejde-637	354	21	x+	x+	ADJ
ejde-637	354	22	e	e	X
ejde-637	354	23	<	<	X
ejde-637	354	24	µ4	µ4	PROPN
ejde-637	354	25	<	<	X
ejde-637	354	26	µ5	µ5	PROPN
ejde-637	354	27	.	.	PUNCT
ejde-637	355	1	in	in	ADP
ejde-637	355	2	addition	addition	NOUN
ejde-637	355	3	,	,	PUNCT
ejde-637	355	4	by	by	ADP
ejde-637	355	5	simple	simple	ADJ
ejde-637	355	6	calculation	calculation	NOUN
ejde-637	355	7	,	,	PUNCT
ejde-637	355	8	it	it	PRON
ejde-637	355	9	follows	follow	VERB
ejde-637	355	10	that	that	SCONJ
ejde-637	355	11	µ6−	µ6−	ADJ
ejde-637	355	12	(	(	PUNCT
ejde-637	355	13	−x+	−x+	NOUN
ejde-637	355	14	e	e	NOUN
ejde-637	355	15	)	)	PUNCT
ejde-637	355	16	=	=	SYM
ejde-637	356	1	(	(	PUNCT
ejde-637	356	2	a22	a22	NOUN
ejde-637	356	3	−	−	NOUN
ejde-637	356	4	a11)x	a11)x	NOUN
ejde-637	356	5	+	+	NOUN
ejde-637	356	6	e	e	NOUN
ejde-637	356	7	−	−	PROPN
ejde-637	356	8	2a12y	2a12y	NOUN
ejde-637	357	1	+	+	CCONJ
ejde-637	357	2	e	e	X
ejde-637	357	3	λ1	λ1	PROPN
ejde-637	357	4	−	−	PROPN
ejde-637	357	5	a11	a11	PROPN
ejde-637	357	6	,	,	PUNCT
ejde-637	357	7	µ7−	µ7−	PROPN
ejde-637	357	8	(	(	PUNCT
ejde-637	357	9	−x+	−x+	NOUN
ejde-637	357	10	e	e	NOUN
ejde-637	357	11	)	)	PUNCT
ejde-637	357	12	=	=	SYM
ejde-637	357	13	λ2	λ2	PROPN
ejde-637	357	14	−	−	PROPN
ejde-637	357	15	a11	a11	PROPN
ejde-637	358	1	−	−	PROPN
ejde-637	358	2	2a12y	2a12y	NOUN
ejde-637	359	1	+	+	CCONJ
ejde-637	359	2	e	e	X
ejde-637	359	3	λ1	λ1	PROPN
ejde-637	359	4	−	−	PROPN
ejde-637	359	5	a11	a11	PROPN
ejde-637	359	6	,	,	PUNCT
ejde-637	359	7	(	(	PUNCT
ejde-637	359	8	4.3	4.3	NUM
ejde-637	359	9	)	)	PUNCT
ejde-637	359	10	the	the	DET
ejde-637	359	11	signs	sign	NOUN
ejde-637	359	12	of	of	ADP
ejde-637	359	13	which	which	PRON
ejde-637	359	14	are	be	AUX
ejde-637	359	15	not	not	PART
ejde-637	359	16	sure	sure	ADJ
ejde-637	359	17	.	.	PUNCT
ejde-637	360	1	then	then	ADV
ejde-637	360	2	−x+	−x+	X
ejde-637	360	3	e	e	X
ejde-637	360	4	<	<	X
ejde-637	360	5	µ6	µ6	PROPN
ejde-637	360	6	<	<	X
ejde-637	360	7	µ7	µ7	PROPN
ejde-637	360	8	<	<	X
ejde-637	360	9	0	0	PROPN
ejde-637	360	10	,	,	PUNCT
ejde-637	360	11	µ6	µ6	NOUN
ejde-637	360	12	<	<	X
ejde-637	360	13	−x+	−x+	X
ejde-637	360	14	e	e	X
ejde-637	360	15	<	<	X
ejde-637	360	16	µ7	µ7	PROPN
ejde-637	360	17	<	<	X
ejde-637	360	18	0	0	PUNCT
ejde-637	360	19	or	or	CCONJ
ejde-637	360	20	µ6	µ6	PROPN
ejde-637	360	21	<	<	X
ejde-637	360	22	µ7	µ7	PROPN
ejde-637	360	23	<	<	X
ejde-637	360	24	−x+	−x+	X
ejde-637	360	25	e	e	X
ejde-637	360	26	<	<	X
ejde-637	360	27	0	0	X
ejde-637	360	28	could	could	AUX
ejde-637	360	29	happen	happen	VERB
ejde-637	360	30	.	.	PUNCT
ejde-637	361	1	firstly	firstly	ADV
ejde-637	361	2	,	,	PUNCT
ejde-637	361	3	according	accord	VERB
ejde-637	361	4	to	to	ADP
ejde-637	361	5	proposition	proposition	NOUN
ejde-637	361	6	3.1	3.1	NUM
ejde-637	361	7	,	,	PUNCT
ejde-637	361	8	proposition	proposition	NOUN
ejde-637	361	9	3.2	3.2	NUM
ejde-637	361	10	and	and	CCONJ
ejde-637	361	11	remark	remark	VERB
ejde-637	361	12	2.6	2.6	NUM
ejde-637	361	13	,	,	PUNCT
ejde-637	361	14	it	it	PRON
ejde-637	361	15	is	be	AUX
ejde-637	361	16	obvious	obvious	ADJ
ejde-637	361	17	to	to	PART
ejde-637	361	18	see	see	VERB
ejde-637	361	19	that	that	SCONJ
ejde-637	361	20	there	there	PRON
ejde-637	361	21	is	be	VERB
ejde-637	361	22	a	a	DET
ejde-637	361	23	sliding	slide	VERB
ejde-637	361	24	heteroclinic	heteroclinic	ADJ
ejde-637	361	25	orbitm1	orbitm1	NOUN
ejde-637	361	26	from	from	ADP
ejde-637	361	27	x+	x+	PROPN
ejde-637	361	28	e	e	NOUN
ejde-637	361	29	to	to	PART
ejde-637	361	30	pey	pey	VERB
ejde-637	361	31	for	for	ADP
ejde-637	361	32	x−	x−	PROPN
ejde-637	361	33	e	e	PROPN
ejde-637	361	34	≤	≤	ADJ
ejde-637	362	1	−x+	−x+	NOUN
ejde-637	362	2	e	e	NOUN
ejde-637	362	3	,	,	PUNCT
ejde-637	362	4	and	and	CCONJ
ejde-637	362	5	a	a	DET
ejde-637	362	6	sliding	slide	VERB
ejde-637	362	7	heteroclinic	heteroclinic	ADJ
ejde-637	362	8	orbit	orbit	NOUN
ejde-637	362	9	m2	m2	PROPN
ejde-637	362	10	from	from	ADP
ejde-637	362	11	x+	x+	PROPN
ejde-637	362	12	e	e	NOUN
ejde-637	362	13	to	to	ADP
ejde-637	362	14	pex	pex	PROPN
ejde-637	362	15	for	for	ADP
ejde-637	362	16	x−	x−	PROPN
ejde-637	362	17	e	e	PROPN
ejde-637	362	18	>	>	PUNCT
ejde-637	362	19	−x+	−x+	X
ejde-637	363	1	e	e	NOUN
ejde-637	363	2	.	.	PUNCT
ejde-637	364	1	moreover	moreover	ADV
ejde-637	364	2	,	,	PUNCT
ejde-637	364	3	a	a	DET
ejde-637	364	4	heteroclinic	heteroclinic	ADJ
ejde-637	364	5	orbit	orbit	NOUN
ejde-637	364	6	m3	m3	PROPN
ejde-637	364	7	from	from	ADP
ejde-637	364	8	x−	x−	PROPN
ejde-637	364	9	e	e	PROPN
ejde-637	364	10	to	to	ADP
ejde-637	364	11	x+	x+	PROPN
ejde-637	364	12	e	e	NOUN
ejde-637	364	13	appears	appear	VERB
ejde-637	364	14	only	only	ADV
ejde-637	364	15	as	as	ADP
ejde-637	364	16	x−	x−	PROPN
ejde-637	364	17	e	e	PROPN
ejde-637	364	18	=	=	PROPN
ejde-637	364	19	µ6	µ6	PROPN
ejde-637	364	20	obviously	obviously	ADV
ejde-637	364	21	.	.	PUNCT
ejde-637	365	1	for	for	ADP
ejde-637	365	2	µ6	µ6	PROPN
ejde-637	365	3	<	<	X
ejde-637	365	4	x−	x−	PROPN
ejde-637	365	5	e	e	PROPN
ejde-637	365	6	<	<	X
ejde-637	365	7	µ7	µ7	PROPN
ejde-637	365	8	,	,	PUNCT
ejde-637	365	9	the	the	DET
ejde-637	365	10	orbit	orbit	NOUN
ejde-637	365	11	of	of	ADP
ejde-637	365	12	system	system	NOUN
ejde-637	365	13	(	(	PUNCT
ejde-637	365	14	1.1	1.1	NUM
ejde-637	365	15	)	)	PUNCT
ejde-637	365	16	starting	start	VERB
ejde-637	365	17	from	from	ADP
ejde-637	365	18	(	(	PUNCT
ejde-637	365	19	0	0	NUM
ejde-637	365	20	,	,	PUNCT
ejde-637	365	21	y−m1	y−m1	NOUN
ejde-637	365	22	)	)	PUNCT
ejde-637	365	23	will	will	AUX
ejde-637	365	24	arrive	arrive	VERB
ejde-637	365	25	at	at	ADP
ejde-637	365	26	the	the	DET
ejde-637	365	27	sliding	slide	VERB
ejde-637	365	28	set	set	NOUN
ejde-637	365	29	σs	σs	ADP
ejde-637	365	30	.	.	PROPN
ejde-637	365	31	and	and	CCONJ
ejde-637	365	32	for	for	ADP
ejde-637	365	33	µ7	µ7	PROPN
ejde-637	365	34	≤	≤	PROPN
ejde-637	365	35	x−	x−	PROPN
ejde-637	365	36	e	e	PROPN
ejde-637	365	37	<	<	X
ejde-637	365	38	µ3	µ3	PROPN
ejde-637	365	39	,	,	PUNCT
ejde-637	365	40	the	the	DET
ejde-637	365	41	invariant	invariant	ADJ
ejde-637	365	42	manifold	manifold	ADJ
ejde-637	365	43	l−1	l−1	PROPN
ejde-637	365	44	of	of	ADP
ejde-637	365	45	x−	x−	PROPN
ejde-637	365	46	e	e	PROPN
ejde-637	365	47	will	will	AUX
ejde-637	365	48	intersects	intersects	VERB
ejde-637	365	49	with	with	ADP
ejde-637	365	50	σs	σs	PROPN
ejde-637	365	51	.	.	PUNCT
ejde-637	366	1	so	so	ADV
ejde-637	366	2	there	there	PRON
ejde-637	366	3	is	be	VERB
ejde-637	366	4	a	a	DET
ejde-637	366	5	sliding	slide	VERB
ejde-637	366	6	heteroclinic	heteroclinic	ADJ
ejde-637	366	7	orbit	orbit	NOUN
ejde-637	366	8	m4	m4	PROPN
ejde-637	366	9	from	from	ADP
ejde-637	366	10	x−	x−	PROPN
ejde-637	366	11	e	e	PROPN
ejde-637	366	12	to	to	ADP
ejde-637	366	13	the	the	DET
ejde-637	366	14	unique	unique	ADJ
ejde-637	366	15	pseudo	pseudo	NOUN
ejde-637	366	16	-	-	NOUN
ejde-637	366	17	equilibrium	equilibrium	NOUN
ejde-637	366	18	point	point	NOUN
ejde-637	366	19	pex	pex	PROPN
ejde-637	366	20	or	or	CCONJ
ejde-637	366	21	pey	pey	NOUN
ejde-637	366	22	for	for	ADP
ejde-637	366	23	µ6	µ6	PROPN
ejde-637	366	24	<	<	X
ejde-637	366	25	x−	x−	PROPN
ejde-637	366	26	e	e	X
ejde-637	366	27	<	<	X
ejde-637	366	28	µ3	µ3	PROPN
ejde-637	366	29	.	.	PUNCT
ejde-637	367	1	thus	thus	ADV
ejde-637	367	2	we	we	PRON
ejde-637	367	3	obtain	obtain	VERB
ejde-637	367	4	that	that	SCONJ
ejde-637	367	5	m1	m1	PROPN
ejde-637	367	6	exists	exist	VERB
ejde-637	367	7	for	for	ADP
ejde-637	367	8	x−	x−	PROPN
ejde-637	367	9	e	e	PROPN
ejde-637	367	10	<	<	X
ejde-637	367	11	min{−x+	min{−x+	PROPN
ejde-637	367	12	e	e	NOUN
ejde-637	367	13	,	,	PUNCT
ejde-637	367	14	µ6	µ6	PROPN
ejde-637	367	15	}	}	PUNCT
ejde-637	367	16	.	.	PUNCT
ejde-637	368	1	when	when	SCONJ
ejde-637	368	2	min{−x+	min{−x+	PROPN
ejde-637	368	3	e	e	NOUN
ejde-637	368	4	,	,	PUNCT
ejde-637	368	5	µ6	µ6	PROPN
ejde-637	368	6	}	}	PUNCT
ejde-637	368	7	<	<	X
ejde-637	368	8	x−	x−	PROPN
ejde-637	368	9	e	e	X
ejde-637	368	10	<	<	X
ejde-637	368	11	µ3	µ3	NOUN
ejde-637	368	12	,	,	PUNCT
ejde-637	368	13	there	there	PRON
ejde-637	368	14	exist	exist	VERB
ejde-637	368	15	two	two	NUM
ejde-637	368	16	sliding	slide	VERB
ejde-637	368	17	heteroclinic	heteroclinic	ADJ
ejde-637	368	18	orbits	orbit	NOUN
ejde-637	368	19	m2	m2	PROPN
ejde-637	368	20	and	and	CCONJ
ejde-637	368	21	m4	m4	PROPN
ejde-637	368	22	.	.	PUNCT
ejde-637	369	1	as	as	ADP
ejde-637	369	2	x−	x−	PROPN
ejde-637	369	3	e	e	PROPN
ejde-637	369	4	=	=	PROPN
ejde-637	369	5	µ6	µ6	PROPN
ejde-637	369	6	,	,	PUNCT
ejde-637	369	7	there	there	PRON
ejde-637	369	8	exists	exist	VERB
ejde-637	369	9	the	the	DET
ejde-637	369	10	heteroclinic	heteroclinic	ADJ
ejde-637	369	11	orbit	orbit	NOUN
ejde-637	369	12	m3	m3	PROPN
ejde-637	369	13	and	and	CCONJ
ejde-637	369	14	the	the	DET
ejde-637	369	15	sliding	slide	VERB
ejde-637	369	16	heteroclinic	heteroclinic	ADJ
ejde-637	369	17	orbit	orbit	NOUN
ejde-637	369	18	m4	m4	PROPN
ejde-637	369	19	.	.	PUNCT
ejde-637	370	1	(	(	PUNCT
ejde-637	370	2	b	b	X
ejde-637	370	3	)	)	PUNCT
ejde-637	370	4	since	since	SCONJ
ejde-637	370	5	a11	a11	PROPN
ejde-637	370	6	<	<	X
ejde-637	370	7	0	0	PROPN
ejde-637	370	8	,	,	PUNCT
ejde-637	370	9	we	we	PRON
ejde-637	370	10	obtain	obtain	VERB
ejde-637	370	11	that	that	DET
ejde-637	370	12	x−	x−	PROPN
ejde-637	370	13	m2	m2	PROPN
ejde-637	370	14	<	<	PROPN
ejde-637	370	15	x−	x−	PROPN
ejde-637	370	16	t	t	PROPN
ejde-637	370	17	<	<	X
ejde-637	370	18	x−	x−	PROPN
ejde-637	370	19	m1	m1	PROPN
ejde-637	370	20	<	<	X
ejde-637	370	21	x−	x−	PROPN
ejde-637	370	22	e	e	PROPN
ejde-637	370	23	,	,	PUNCT
ejde-637	370	24	0	0	PUNCT
ejde-637	370	25	<	<	X
ejde-637	370	26	x+	x+	X
ejde-637	370	27	e	e	X
ejde-637	370	28	<	<	X
ejde-637	370	29	x+	x+	X
ejde-637	370	30	m1	m1	PROPN
ejde-637	370	31	<	<	X
ejde-637	370	32	x+	x+	PROPN
ejde-637	370	33	t	t	X
ejde-637	370	34	<	<	X
ejde-637	370	35	x+	x+	PROPN
ejde-637	370	36	m2	m2	PROPN
ejde-637	370	37	.	.	PUNCT
ejde-637	371	1	by	by	ADP
ejde-637	371	2	(	(	PUNCT
ejde-637	371	3	2.6	2.6	NUM
ejde-637	371	4	)	)	PUNCT
ejde-637	371	5	and	and	CCONJ
ejde-637	371	6	(	(	PUNCT
ejde-637	371	7	3.18	3.18	NUM
ejde-637	371	8	)	)	PUNCT
ejde-637	371	9	,	,	PUNCT
ejde-637	371	10	we	we	PRON
ejde-637	371	11	know	know	VERB
ejde-637	371	12	x−	x−	PROPN
ejde-637	371	13	m1	m1	PROPN
ejde-637	371	14	=	=	PUNCT
ejde-637	371	15	y−m1	y−m1	NOUN
ejde-637	371	16	=	=	SYM
ejde-637	371	17	0	0	PUNCT
ejde-637	371	18	as	as	ADP
ejde-637	371	19	x−	x−	PROPN
ejde-637	371	20	e	e	PROPN
ejde-637	371	21	=	=	PROPN
ejde-637	371	22	µ9	µ9	PROPN
ejde-637	371	23	,	,	PUNCT
ejde-637	371	24	then	then	ADV
ejde-637	371	25	0	0	NUM
ejde-637	371	26	<	<	X
ejde-637	371	27	µ9	µ9	PROPN
ejde-637	371	28	<	<	X
ejde-637	371	29	min{2µ1	min{2µ1	PROPN
ejde-637	371	30	+	+	CCONJ
ejde-637	371	31	x+	x+	ADJ
ejde-637	371	32	e	e	X
ejde-637	371	33	,	,	PUNCT
ejde-637	371	34	µ3	µ3	NOUN
ejde-637	371	35	}	}	PUNCT
ejde-637	371	36	can	can	AUX
ejde-637	371	37	be	be	AUX
ejde-637	371	38	obtained	obtain	VERB
ejde-637	371	39	directly	directly	ADV
ejde-637	371	40	.	.	PUNCT
ejde-637	372	1	and	and	CCONJ
ejde-637	372	2	by	by	ADP
ejde-637	372	3	theorem	theorem	NOUN
ejde-637	372	4	3.4	3.4	NUM
ejde-637	372	5	,	,	PUNCT
ejde-637	372	6	we	we	PRON
ejde-637	372	7	have	have	VERB
ejde-637	372	8	−x+	−x+	NOUN
ejde-637	372	9	e	e	NOUN
ejde-637	372	10	<	<	X
ejde-637	372	11	0	0	PUNCT
ejde-637	372	12	<	<	X
ejde-637	372	13	µ9	µ9	PROPN
ejde-637	372	14	<	<	X
ejde-637	372	15	min{2µ1	min{2µ1	NOUN
ejde-637	372	16	+	+	CCONJ
ejde-637	372	17	x+	x+	PROPN
ejde-637	372	18	e	e	X
ejde-637	372	19	,	,	PUNCT
ejde-637	372	20	µ3	µ3	NUM
ejde-637	372	21	}	}	PUNCT
ejde-637	372	22	<	<	X
ejde-637	372	23	max{2µ1	max{2µ1	PROPN
ejde-637	372	24	+	+	CCONJ
ejde-637	372	25	x+	x+	PROPN
ejde-637	372	26	e	e	X
ejde-637	372	27	,	,	PUNCT
ejde-637	372	28	µ3	µ3	NUM
ejde-637	372	29	}	}	PUNCT
ejde-637	372	30	<	<	X
ejde-637	372	31	µ4	µ4	PROPN
ejde-637	372	32	<	<	X
ejde-637	372	33	µ5	µ5	PROPN
ejde-637	372	34	.	.	PUNCT
ejde-637	373	1	according	accord	VERB
ejde-637	373	2	to	to	ADP
ejde-637	373	3	propositions	proposition	NOUN
ejde-637	373	4	3.1	3.1	NUM
ejde-637	373	5	,	,	PUNCT
ejde-637	373	6	3.2	3.2	NUM
ejde-637	373	7	and	and	CCONJ
ejde-637	373	8	3.3	3.3	NUM
ejde-637	373	9	,	,	PUNCT
ejde-637	373	10	it	it	PRON
ejde-637	373	11	is	be	AUX
ejde-637	373	12	easy	easy	ADJ
ejde-637	373	13	to	to	PART
ejde-637	373	14	see	see	VERB
ejde-637	373	15	there	there	PRON
ejde-637	373	16	exists	exist	VERB
ejde-637	373	17	a	a	DET
ejde-637	373	18	sliding	slide	VERB
ejde-637	373	19	orbit	orbit	NOUN
ejde-637	373	20	connecting	connect	VERB
ejde-637	373	21	x+	x+	ADJ
ejde-637	373	22	e	e	X
ejde-637	373	23	,	,	PUNCT
ejde-637	373	24	pey	pey	PROPN
ejde-637	373	25	and	and	CCONJ
ejde-637	373	26	the	the	DET
ejde-637	373	27	non	non	ADJ
ejde-637	373	28	-	-	ADJ
ejde-637	373	29	regular	regular	ADJ
ejde-637	373	30	boundary	boundary	ADJ
ejde-637	373	31	sink	sink	NOUN
ejde-637	373	32	p0	p0	NOUN
ejde-637	373	33	for	for	ADP
ejde-637	373	34	x−	x−	PROPN
ejde-637	373	35	e	e	PROPN
ejde-637	373	36	<	<	X
ejde-637	373	37	−x+	−x+	X
ejde-637	373	38	e	e	NOUN
ejde-637	373	39	,	,	PUNCT
ejde-637	373	40	which	which	PRON
ejde-637	373	41	will	will	AUX
ejde-637	373	42	become	become	VERB
ejde-637	373	43	a	a	DET
ejde-637	373	44	sliding	slide	VERB
ejde-637	373	45	heteroclinic	heteroclinic	ADJ
ejde-637	373	46	orbit	orbit	NOUN
ejde-637	373	47	from	from	ADP
ejde-637	373	48	x+	x+	PROPN
ejde-637	373	49	e	e	PROPN
ejde-637	373	50	,	,	PUNCT
ejde-637	373	51	pex	pex	PROPN
ejde-637	373	52	for	for	ADP
ejde-637	373	53	−x+	−x+	NOUN
ejde-637	373	54	e	e	NOUN
ejde-637	373	55	≤	≤	NOUN
ejde-637	373	56	x−	x−	PROPN
ejde-637	374	1	e	e	PROPN
ejde-637	374	2	<	<	X
ejde-637	374	3	min{2µ1+x+	min{2µ1+x+	PROPN
ejde-637	374	4	e	e	NOUN
ejde-637	374	5	,	,	PUNCT
ejde-637	374	6	µ3	µ3	NUM
ejde-637	374	7	}	}	PUNCT
ejde-637	374	8	.	.	PUNCT
ejde-637	375	1	once	once	ADV
ejde-637	375	2	x−	x−	PROPN
ejde-637	375	3	e	e	PROPN
ejde-637	375	4	=	=	PROPN
ejde-637	375	5	µ9	µ9	PROPN
ejde-637	375	6	,	,	PUNCT
ejde-637	375	7	there	there	PRON
ejde-637	375	8	appears	appear	VERB
ejde-637	375	9	a	a	DET
ejde-637	375	10	sliding	slide	VERB
ejde-637	375	11	heteroclinic	heteroclinic	ADJ
ejde-637	375	12	orbit	orbit	NOUN
ejde-637	375	13	from	from	ADP
ejde-637	375	14	x−	x−	PROPN
ejde-637	375	15	e	e	PROPN
ejde-637	375	16	to	to	ADP
ejde-637	375	17	pex	pex	PROPN
ejde-637	375	18	,	,	PUNCT
ejde-637	375	19	which	which	PRON
ejde-637	375	20	will	will	AUX
ejde-637	375	21	persist	persist	VERB
ejde-637	375	22	until	until	ADP
ejde-637	375	23	x−	x−	PROPN
ejde-637	375	24	e	e	PROPN
ejde-637	375	25	=	=	PROPN
ejde-637	375	26	min{2µ1+x+	min{2µ1+x+	PROPN
ejde-637	375	27	e	e	NOUN
ejde-637	375	28	,	,	PUNCT
ejde-637	375	29	µ3	µ3	NUM
ejde-637	375	30	}	}	PUNCT
ejde-637	375	31	.	.	PUNCT
ejde-637	376	1	the	the	DET
ejde-637	376	2	proof	proof	NOUN
ejde-637	376	3	is	be	AUX
ejde-637	376	4	complete	complete	ADJ
ejde-637	376	5	.	.	PUNCT
ejde-637	377	1	□	□	PUNCT
ejde-637	377	2	proof	proof	NOUN
ejde-637	377	3	of	of	ADP
ejde-637	377	4	theorem	theorem	NOUN
ejde-637	377	5	3.6	3.6	NUM
ejde-637	377	6	.	.	PUNCT
ejde-637	378	1	when	when	SCONJ
ejde-637	378	2	a	a	DET
ejde-637	378	3	∈	∈	PROPN
ejde-637	378	4	ω2	ω2	NOUN
ejde-637	378	5	,	,	PUNCT
ejde-637	378	6	it	it	PRON
ejde-637	378	7	is	be	AUX
ejde-637	378	8	not	not	PART
ejde-637	378	9	difficult	difficult	ADJ
ejde-637	378	10	to	to	PART
ejde-637	378	11	verify	verify	VERB
ejde-637	378	12	that	that	SCONJ
ejde-637	378	13	the	the	DET
ejde-637	378	14	case	case	NOUN
ejde-637	378	15	of	of	ADP
ejde-637	378	16	matrix	matrix	NOUN
ejde-637	378	17	a	a	PRON
ejde-637	378	18	with	with	ADP
ejde-637	378	19	a21	a21	PROPN
ejde-637	378	20	>	>	X
ejde-637	378	21	0	0	PROPN
ejde-637	378	22	,	,	PUNCT
ejde-637	378	23	a22	a22	X
ejde-637	378	24	>	>	X
ejde-637	378	25	0	0	PROPN
ejde-637	378	26	,	,	PUNCT
ejde-637	378	27	a12	a12	NOUN
ejde-637	378	28	<	<	X
ejde-637	378	29	0	0	PROPN
ejde-637	378	30	,	,	PUNCT
ejde-637	378	31	a11	a11	PROPN
ejde-637	378	32	>	>	X
ejde-637	378	33	0	0	NUM
ejde-637	378	34	is	be	AUX
ejde-637	378	35	invalid	invalid	ADJ
ejde-637	378	36	since	since	SCONJ
ejde-637	378	37	det(a	det(a	PROPN
ejde-637	378	38	)	)	PUNCT
ejde-637	378	39	=	=	SYM
ejde-637	378	40	a11a22	a11a22	PROPN
ejde-637	378	41	−	−	PROPN
ejde-637	378	42	a12a21	a12a21	NOUN
ejde-637	378	43	>	>	X
ejde-637	378	44	0	0	NUM
ejde-637	378	45	,	,	PUNCT
ejde-637	378	46	which	which	PRON
ejde-637	378	47	contradicts	contradict	VERB
ejde-637	378	48	that	that	DET
ejde-637	378	49	det(a	det(a	NOUN
ejde-637	378	50	)	)	PUNCT
ejde-637	378	51	<	<	X
ejde-637	378	52	0	0	PUNCT
ejde-637	378	53	in	in	ADP
ejde-637	378	54	the	the	DET
ejde-637	378	55	condition	condition	NOUN
ejde-637	378	56	(	(	PUNCT
ejde-637	378	57	3.1	3.1	NUM
ejde-637	378	58	)	)	PUNCT
ejde-637	378	59	.	.	PUNCT
ejde-637	379	1	so	so	ADV
ejde-637	379	2	14	14	NUM
ejde-637	379	3	q.-q	q.-q	PROPN
ejde-637	379	4	.	.	PUNCT
ejde-637	380	1	han	han	PROPN
ejde-637	380	2	,	,	PUNCT
ejde-637	380	3	s.-m	s.-m	PROPN
ejde-637	380	4	.	.	PUNCT
ejde-637	381	1	huan	huan	PROPN
ejde-637	381	2	ejde-2024/57	ejde-2024/57	PROPN
ejde-637	381	3	we	we	PRON
ejde-637	381	4	just	just	ADV
ejde-637	381	5	need	need	VERB
ejde-637	381	6	to	to	PART
ejde-637	381	7	give	give	VERB
ejde-637	381	8	the	the	DET
ejde-637	381	9	discussion	discussion	NOUN
ejde-637	381	10	of	of	ADP
ejde-637	381	11	system	system	NOUN
ejde-637	381	12	(	(	PUNCT
ejde-637	381	13	1.1	1.1	NUM
ejde-637	381	14	)	)	PUNCT
ejde-637	381	15	with	with	ADP
ejde-637	381	16	a	a	DET
ejde-637	381	17	∈	∈	PROPN
ejde-637	381	18	ω2	ω2	NOUN
ejde-637	381	19	and	and	CCONJ
ejde-637	381	20	a11	a11	PROPN
ejde-637	381	21	<	<	X
ejde-637	381	22	0	0	PUNCT
ejde-637	381	23	under	under	ADP
ejde-637	381	24	assumption	assumption	NOUN
ejde-637	381	25	(	(	PUNCT
ejde-637	381	26	3.19	3.19	NUM
ejde-637	381	27	)	)	PUNCT
ejde-637	381	28	as	as	SCONJ
ejde-637	381	29	follows	follow	VERB
ejde-637	381	30	.	.	PUNCT
ejde-637	382	1	(	(	PUNCT
ejde-637	382	2	a	a	X
ejde-637	382	3	)	)	PUNCT
ejde-637	382	4	when	when	SCONJ
ejde-637	382	5	a11	a11	PROPN
ejde-637	382	6	<	<	X
ejde-637	382	7	0	0	PROPN
ejde-637	382	8	and	and	CCONJ
ejde-637	382	9	0	0	NUM
ejde-637	382	10	<	<	X
ejde-637	382	11	y+e	y+e	NUM
ejde-637	382	12	<	<	X
ejde-637	382	13	−a11	−a11	PROPN
ejde-637	382	14	a12	a12	NOUN
ejde-637	382	15	x+	x+	PROPN
ejde-637	383	1	e	e	X
ejde-637	383	2	,	,	PUNCT
ejde-637	383	3	we	we	PRON
ejde-637	383	4	know	know	VERB
ejde-637	383	5	that	that	SCONJ
ejde-637	383	6	y+t	y+t	PROPN
ejde-637	383	7	<	<	X
ejde-637	383	8	0	0	PUNCT
ejde-637	383	9	by	by	ADP
ejde-637	383	10	(	(	PUNCT
ejde-637	383	11	3.9	3.9	NUM
ejde-637	383	12	)	)	PUNCT
ejde-637	383	13	.	.	PUNCT
ejde-637	384	1	in	in	ADP
ejde-637	384	2	addition	addition	NOUN
ejde-637	384	3	,	,	PUNCT
ejde-637	384	4	we	we	PRON
ejde-637	384	5	obtain	obtain	VERB
ejde-637	384	6	that	that	DET
ejde-637	384	7	y+m2	y+m2	PROPN
ejde-637	384	8	>	>	X
ejde-637	384	9	y+e	y+e	NUM
ejde-637	384	10	>	>	X
ejde-637	384	11	0	0	PUNCT
ejde-637	384	12	>	>	X
ejde-637	384	13	y+t	y+t	PROPN
ejde-637	384	14	>	>	X
ejde-637	384	15	y+m1	y+m1	PROPN
ejde-637	384	16	,	,	PUNCT
ejde-637	384	17	0	0	PUNCT
ejde-637	384	18	<	<	X
ejde-637	384	19	x+	x+	X
ejde-637	384	20	m1	m1	PROPN
ejde-637	384	21	<	<	X
ejde-637	384	22	x+	x+	X
ejde-637	384	23	e	e	X
ejde-637	384	24	<	<	X
ejde-637	384	25	x+	x+	PROPN
ejde-637	384	26	t	t	X
ejde-637	384	27	<	<	X
ejde-637	384	28	x+	x+	PROPN
ejde-637	384	29	m2	m2	PROPN
ejde-637	384	30	.	.	PROPN
ejde-637	384	31	note	note	VERB
ejde-637	384	32	that	that	SCONJ
ejde-637	384	33	y−m1	y−m1	NOUN
ejde-637	384	34	>	>	PUNCT
ejde-637	384	35	y−t	y−t	NOUN
ejde-637	384	36	and	and	CCONJ
ejde-637	384	37	both	both	PRON
ejde-637	384	38	of	of	ADP
ejde-637	384	39	them	they	PRON
ejde-637	384	40	decrease	decrease	VERB
ejde-637	384	41	with	with	ADP
ejde-637	384	42	respect	respect	NOUN
ejde-637	384	43	to	to	ADP
ejde-637	384	44	x−	x−	PROPN
ejde-637	384	45	e	e	PROPN
ejde-637	384	46	by	by	ADP
ejde-637	384	47	(	(	PUNCT
ejde-637	384	48	2.5	2.5	NUM
ejde-637	384	49	)	)	PUNCT
ejde-637	384	50	and	and	CCONJ
ejde-637	384	51	(	(	PUNCT
ejde-637	384	52	2.6	2.6	NUM
ejde-637	384	53	)	)	PUNCT
ejde-637	384	54	.	.	PUNCT
ejde-637	385	1	then	then	ADV
ejde-637	385	2	as	as	ADP
ejde-637	385	3	x−	x−	PROPN
ejde-637	385	4	e	e	PROPN
ejde-637	385	5	=	=	PROPN
ejde-637	385	6	µ8	µ8	PROPN
ejde-637	385	7	,	,	PUNCT
ejde-637	385	8	we	we	PRON
ejde-637	385	9	must	must	AUX
ejde-637	385	10	have	have	VERB
ejde-637	385	11	y−m1	y−m1	NOUN
ejde-637	385	12	>	>	PUNCT
ejde-637	385	13	y−t	y−t	PROPN
ejde-637	385	14	=	=	PUNCT
ejde-637	385	15	y+m2	y+m2	PROPN
ejde-637	385	16	>	>	X
ejde-637	385	17	0	0	NUM
ejde-637	385	18	,	,	PUNCT
ejde-637	385	19	which	which	PRON
ejde-637	385	20	means	mean	VERB
ejde-637	385	21	µ8	µ8	PROPN
ejde-637	385	22	<	<	X
ejde-637	385	23	µ6	µ6	PROPN
ejde-637	385	24	<	<	X
ejde-637	385	25	0	0	PUNCT
ejde-637	385	26	and	and	CCONJ
ejde-637	385	27	µ8	µ8	NOUN
ejde-637	385	28	<	<	X
ejde-637	385	29	µ2	µ2	PROPN
ejde-637	385	30	<	<	X
ejde-637	385	31	0	0	PUNCT
ejde-637	385	32	since	since	SCONJ
ejde-637	385	33	(	(	PUNCT
ejde-637	385	34	3.8	3.8	NUM
ejde-637	385	35	)	)	PUNCT
ejde-637	385	36	and	and	CCONJ
ejde-637	385	37	(	(	PUNCT
ejde-637	385	38	3.18	3.18	NUM
ejde-637	385	39	)	)	PUNCT
ejde-637	385	40	.	.	PUNCT
ejde-637	386	1	moreover	moreover	ADV
ejde-637	386	2	,	,	PUNCT
ejde-637	386	3	by	by	ADP
ejde-637	386	4	simple	simple	ADJ
ejde-637	386	5	calculation	calculation	NOUN
ejde-637	386	6	,	,	PUNCT
ejde-637	386	7	it	it	PRON
ejde-637	386	8	follows	follow	VERB
ejde-637	386	9	that	that	SCONJ
ejde-637	386	10	µ8	µ8	PROPN
ejde-637	386	11	−	−	PROPN
ejde-637	386	12	(	(	PUNCT
ejde-637	386	13	−x+	−x+	NOUN
ejde-637	386	14	e	e	NOUN
ejde-637	386	15	)	)	PUNCT
ejde-637	386	16	=	=	SYM
ejde-637	387	1	2a11y	2a11y	NUM
ejde-637	388	1	+	+	CCONJ
ejde-637	388	2	e	e	X
ejde-637	388	3	−	−	PROPN
ejde-637	388	4	(	(	PUNCT
ejde-637	388	5	λ2	λ2	NOUN
ejde-637	388	6	−	−	NOUN
ejde-637	388	7	2a11)x	2a11)x	NUM
ejde-637	389	1	+	+	NUM
ejde-637	389	2	e	e	PROPN
ejde-637	389	3	a11	a11	PROPN
ejde-637	389	4	,	,	PUNCT
ejde-637	389	5	µ2	µ2	PROPN
ejde-637	389	6	−	−	PROPN
ejde-637	389	7	µ6	µ6	PROPN
ejde-637	389	8	=	=	SYM
ejde-637	389	9	(	(	PUNCT
ejde-637	389	10	λ1	λ1	PROPN
ejde-637	389	11	+	+	NUM
ejde-637	389	12	a11)a12y	a11)a12y	PROPN
ejde-637	389	13	+	+	NUM
ejde-637	389	14	e	e	X
ejde-637	389	15	−	−	PROPN
ejde-637	389	16	a11(λ2	a11(λ2	PROPN
ejde-637	389	17	−	−	PROPN
ejde-637	389	18	a11)x	a11)x	NOUN
ejde-637	389	19	+	+	CCONJ
ejde-637	389	20	e	e	X
ejde-637	389	21	(	(	PUNCT
ejde-637	389	22	λ1	λ1	PROPN
ejde-637	389	23	−	−	PROPN
ejde-637	389	24	a11)a11	a11)a11	PROPN
ejde-637	389	25	.	.	PUNCT
ejde-637	390	1	(	(	PUNCT
ejde-637	390	2	4.4	4.4	NUM
ejde-637	390	3	)	)	PUNCT
ejde-637	390	4	and	and	CCONJ
ejde-637	390	5	by	by	ADP
ejde-637	390	6	(	(	PUNCT
ejde-637	390	7	4.3	4.3	NUM
ejde-637	390	8	)	)	PUNCT
ejde-637	390	9	,	,	PUNCT
ejde-637	390	10	we	we	PRON
ejde-637	390	11	know	know	VERB
ejde-637	390	12	the	the	DET
ejde-637	390	13	signs	sign	NOUN
ejde-637	390	14	of	of	ADP
ejde-637	390	15	µ8	µ8	ADJ
ejde-637	390	16	−	−	PROPN
ejde-637	390	17	(	(	PUNCT
ejde-637	390	18	−x+	−x+	NOUN
ejde-637	390	19	e	e	NOUN
ejde-637	390	20	)	)	PUNCT
ejde-637	390	21	,	,	PUNCT
ejde-637	390	22	µ2	µ2	PROPN
ejde-637	390	23	−	−	PROPN
ejde-637	390	24	µ6	µ6	PROPN
ejde-637	390	25	and	and	CCONJ
ejde-637	390	26	µ6	µ6	PROPN
ejde-637	390	27	−	−	PROPN
ejde-637	390	28	(	(	PUNCT
ejde-637	390	29	−x+	−x+	NOUN
ejde-637	390	30	e	e	NOUN
ejde-637	390	31	)	)	PUNCT
ejde-637	390	32	are	be	AUX
ejde-637	390	33	not	not	PART
ejde-637	390	34	sure	sure	ADJ
ejde-637	390	35	.	.	PUNCT
ejde-637	391	1	then	then	ADV
ejde-637	391	2	by	by	ADP
ejde-637	391	3	(	(	PUNCT
ejde-637	391	4	3.15	3.15	NUM
ejde-637	391	5	)	)	PUNCT
ejde-637	391	6	and	and	CCONJ
ejde-637	391	7	theorem	theorem	VERB
ejde-637	391	8	3.4	3.4	NUM
ejde-637	391	9	,	,	PUNCT
ejde-637	391	10	we	we	PRON
ejde-637	391	11	know	know	VERB
ejde-637	391	12	µ8	µ8	PROPN
ejde-637	391	13	<	<	X
ejde-637	391	14	min{µ6	min{µ6	NUM
ejde-637	391	15	,	,	PUNCT
ejde-637	391	16	µ2	µ2	ADJ
ejde-637	391	17	}	}	PUNCT
ejde-637	391	18	<	<	X
ejde-637	391	19	0	0	PUNCT
ejde-637	391	20	<	<	X
ejde-637	391	21	µ1	µ1	PROPN
ejde-637	391	22	<	<	X
ejde-637	391	23	max{2µ1	max{2µ1	PROPN
ejde-637	391	24	+	+	CCONJ
ejde-637	391	25	x+	x+	PROPN
ejde-637	391	26	e	e	X
ejde-637	391	27	,	,	PUNCT
ejde-637	391	28	µ3	µ3	NUM
ejde-637	391	29	}	}	PUNCT
ejde-637	391	30	<	<	X
ejde-637	391	31	µ4	µ4	PROPN
ejde-637	391	32	<	<	X
ejde-637	391	33	µ5	µ5	PROPN
ejde-637	391	34	.	.	PUNCT
ejde-637	392	1	meanwhile	meanwhile	ADV
ejde-637	392	2	,	,	PUNCT
ejde-637	392	3	we	we	PRON
ejde-637	392	4	obtain	obtain	VERB
ejde-637	392	5	that	that	DET
ejde-637	392	6	−x+	−x+	NOUN
ejde-637	392	7	e	e	X
ejde-637	392	8	<	<	X
ejde-637	392	9	µ8	µ8	PROPN
ejde-637	392	10	<	<	X
ejde-637	392	11	min{µ6	min{µ6	NUM
ejde-637	392	12	,	,	PUNCT
ejde-637	392	13	µ2	µ2	PROPN
ejde-637	392	14	}	}	PUNCT
ejde-637	392	15	,	,	PUNCT
ejde-637	392	16	µ8	µ8	ADJ
ejde-637	392	17	<	<	X
ejde-637	392	18	−x+	−x+	X
ejde-637	392	19	e	e	X
ejde-637	392	20	<	<	X
ejde-637	392	21	min{µ6	min{µ6	NUM
ejde-637	392	22	,	,	PUNCT
ejde-637	392	23	µ2	µ2	ADJ
ejde-637	392	24	}	}	PUNCT
ejde-637	392	25	or	or	CCONJ
ejde-637	392	26	µ8	µ8	PROPN
ejde-637	392	27	<	<	X
ejde-637	392	28	µ6	µ6	PROPN
ejde-637	392	29	<	<	X
ejde-637	392	30	−x+	−x+	X
ejde-637	392	31	e	e	X
ejde-637	392	32	<	<	X
ejde-637	392	33	µ2	µ2	PROPN
ejde-637	392	34	could	could	AUX
ejde-637	392	35	take	take	VERB
ejde-637	392	36	place	place	NOUN
ejde-637	392	37	.	.	PUNCT
ejde-637	393	1	by	by	ADP
ejde-637	393	2	propositions	proposition	NOUN
ejde-637	393	3	3.1	3.1	NUM
ejde-637	393	4	,	,	PUNCT
ejde-637	393	5	3.2	3.2	NUM
ejde-637	393	6	and	and	CCONJ
ejde-637	393	7	3.3	3.3	NUM
ejde-637	393	8	,	,	PUNCT
ejde-637	393	9	and	and	CCONJ
ejde-637	393	10	remark	remark	VERB
ejde-637	393	11	2.6	2.6	NUM
ejde-637	393	12	,	,	PUNCT
ejde-637	393	13	for	for	ADP
ejde-637	393	14	x−	x−	PROPN
ejde-637	393	15	e	e	PROPN
ejde-637	393	16	<	<	X
ejde-637	393	17	min{µ8,−x+	min{µ8,−x+	X
ejde-637	393	18	e	e	NOUN
ejde-637	393	19	}	}	PUNCT
ejde-637	393	20	,	,	PUNCT
ejde-637	393	21	there	there	PRON
ejde-637	393	22	is	be	VERB
ejde-637	393	23	a	a	DET
ejde-637	393	24	sliding	slide	VERB
ejde-637	393	25	orbit	orbit	NOUN
ejde-637	393	26	j1	j1	NOUN
ejde-637	393	27	containing	contain	VERB
ejde-637	393	28	pey	pey	NOUN
ejde-637	393	29	,	,	PUNCT
ejde-637	393	30	x	x	PUNCT
ejde-637	394	1	+	+	NUM
ejde-637	394	2	e	e	NOUN
ejde-637	394	3	and	and	CCONJ
ejde-637	394	4	p0	p0	NOUN
ejde-637	394	5	,	,	PUNCT
ejde-637	394	6	which	which	PRON
ejde-637	394	7	is	be	AUX
ejde-637	394	8	a	a	DET
ejde-637	394	9	non	non	ADJ
ejde-637	394	10	-	-	ADJ
ejde-637	394	11	regular	regular	ADJ
ejde-637	394	12	boundary	boundary	ADJ
ejde-637	394	13	sink	sink	NOUN
ejde-637	394	14	.	.	PUNCT
ejde-637	395	1	as	as	ADP
ejde-637	395	2	x−	x−	PROPN
ejde-637	395	3	e	e	PROPN
ejde-637	395	4	=	=	PROPN
ejde-637	395	5	µ8	µ8	PROPN
ejde-637	395	6	,	,	PUNCT
ejde-637	396	1	if	if	SCONJ
ejde-637	396	2	µ8	µ8	PROPN
ejde-637	396	3	<	<	X
ejde-637	396	4	−x+	−x+	X
ejde-637	396	5	e	e	NOUN
ejde-637	396	6	,	,	PUNCT
ejde-637	396	7	there	there	PRON
ejde-637	396	8	is	be	VERB
ejde-637	396	9	a	a	DET
ejde-637	396	10	sliding	slide	VERB
ejde-637	396	11	cycle	cycle	NOUN
ejde-637	396	12	j2	j2	NOUN
ejde-637	396	13	connecting	connect	VERB
ejde-637	396	14	pey	pey	NOUN
ejde-637	396	15	,	,	PUNCT
ejde-637	396	16	x	x	PUNCT
ejde-637	397	1	+	+	NUM
ejde-637	397	2	e	e	NOUN
ejde-637	397	3	and	and	CCONJ
ejde-637	397	4	p0	p0	NOUN
ejde-637	397	5	,	,	PUNCT
ejde-637	397	6	which	which	PRON
ejde-637	397	7	is	be	AUX
ejde-637	397	8	a	a	DET
ejde-637	397	9	non	non	ADJ
ejde-637	397	10	-	-	ADJ
ejde-637	397	11	regular	regular	ADJ
ejde-637	397	12	boundary	boundary	ADJ
ejde-637	397	13	sink	sink	NOUN
ejde-637	397	14	;	;	PUNCT
ejde-637	397	15	if	if	SCONJ
ejde-637	397	16	µ8	µ8	PROPN
ejde-637	397	17	>	>	PUNCT
ejde-637	397	18	−x+	−x+	X
ejde-637	398	1	e	e	NOUN
ejde-637	398	2	,	,	PUNCT
ejde-637	398	3	there	there	PRON
ejde-637	398	4	is	be	VERB
ejde-637	398	5	a	a	DET
ejde-637	398	6	sliding	slide	VERB
ejde-637	398	7	cycle	cycle	NOUN
ejde-637	398	8	j3	j3	PROPN
ejde-637	398	9	connecting	connect	VERB
ejde-637	398	10	pex	pex	PROPN
ejde-637	398	11	,	,	PUNCT
ejde-637	398	12	x	x	X
ejde-637	398	13	+	+	NUM
ejde-637	398	14	e	e	NOUN
ejde-637	398	15	and	and	CCONJ
ejde-637	398	16	p0	p0	NOUN
ejde-637	398	17	,	,	PUNCT
ejde-637	398	18	which	which	PRON
ejde-637	398	19	is	be	AUX
ejde-637	398	20	a	a	DET
ejde-637	398	21	non	non	ADJ
ejde-637	398	22	-	-	ADJ
ejde-637	398	23	regular	regular	ADJ
ejde-637	398	24	boundary	boundary	ADJ
ejde-637	398	25	source	source	NOUN
ejde-637	398	26	.	.	PUNCT
ejde-637	399	1	moreover	moreover	ADV
ejde-637	399	2	,	,	PUNCT
ejde-637	399	3	as	as	ADP
ejde-637	399	4	x−	x−	PROPN
ejde-637	399	5	e	e	PROPN
ejde-637	399	6	=	=	PROPN
ejde-637	399	7	µ6	µ6	PROPN
ejde-637	399	8	,	,	PUNCT
ejde-637	399	9	there	there	PRON
ejde-637	399	10	is	be	VERB
ejde-637	399	11	a	a	DET
ejde-637	399	12	heteroclnic	heteroclnic	ADJ
ejde-637	399	13	orbit	orbit	NOUN
ejde-637	399	14	j4	j4	PROPN
ejde-637	399	15	from	from	ADP
ejde-637	399	16	x−	x−	PROPN
ejde-637	399	17	e	e	PROPN
ejde-637	399	18	to	to	ADP
ejde-637	399	19	x+	x+	PROPN
ejde-637	399	20	e	e	X
ejde-637	399	21	.	.	PUNCT
ejde-637	400	1	as	as	SCONJ
ejde-637	400	2	µ8	µ8	PROPN
ejde-637	400	3	<	<	X
ejde-637	400	4	x−	x−	PROPN
ejde-637	400	5	e	e	PROPN
ejde-637	400	6	<	<	X
ejde-637	400	7	µ3	µ3	PROPN
ejde-637	400	8	,	,	PUNCT
ejde-637	400	9	the	the	DET
ejde-637	400	10	orbits	orbit	NOUN
ejde-637	400	11	of	of	ADP
ejde-637	400	12	⊕-system	⊕-system	NOUN
ejde-637	400	13	starting	start	VERB
ejde-637	400	14	from	from	ADP
ejde-637	400	15	(	(	PUNCT
ejde-637	400	16	0	0	NUM
ejde-637	400	17	,	,	PUNCT
ejde-637	400	18	y−t	y−t	NOUN
ejde-637	400	19	)	)	PUNCT
ejde-637	400	20	will	will	AUX
ejde-637	400	21	arrive	arrive	VERB
ejde-637	400	22	at	at	ADP
ejde-637	400	23	σx	σx	NOUN
ejde-637	400	24	s	s	NUM
ejde-637	400	25	since	since	SCONJ
ejde-637	400	26	y+t	y+t	PROPN
ejde-637	400	27	<	<	X
ejde-637	400	28	0	0	PUNCT
ejde-637	401	1	and	and	CCONJ
ejde-637	401	2	σx	σx	NOUN
ejde-637	401	3	s	s	NOUN
ejde-637	401	4	is	be	AUX
ejde-637	401	5	attractive	attractive	ADJ
ejde-637	401	6	before	before	ADP
ejde-637	401	7	x−	x−	PROPN
ejde-637	401	8	e	e	PROPN
ejde-637	401	9	=	=	NOUN
ejde-637	401	10	µ3	µ3	PROPN
ejde-637	401	11	.	.	PUNCT
ejde-637	402	1	then	then	ADV
ejde-637	402	2	on	on	ADP
ejde-637	402	3	the	the	DET
ejde-637	402	4	one	one	NUM
ejde-637	402	5	hand	hand	NOUN
ejde-637	402	6	,	,	PUNCT
ejde-637	402	7	if	if	SCONJ
ejde-637	402	8	µ8	µ8	PROPN
ejde-637	402	9	<	<	X
ejde-637	402	10	−x+	−x+	X
ejde-637	402	11	e	e	NOUN
ejde-637	402	12	,	,	PUNCT
ejde-637	402	13	for	for	ADP
ejde-637	402	14	µ8	µ8	PROPN
ejde-637	402	15	<	<	X
ejde-637	402	16	x−	x−	PROPN
ejde-637	402	17	e	e	X
ejde-637	402	18	<	<	X
ejde-637	402	19	−x+	−x+	X
ejde-637	402	20	e	e	NOUN
ejde-637	402	21	,	,	PUNCT
ejde-637	402	22	j2	j2	PROPN
ejde-637	402	23	will	will	AUX
ejde-637	402	24	become	become	VERB
ejde-637	402	25	a	a	DET
ejde-637	402	26	sliding	slide	VERB
ejde-637	402	27	cycle	cycle	NOUN
ejde-637	402	28	j21	j21	NOUN
ejde-637	402	29	connecting	connect	VERB
ejde-637	402	30	pey	pey	NOUN
ejde-637	402	31	and	and	CCONJ
ejde-637	402	32	the	the	DET
ejde-637	402	33	non	non	ADJ
ejde-637	402	34	-	-	ADJ
ejde-637	402	35	regular	regular	ADJ
ejde-637	402	36	boundary	boundary	ADJ
ejde-637	402	37	sink	sink	NOUN
ejde-637	402	38	p0	p0	NOUN
ejde-637	402	39	.	.	PUNCT
ejde-637	403	1	then	then	ADV
ejde-637	403	2	j21	j21	PROPN
ejde-637	403	3	will	will	AUX
ejde-637	403	4	turn	turn	VERB
ejde-637	403	5	into	into	ADP
ejde-637	403	6	a	a	DET
ejde-637	403	7	sliding	slide	VERB
ejde-637	403	8	homoclinic	homoclinic	ADJ
ejde-637	403	9	cycle	cycle	NOUN
ejde-637	403	10	j22	j22	NOUN
ejde-637	403	11	as	as	ADP
ejde-637	403	12	x−	x−	PROPN
ejde-637	403	13	e	e	PROPN
ejde-637	403	14	=	=	PUNCT
ejde-637	403	15	−x+	−x+	NUM
ejde-637	403	16	e	e	NOUN
ejde-637	403	17	,	,	PUNCT
ejde-637	403	18	which	which	PRON
ejde-637	403	19	containing	contain	VERB
ejde-637	403	20	the	the	DET
ejde-637	403	21	pseudo	pseudo	NOUN
ejde-637	403	22	-	-	ADJ
ejde-637	403	23	saddle	saddle	NOUN
ejde-637	403	24	-	-	PUNCT
ejde-637	403	25	node	node	NOUN
ejde-637	403	26	pex	pex	NOUN
ejde-637	403	27	=	=	NOUN
ejde-637	403	28	pey	pey	PROPN
ejde-637	403	29	=	=	NOUN
ejde-637	403	30	p0	p0	NOUN
ejde-637	403	31	,	,	PUNCT
ejde-637	403	32	meanwhile	meanwhile	ADV
ejde-637	403	33	,	,	PUNCT
ejde-637	403	34	a	a	DET
ejde-637	403	35	sliding	slide	VERB
ejde-637	403	36	heteroclinic	heteroclinic	ADJ
ejde-637	403	37	orbit	orbit	NOUN
ejde-637	403	38	j5	j5	PROPN
ejde-637	403	39	from	from	ADP
ejde-637	403	40	x+	x+	PROPN
ejde-637	403	41	e	e	NOUN
ejde-637	403	42	to	to	ADP
ejde-637	403	43	pex	pex	PROPN
ejde-637	403	44	occurs	occur	VERB
ejde-637	403	45	,	,	PUNCT
ejde-637	403	46	which	which	PRON
ejde-637	403	47	will	will	AUX
ejde-637	403	48	exist	exist	VERB
ejde-637	403	49	until	until	ADP
ejde-637	403	50	x−	x−	PROPN
ejde-637	403	51	e	e	PROPN
ejde-637	403	52	=	=	PROPN
ejde-637	403	53	min{2µ1+x+	min{2µ1+x+	PROPN
ejde-637	403	54	e	e	NOUN
ejde-637	403	55	,	,	PUNCT
ejde-637	403	56	µ3	µ3	NUM
ejde-637	403	57	}	}	PUNCT
ejde-637	403	58	.	.	PUNCT
ejde-637	404	1	and	and	CCONJ
ejde-637	404	2	j22	j22	PROPN
ejde-637	404	3	will	will	AUX
ejde-637	404	4	turn	turn	VERB
ejde-637	404	5	into	into	ADP
ejde-637	404	6	a	a	DET
ejde-637	404	7	sliding	slide	VERB
ejde-637	404	8	cycle	cycle	NOUN
ejde-637	404	9	j23	j23	NOUN
ejde-637	404	10	connecting	connect	VERB
ejde-637	404	11	pex	pex	PROPN
ejde-637	404	12	and	and	CCONJ
ejde-637	404	13	the	the	DET
ejde-637	404	14	non	non	ADJ
ejde-637	404	15	-	-	ADJ
ejde-637	404	16	regular	regular	ADJ
ejde-637	404	17	boundary	boundary	ADJ
ejde-637	404	18	source	source	NOUN
ejde-637	404	19	p0	p0	NOUN
ejde-637	404	20	as	as	ADV
ejde-637	404	21	long	long	ADV
ejde-637	404	22	as	as	SCONJ
ejde-637	404	23	the	the	DET
ejde-637	404	24	first	first	ADJ
ejde-637	404	25	arriving	arriving	NOUN
ejde-637	404	26	point	point	NOUN
ejde-637	404	27	on	on	ADP
ejde-637	404	28	σx	σx	ADP
ejde-637	404	29	s	s	NOUN
ejde-637	404	30	of	of	ADP
ejde-637	404	31	the	the	DET
ejde-637	404	32	orbit	orbit	NOUN
ejde-637	404	33	of	of	ADP
ejde-637	404	34	⊕-system	⊕-system	NOUN
ejde-637	404	35	starting	start	VERB
ejde-637	404	36	from	from	ADP
ejde-637	404	37	(	(	PUNCT
ejde-637	404	38	0	0	NUM
ejde-637	404	39	,	,	PUNCT
ejde-637	404	40	y−t	y−t	NOUN
ejde-637	404	41	)	)	PUNCT
ejde-637	404	42	is	be	AUX
ejde-637	404	43	on	on	ADP
ejde-637	404	44	the	the	DET
ejde-637	404	45	right	right	NOUN
ejde-637	404	46	of	of	ADP
ejde-637	404	47	pex	pex	PROPN
ejde-637	404	48	.	.	PUNCT
ejde-637	405	1	however	however	ADV
ejde-637	405	2	,	,	PUNCT
ejde-637	405	3	if	if	SCONJ
ejde-637	405	4	µ8	µ8	PROPN
ejde-637	405	5	>	>	PUNCT
ejde-637	405	6	−x+	−x+	X
ejde-637	405	7	e	e	NOUN
ejde-637	405	8	,	,	PUNCT
ejde-637	405	9	j3	j3	PROPN
ejde-637	405	10	can	can	AUX
ejde-637	405	11	only	only	ADV
ejde-637	405	12	becomes	become	VERB
ejde-637	405	13	j23	j23	PROPN
ejde-637	405	14	before	before	ADP
ejde-637	405	15	x−	x−	PROPN
ejde-637	405	16	e	e	PROPN
ejde-637	405	17	=	=	NOUN
ejde-637	405	18	µ3	µ3	PROPN
ejde-637	405	19	.	.	PUNCT
ejde-637	406	1	on	on	ADP
ejde-637	406	2	the	the	DET
ejde-637	406	3	other	other	ADJ
ejde-637	406	4	hand	hand	NOUN
ejde-637	406	5	,	,	PUNCT
ejde-637	406	6	if	if	SCONJ
ejde-637	406	7	µ6	µ6	PROPN
ejde-637	406	8	<	<	X
ejde-637	406	9	−x+	−x+	X
ejde-637	406	10	e	e	X
ejde-637	406	11	<	<	X
ejde-637	406	12	µ2	µ2	PROPN
ejde-637	406	13	,	,	PUNCT
ejde-637	406	14	we	we	PRON
ejde-637	406	15	have	have	VERB
ejde-637	406	16	as	as	ADP
ejde-637	406	17	µ6	µ6	PROPN
ejde-637	406	18	<	<	X
ejde-637	406	19	x−	x−	PROPN
ejde-637	406	20	e	e	X
ejde-637	406	21	<	<	X
ejde-637	406	22	µ2	µ2	PROPN
ejde-637	406	23	,	,	PUNCT
ejde-637	406	24	j4	j4	PROPN
ejde-637	406	25	will	will	AUX
ejde-637	406	26	firstly	firstly	ADV
ejde-637	406	27	become	become	VERB
ejde-637	406	28	a	a	DET
ejde-637	406	29	sliding	slide	VERB
ejde-637	406	30	heteroclinic	heteroclinic	ADJ
ejde-637	406	31	orbit	orbit	NOUN
ejde-637	406	32	j41	j41	NOUN
ejde-637	406	33	from	from	ADP
ejde-637	406	34	x−	x−	PROPN
ejde-637	406	35	e	e	PROPN
ejde-637	406	36	to	to	PART
ejde-637	406	37	pey	pey	VERB
ejde-637	406	38	for	for	ADP
ejde-637	406	39	x−	x−	PROPN
ejde-637	406	40	e	e	PROPN
ejde-637	406	41	<	<	X
ejde-637	406	42	−x+	−x+	X
ejde-637	406	43	e	e	NOUN
ejde-637	406	44	,	,	PUNCT
ejde-637	406	45	then	then	ADV
ejde-637	406	46	j41	j41	NOUN
ejde-637	406	47	will	will	AUX
ejde-637	406	48	become	become	VERB
ejde-637	406	49	a	a	DET
ejde-637	406	50	sliding	slide	VERB
ejde-637	406	51	heteroclinic	heteroclinic	ADJ
ejde-637	406	52	orbit	orbit	NOUN
ejde-637	406	53	j42	j42	PROPN
ejde-637	406	54	from	from	ADP
ejde-637	406	55	x−	x−	PROPN
ejde-637	406	56	e	e	PROPN
ejde-637	406	57	to	to	ADP
ejde-637	406	58	pex	pex	PROPN
ejde-637	406	59	for	for	ADP
ejde-637	406	60	x−	x−	PROPN
ejde-637	406	61	e	e	PROPN
ejde-637	406	62	≥	≥	X
ejde-637	406	63	−x+	−x+	X
ejde-637	406	64	e	e	NOUN
ejde-637	406	65	,	,	PUNCT
ejde-637	406	66	which	which	PRON
ejde-637	406	67	will	will	AUX
ejde-637	406	68	persist	persist	VERB
ejde-637	406	69	until	until	ADP
ejde-637	406	70	x−	x−	PROPN
ejde-637	406	71	e	e	PROPN
ejde-637	406	72	=	=	PROPN
ejde-637	406	73	min{2µ1	min{2µ1	PROPN
ejde-637	406	74	+	+	CCONJ
ejde-637	406	75	x+	x+	PROPN
ejde-637	406	76	e	e	X
ejde-637	406	77	,	,	PUNCT
ejde-637	406	78	µ3	µ3	PROPN
ejde-637	406	79	}	}	PUNCT
ejde-637	406	80	;	;	PUNCT
ejde-637	406	81	if	if	SCONJ
ejde-637	406	82	−x+	−x+	X
ejde-637	406	83	e	e	X
ejde-637	406	84	<	<	X
ejde-637	406	85	min{µ6	min{µ6	NUM
ejde-637	406	86	,	,	PUNCT
ejde-637	406	87	µ2	µ2	PROPN
ejde-637	406	88	}	}	PUNCT
ejde-637	406	89	,	,	PUNCT
ejde-637	406	90	we	we	PRON
ejde-637	406	91	obtain	obtain	VERB
ejde-637	406	92	that	that	SCONJ
ejde-637	406	93	j4	j4	PROPN
ejde-637	406	94	will	will	AUX
ejde-637	406	95	only	only	ADV
ejde-637	406	96	become	become	VERB
ejde-637	406	97	j42	j42	ADJ
ejde-637	406	98	.	.	PUNCT
ejde-637	407	1	(	(	PUNCT
ejde-637	407	2	b	b	X
ejde-637	407	3	)	)	PUNCT
ejde-637	407	4	in	in	ADP
ejde-637	407	5	this	this	DET
ejde-637	407	6	case	case	NOUN
ejde-637	407	7	,	,	PUNCT
ejde-637	407	8	we	we	PRON
ejde-637	407	9	know	know	VERB
ejde-637	407	10	y+t	y+t	PROPN
ejde-637	407	11	>	>	X
ejde-637	407	12	0	0	PUNCT
ejde-637	408	1	by	by	ADP
ejde-637	408	2	(	(	PUNCT
ejde-637	408	3	3.9	3.9	NUM
ejde-637	408	4	)	)	PUNCT
ejde-637	408	5	.	.	PUNCT
ejde-637	409	1	in	in	ADP
ejde-637	409	2	addition	addition	NOUN
ejde-637	409	3	,	,	PUNCT
ejde-637	409	4	we	we	PRON
ejde-637	409	5	obtain	obtain	VERB
ejde-637	409	6	that	that	DET
ejde-637	409	7	y+m2	y+m2	PROPN
ejde-637	409	8	>	>	X
ejde-637	409	9	y+e	y+e	NUM
ejde-637	409	10	>	>	X
ejde-637	409	11	y+t	y+t	PROPN
ejde-637	409	12	>	>	X
ejde-637	409	13	0	0	PUNCT
ejde-637	409	14	>	>	X
ejde-637	409	15	y+m1	y+m1	PROPN
ejde-637	409	16	,	,	PUNCT
ejde-637	409	17	y−m1	y−m1	PROPN
ejde-637	409	18	>	>	X
ejde-637	409	19	y−t	y−t	PROPN
ejde-637	409	20	<	<	X
ejde-637	409	21	y−m2	y−m2	NUM
ejde-637	409	22	.	.	PUNCT
ejde-637	410	1	then	then	ADV
ejde-637	410	2	since	since	SCONJ
ejde-637	410	3	y−t	y−t	NOUN
ejde-637	410	4	decreases	decrease	VERB
ejde-637	410	5	with	with	ADP
ejde-637	410	6	respect	respect	NOUN
ejde-637	410	7	to	to	ADP
ejde-637	410	8	x−	x−	PROPN
ejde-637	410	9	e	e	PROPN
ejde-637	410	10	,	,	PUNCT
ejde-637	410	11	we	we	PRON
ejde-637	410	12	obtain	obtain	VERB
ejde-637	410	13	µ8	µ8	ADJ
ejde-637	410	14	<	<	X
ejde-637	410	15	2µ2+x+	2µ2+x+	NUM
ejde-637	410	16	e	e	NOUN
ejde-637	410	17	<	<	X
ejde-637	410	18	µ2	µ2	PROPN
ejde-637	410	19	directly	directly	ADV
ejde-637	410	20	by	by	ADP
ejde-637	410	21	(	(	PUNCT
ejde-637	410	22	3.8	3.8	NUM
ejde-637	410	23	)	)	PUNCT
ejde-637	410	24	and	and	CCONJ
ejde-637	410	25	(	(	PUNCT
ejde-637	410	26	3.18	3.18	NUM
ejde-637	410	27	)	)	PUNCT
ejde-637	410	28	.	.	PUNCT
ejde-637	411	1	note	note	VERB
ejde-637	411	2	that	that	SCONJ
ejde-637	411	3	µ2	µ2	PROPN
ejde-637	411	4	<	<	X
ejde-637	411	5	−x+	−x+	PRON
ejde-637	411	6	e	e	X
ejde-637	411	7	by	by	ADP
ejde-637	411	8	(	(	PUNCT
ejde-637	411	9	3.16	3.16	NUM
ejde-637	411	10	)	)	PUNCT
ejde-637	411	11	.	.	PUNCT
ejde-637	412	1	so	so	ADV
ejde-637	412	2	by	by	ADP
ejde-637	412	3	theorem	theorem	NOUN
ejde-637	412	4	3.4	3.4	NUM
ejde-637	412	5	,	,	PUNCT
ejde-637	412	6	we	we	PRON
ejde-637	412	7	obtain	obtain	VERB
ejde-637	412	8	µ8	µ8	PROPN
ejde-637	412	9	<	<	X
ejde-637	412	10	2µ2	2µ2	NUM
ejde-637	413	1	+	+	CCONJ
ejde-637	413	2	x+	x+	ADJ
ejde-637	413	3	e	e	X
ejde-637	413	4	<	<	X
ejde-637	413	5	µ2	µ2	PROPN
ejde-637	413	6	<	<	X
ejde-637	413	7	−x+	−x+	X
ejde-637	413	8	e	e	X
ejde-637	413	9	<	<	X
ejde-637	413	10	0	0	PUNCT
ejde-637	413	11	<	<	X
ejde-637	413	12	max{2µ1	max{2µ1	PROPN
ejde-637	413	13	+	+	CCONJ
ejde-637	413	14	x+	x+	PROPN
ejde-637	413	15	e	e	X
ejde-637	413	16	,	,	PUNCT
ejde-637	413	17	µ3	µ3	NUM
ejde-637	413	18	}	}	PUNCT
ejde-637	413	19	<	<	X
ejde-637	413	20	µ4	µ4	PROPN
ejde-637	413	21	<	<	X
ejde-637	413	22	µ5	µ5	PROPN
ejde-637	413	23	.	.	PUNCT
ejde-637	414	1	ejde-2024/57	ejde-2024/57	NOUN
ejde-637	414	2	planar	planar	VERB
ejde-637	414	3	sector	sector	NOUN
ejde-637	414	4	-	-	PUNCT
ejde-637	414	5	wise	wise	ADJ
ejde-637	414	6	linear	linear	NOUN
ejde-637	414	7	systems	system	NOUN
ejde-637	414	8	15	15	NUM
ejde-637	414	9	by	by	ADP
ejde-637	414	10	(	(	PUNCT
ejde-637	414	11	3.8	3.8	NUM
ejde-637	414	12	)	)	PUNCT
ejde-637	414	13	and	and	CCONJ
ejde-637	414	14	(	(	PUNCT
ejde-637	414	15	3.18	3.18	NUM
ejde-637	414	16	)	)	PUNCT
ejde-637	414	17	,	,	PUNCT
ejde-637	414	18	it	it	PRON
ejde-637	414	19	easy	easy	ADJ
ejde-637	414	20	to	to	PART
ejde-637	414	21	see	see	VERB
ejde-637	414	22	that	that	SCONJ
ejde-637	414	23	µ8	µ8	PROPN
ejde-637	414	24	<	<	X
ejde-637	414	25	µ6	µ6	PROPN
ejde-637	414	26	<	<	X
ejde-637	414	27	µ7	µ7	PROPN
ejde-637	414	28	and	and	CCONJ
ejde-637	414	29	2µ3+x+	2µ3+x+	NUM
ejde-637	414	30	e	e	NOUN
ejde-637	414	31	<	<	X
ejde-637	414	32	µ7	µ7	PROPN
ejde-637	414	33	.	.	PUNCT
ejde-637	415	1	however	however	ADV
ejde-637	415	2	,	,	PUNCT
ejde-637	415	3	the	the	DET
ejde-637	415	4	signs	sign	NOUN
ejde-637	415	5	of	of	ADP
ejde-637	415	6	µ7	µ7	PROPN
ejde-637	415	7	−	−	PROPN
ejde-637	415	8	(	(	PUNCT
ejde-637	415	9	−x+	−x+	NOUN
ejde-637	415	10	e	e	NOUN
ejde-637	415	11	)	)	PUNCT
ejde-637	415	12	and	and	CCONJ
ejde-637	415	13	µ2	µ2	PROPN
ejde-637	415	14	−	−	PROPN
ejde-637	415	15	µ6	µ6	PROPN
ejde-637	415	16	in	in	ADP
ejde-637	415	17	this	this	DET
ejde-637	415	18	case	case	NOUN
ejde-637	415	19	are	be	AUX
ejde-637	415	20	not	not	PART
ejde-637	415	21	sure	sure	ADJ
ejde-637	415	22	by	by	ADP
ejde-637	415	23	(	(	PUNCT
ejde-637	415	24	4.3	4.3	NUM
ejde-637	415	25	)	)	PUNCT
ejde-637	415	26	and	and	CCONJ
ejde-637	415	27	(	(	PUNCT
ejde-637	415	28	4.4	4.4	NUM
ejde-637	415	29	)	)	PUNCT
ejde-637	415	30	,	,	PUNCT
ejde-637	415	31	respectively	respectively	ADV
ejde-637	415	32	.	.	PUNCT
ejde-637	416	1	and	and	CCONJ
ejde-637	416	2	by	by	ADP
ejde-637	416	3	easy	easy	ADJ
ejde-637	416	4	computation	computation	NOUN
ejde-637	416	5	,	,	PUNCT
ejde-637	416	6	we	we	PRON
ejde-637	416	7	obtain	obtain	VERB
ejde-637	416	8	that	that	PRON
ejde-637	416	9	2µ2	2µ2	NUM
ejde-637	417	1	+	+	CCONJ
ejde-637	417	2	x+	x+	ADJ
ejde-637	417	3	e	e	NOUN
ejde-637	417	4	−	−	PROPN
ejde-637	417	5	µ6	µ6	NOUN
ejde-637	417	6	=	=	SYM
ejde-637	417	7	λ1	λ1	PROPN
ejde-637	417	8	−	−	PROPN
ejde-637	417	9	λ2	λ2	PROPN
ejde-637	417	10	λ1	λ1	PROPN
ejde-637	417	11	−	−	PROPN
ejde-637	417	12	a11	a11	PROPN
ejde-637	417	13	x+	x+	PROPN
ejde-637	418	1	e	e	X
ejde-637	418	2	+	+	CCONJ
ejde-637	418	3	2a12λ1	2a12λ1	NUM
ejde-637	418	4	a11(λ1	a11(λ1	PROPN
ejde-637	418	5	−	−	PROPN
ejde-637	418	6	a11	a11	PROPN
ejde-637	418	7	)	)	PUNCT
ejde-637	418	8	y+e	y+e	PROPN
ejde-637	418	9	,	,	PUNCT
ejde-637	418	10	which	which	PRON
ejde-637	418	11	implies	imply	VERB
ejde-637	418	12	2µ2	2µ2	NUM
ejde-637	419	1	+	+	CCONJ
ejde-637	419	2	x+	x+	ADJ
ejde-637	419	3	e	e	X
ejde-637	419	4	<	<	X
ejde-637	419	5	µ6	µ6	PROPN
ejde-637	419	6	and	and	CCONJ
ejde-637	419	7	2µ2	2µ2	NUM
ejde-637	419	8	+	+	CCONJ
ejde-637	419	9	x+	x+	ADJ
ejde-637	419	10	e	e	X
ejde-637	419	11	>	>	X
ejde-637	419	12	µ6	µ6	PROPN
ejde-637	419	13	both	both	PRON
ejde-637	419	14	may	may	AUX
ejde-637	419	15	be	be	AUX
ejde-637	419	16	true	true	ADJ
ejde-637	419	17	.	.	PUNCT
ejde-637	420	1	by	by	ADP
ejde-637	420	2	propositions	proposition	NOUN
ejde-637	420	3	3.1	3.1	NUM
ejde-637	420	4	,	,	PUNCT
ejde-637	420	5	3.2	3.2	NUM
ejde-637	420	6	and	and	CCONJ
ejde-637	420	7	3.3	3.3	NUM
ejde-637	420	8	,	,	PUNCT
ejde-637	420	9	and	and	CCONJ
ejde-637	420	10	remark	remark	VERB
ejde-637	420	11	2.6	2.6	NUM
ejde-637	420	12	,	,	PUNCT
ejde-637	420	13	we	we	PRON
ejde-637	420	14	see	see	VERB
ejde-637	420	15	that	that	SCONJ
ejde-637	420	16	there	there	PRON
ejde-637	420	17	is	be	VERB
ejde-637	420	18	no	no	DET
ejde-637	420	19	special	special	ADJ
ejde-637	420	20	separatrixes	separatrix	NOUN
ejde-637	420	21	as	as	ADP
ejde-637	420	22	x−	x−	PROPN
ejde-637	420	23	e	e	PROPN
ejde-637	420	24	<	<	X
ejde-637	420	25	µ8	µ8	PROPN
ejde-637	420	26	.	.	PUNCT
ejde-637	421	1	as	as	ADP
ejde-637	421	2	x−	x−	PROPN
ejde-637	421	3	e	e	PROPN
ejde-637	421	4	=	=	PROPN
ejde-637	421	5	µ8	µ8	PROPN
ejde-637	421	6	,	,	PUNCT
ejde-637	421	7	there	there	PRON
ejde-637	421	8	exists	exist	VERB
ejde-637	421	9	a	a	DET
ejde-637	421	10	sliding	slide	VERB
ejde-637	421	11	heteroclinic	heteroclinic	ADJ
ejde-637	421	12	orbit	orbit	NOUN
ejde-637	421	13	from	from	ADP
ejde-637	421	14	pey	pey	NOUN
ejde-637	421	15	to	to	ADP
ejde-637	421	16	x+	x+	PROPN
ejde-637	421	17	e	e	X
ejde-637	421	18	.	.	PUNCT
ejde-637	422	1	in	in	ADP
ejde-637	422	2	addition	addition	NOUN
ejde-637	422	3	,	,	PUNCT
ejde-637	422	4	it	it	PRON
ejde-637	422	5	is	be	AUX
ejde-637	422	6	obvious	obvious	ADJ
ejde-637	422	7	that	that	SCONJ
ejde-637	422	8	a	a	DET
ejde-637	422	9	heteroclinic	heteroclinic	ADJ
ejde-637	422	10	orbit	orbit	NOUN
ejde-637	422	11	from	from	ADP
ejde-637	422	12	x−	x−	PROPN
ejde-637	422	13	e	e	PROPN
ejde-637	422	14	to	to	ADP
ejde-637	422	15	x+	x+	PROPN
ejde-637	422	16	e	e	PROPN
ejde-637	422	17	appears	appear	VERB
ejde-637	422	18	as	as	ADP
ejde-637	422	19	x−	x−	PROPN
ejde-637	422	20	e	e	PROPN
ejde-637	422	21	=	=	PROPN
ejde-637	422	22	µ6	µ6	PROPN
ejde-637	422	23	.	.	PUNCT
ejde-637	423	1	furthermore	furthermore	ADV
ejde-637	423	2	,	,	PUNCT
ejde-637	423	3	as	as	ADP
ejde-637	423	4	x−	x−	PROPN
ejde-637	423	5	e	e	PROPN
ejde-637	423	6	>	>	X
ejde-637	423	7	max{µ6	max{µ6	NOUN
ejde-637	423	8	,	,	PUNCT
ejde-637	423	9	µ2	µ2	PROPN
ejde-637	423	10	}	}	PUNCT
ejde-637	423	11	,	,	PUNCT
ejde-637	423	12	the	the	DET
ejde-637	423	13	orbit	orbit	NOUN
ejde-637	423	14	of	of	ADP
ejde-637	423	15	⊕-system	⊕-system	NOUN
ejde-637	423	16	starting	start	VERB
ejde-637	423	17	from	from	ADP
ejde-637	423	18	y−	y−	NOUN
ejde-637	423	19	m1	m1	PROPN
ejde-637	423	20	will	will	AUX
ejde-637	423	21	arrive	arrive	VERB
ejde-637	423	22	σs	σs	ADP
ejde-637	423	23	.	.	PROPN
ejde-637	424	1	thus	thus	ADV
ejde-637	424	2	there	there	PRON
ejde-637	424	3	will	will	AUX
ejde-637	424	4	exist	exist	VERB
ejde-637	424	5	a	a	DET
ejde-637	424	6	sliding	slide	VERB
ejde-637	424	7	heteroclinic	heteroclinic	ADJ
ejde-637	424	8	orbit	orbit	NOUN
ejde-637	424	9	from	from	ADP
ejde-637	424	10	x−	x−	PROPN
ejde-637	424	11	e	e	PROPN
ejde-637	424	12	to	to	ADP
ejde-637	424	13	pey	pey	VERB
ejde-637	424	14	if	if	SCONJ
ejde-637	424	15	x−	x−	PROPN
ejde-637	424	16	e	e	PROPN
ejde-637	424	17	<	<	X
ejde-637	424	18	−x+	−x+	X
ejde-637	424	19	e	e	NOUN
ejde-637	424	20	,	,	PUNCT
ejde-637	424	21	or	or	CCONJ
ejde-637	424	22	from	from	ADP
ejde-637	424	23	x−	x−	PROPN
ejde-637	424	24	e	e	PROPN
ejde-637	424	25	to	to	ADP
ejde-637	424	26	pex	pex	PROPN
ejde-637	424	27	if	if	SCONJ
ejde-637	424	28	x−	x−	PROPN
ejde-637	424	29	e	e	PROPN
ejde-637	424	30	≥	≥	X
ejde-637	424	31	−x+	−x+	X
ejde-637	424	32	e	e	NOUN
ejde-637	424	33	until	until	ADP
ejde-637	424	34	x−	x−	PROPN
ejde-637	424	35	e	e	PROPN
ejde-637	424	36	=	=	PROPN
ejde-637	424	37	min{2µ1+x+	min{2µ1+x+	PROPN
ejde-637	424	38	e	e	NOUN
ejde-637	424	39	,	,	PUNCT
ejde-637	424	40	µ3	µ3	NUM
ejde-637	424	41	}	}	PUNCT
ejde-637	424	42	.	.	PUNCT
ejde-637	425	1	in	in	ADP
ejde-637	425	2	addition	addition	NOUN
ejde-637	425	3	to	to	ADP
ejde-637	425	4	this	this	PRON
ejde-637	425	5	,	,	PUNCT
ejde-637	425	6	when	when	SCONJ
ejde-637	425	7	x−	x−	PROPN
ejde-637	425	8	e	e	PROPN
ejde-637	425	9	<	<	X
ejde-637	425	10	2µ2	2µ2	NUM
ejde-637	425	11	+	+	CCONJ
ejde-637	425	12	x+	x+	ADJ
ejde-637	425	13	e	e	X
ejde-637	425	14	,	,	PUNCT
ejde-637	425	15	we	we	PRON
ejde-637	425	16	have	have	VERB
ejde-637	425	17	y−t	y−t	NOUN
ejde-637	425	18	>	>	X
ejde-637	425	19	y+t	y+t	PROPN
ejde-637	425	20	>	>	X
ejde-637	425	21	0	0	PROPN
ejde-637	425	22	,	,	PUNCT
ejde-637	425	23	then	then	ADV
ejde-637	425	24	let	let	VERB
ejde-637	425	25	y1	y1	NOUN
ejde-637	425	26	=	=	SYM
ejde-637	425	27	(	(	PUNCT
ejde-637	425	28	0	0	NUM
ejde-637	425	29	,	,	PUNCT
ejde-637	425	30	y1	y1	NOUN
ejde-637	425	31	)	)	PUNCT
ejde-637	425	32	and	and	CCONJ
ejde-637	425	33	y2	y2	NOUN
ejde-637	425	34	=	=	SYM
ejde-637	425	35	(	(	PUNCT
ejde-637	425	36	0	0	NUM
ejde-637	425	37	,	,	PUNCT
ejde-637	425	38	y2	y2	PROPN
ejde-637	425	39	)	)	PUNCT
ejde-637	425	40	be	be	AUX
ejde-637	425	41	the	the	DET
ejde-637	425	42	first	first	ADJ
ejde-637	425	43	arriving	arriving	NOUN
ejde-637	425	44	point	point	NOUN
ejde-637	425	45	on	on	ADP
ejde-637	425	46	the	the	DET
ejde-637	425	47	positive	positive	ADJ
ejde-637	425	48	y	y	NOUN
ejde-637	425	49	-	-	PUNCT
ejde-637	425	50	axis	axis	NOUN
ejde-637	425	51	of	of	ADP
ejde-637	425	52	the	the	DET
ejde-637	425	53	forward	forward	ADJ
ejde-637	425	54	orbits	orbit	NOUN
ejde-637	425	55	of	of	ADP
ejde-637	425	56	⊖-system	⊖-system	NOUN
ejde-637	425	57	starting	start	VERB
ejde-637	425	58	from	from	ADP
ejde-637	425	59	y+	y+	PROPN
ejde-637	425	60	t	t	PROPN
ejde-637	425	61	and	and	CCONJ
ejde-637	425	62	pey	pey	NOUN
ejde-637	425	63	,	,	PUNCT
ejde-637	425	64	respectively	respectively	ADV
ejde-637	425	65	.	.	PUNCT
ejde-637	426	1	and	and	CCONJ
ejde-637	426	2	when	when	SCONJ
ejde-637	426	3	x−	x−	PROPN
ejde-637	426	4	e	e	PROPN
ejde-637	426	5	<	<	X
ejde-637	426	6	µ2	µ2	PROPN
ejde-637	426	7	,	,	PUNCT
ejde-637	426	8	denote	denote	VERB
ejde-637	426	9	by	by	ADP
ejde-637	426	10	y−	y−	NOUN
ejde-637	426	11	=	=	SYM
ejde-637	426	12	(	(	PUNCT
ejde-637	426	13	0	0	NUM
ejde-637	426	14	,	,	PUNCT
ejde-637	426	15	y−	y−	NOUN
ejde-637	426	16	)	)	PUNCT
ejde-637	426	17	and	and	CCONJ
ejde-637	426	18	y+	y+	NUM
ejde-637	426	19	=	=	SYM
ejde-637	426	20	(	(	PUNCT
ejde-637	426	21	0	0	NUM
ejde-637	426	22	,	,	PUNCT
ejde-637	426	23	y+	y+	NOUN
ejde-637	426	24	)	)	PUNCT
ejde-637	426	25	the	the	DET
ejde-637	426	26	first	first	ADJ
ejde-637	426	27	arriving	arriving	NOUN
ejde-637	426	28	point	point	NOUN
ejde-637	426	29	on	on	ADP
ejde-637	426	30	the	the	DET
ejde-637	426	31	positive	positive	ADJ
ejde-637	426	32	y	y	NOUN
ejde-637	426	33	-	-	PUNCT
ejde-637	426	34	axis	axis	NOUN
ejde-637	426	35	of	of	ADP
ejde-637	426	36	the	the	DET
ejde-637	426	37	forward	forward	ADJ
ejde-637	426	38	and	and	CCONJ
ejde-637	426	39	backward	backward	ADJ
ejde-637	426	40	orbits	orbit	NOUN
ejde-637	426	41	of	of	ADP
ejde-637	426	42	⊖-system	⊖-system	NOUN
ejde-637	426	43	and	and	CCONJ
ejde-637	426	44	⊕-system	⊕-system	NOUN
ejde-637	426	45	with	with	ADP
ejde-637	426	46	initial	initial	ADJ
ejde-637	426	47	condition	condition	NOUN
ejde-637	426	48	p0	p0	NOUN
ejde-637	426	49	,	,	PUNCT
ejde-637	426	50	respectively	respectively	ADV
ejde-637	426	51	.	.	PUNCT
ejde-637	427	1	then	then	ADV
ejde-637	427	2	when	when	SCONJ
ejde-637	427	3	x−	x−	PROPN
ejde-637	427	4	e	e	PROPN
ejde-637	427	5	<	<	X
ejde-637	427	6	2µ2	2µ2	NUM
ejde-637	427	7	+	+	CCONJ
ejde-637	427	8	x+	x+	ADJ
ejde-637	427	9	e	e	X
ejde-637	427	10	<	<	X
ejde-637	427	11	µ2	µ2	PROPN
ejde-637	427	12	,	,	PUNCT
ejde-637	427	13	we	we	PRON
ejde-637	427	14	must	must	AUX
ejde-637	427	15	have	have	VERB
ejde-637	427	16	y−m1	y−m1	NOUN
ejde-637	427	17	>	>	X
ejde-637	427	18	y−	y−	X
ejde-637	427	19	>	>	X
ejde-637	427	20	y1	y1	INTJ
ejde-637	427	21	>	>	X
ejde-637	427	22	y2	y2	PROPN
ejde-637	427	23	.	.	PUNCT
ejde-637	428	1	since	since	SCONJ
ejde-637	428	2	y+	y+	PROPN
ejde-637	428	3	=	=	SYM
ejde-637	428	4	(	(	PUNCT
ejde-637	428	5	0	0	NUM
ejde-637	428	6	,	,	PUNCT
ejde-637	428	7	y+	y+	NUM
ejde-637	428	8	)	)	PUNCT
ejde-637	428	9	and	and	CCONJ
ejde-637	428	10	y+	y+	NUM
ejde-637	428	11	m2	m2	PROPN
ejde-637	428	12	=	=	SYM
ejde-637	428	13	(	(	PUNCT
ejde-637	428	14	0	0	NUM
ejde-637	428	15	,	,	PUNCT
ejde-637	428	16	y+m2	y+m2	NOUN
ejde-637	428	17	)	)	PUNCT
ejde-637	428	18	will	will	AUX
ejde-637	428	19	not	not	PART
ejde-637	428	20	change	change	VERB
ejde-637	428	21	with	with	ADP
ejde-637	428	22	the	the	DET
ejde-637	428	23	value	value	NOUN
ejde-637	428	24	of	of	ADP
ejde-637	428	25	x−	x−	PROPN
ejde-637	428	26	e	e	PROPN
ejde-637	428	27	,	,	PUNCT
ejde-637	428	28	moreover	moreover	ADV
ejde-637	428	29	,	,	PUNCT
ejde-637	428	30	y+m2	y+m2	INTJ
ejde-637	428	31	>	>	X
ejde-637	428	32	y+	y+	NOUN
ejde-637	428	33	,	,	PUNCT
ejde-637	428	34	so	so	SCONJ
ejde-637	428	35	there	there	PRON
ejde-637	428	36	must	must	AUX
ejde-637	428	37	be	be	AUX
ejde-637	428	38	ξ1	ξ1	PROPN
ejde-637	428	39	<	<	X
ejde-637	428	40	ξ2	ξ2	PROPN
ejde-637	428	41	,	,	PUNCT
ejde-637	428	42	ξ1	ξ1	NOUN
ejde-637	428	43	<	<	X
ejde-637	428	44	µ6	µ6	PROPN
ejde-637	428	45	,	,	PUNCT
ejde-637	428	46	ξ2	ξ2	NOUN
ejde-637	428	47	<	<	X
ejde-637	428	48	µ7	µ7	PROPN
ejde-637	428	49	such	such	ADJ
ejde-637	428	50	that	that	SCONJ
ejde-637	428	51	y−	y−	NOUN
ejde-637	428	52	=	=	SYM
ejde-637	428	53	y+m2	y+m2	PROPN
ejde-637	428	54	,	,	PUNCT
ejde-637	428	55	if	if	SCONJ
ejde-637	428	56	x−	x−	PROPN
ejde-637	428	57	e	e	PROPN
ejde-637	428	58	=	=	PROPN
ejde-637	428	59	ξ1	ξ1	PROPN
ejde-637	428	60	;	;	PUNCT
ejde-637	428	61	y−	y−	X
ejde-637	428	62	=	=	SYM
ejde-637	428	63	y+	y+	PROPN
ejde-637	428	64	,	,	PUNCT
ejde-637	429	1	if	if	SCONJ
ejde-637	429	2	x−	x−	PROPN
ejde-637	429	3	e	e	PROPN
ejde-637	429	4	=	=	PROPN
ejde-637	429	5	ξ2	ξ2	PROPN
ejde-637	429	6	.	.	PUNCT
ejde-637	430	1	this	this	DET
ejde-637	430	2	mean	mean	VERB
ejde-637	430	3	there	there	PRON
ejde-637	430	4	exist	exist	VERB
ejde-637	430	5	a	a	DET
ejde-637	430	6	sliding	slide	VERB
ejde-637	430	7	homoclinic	homoclinic	ADJ
ejde-637	430	8	cycle	cycle	NOUN
ejde-637	430	9	containing	contain	VERB
ejde-637	430	10	x+	x+	PROPN
ejde-637	430	11	e	e	NOUN
ejde-637	430	12	called	call	VERB
ejde-637	430	13	h1	h1	PROPN
ejde-637	430	14	and	and	CCONJ
ejde-637	430	15	a	a	DET
ejde-637	430	16	sliding	sliding	ADJ
ejde-637	430	17	-	-	PUNCT
ejde-637	430	18	zero	zero	NUM
ejde-637	430	19	cycle	cycle	NOUN
ejde-637	430	20	containing	contain	VERB
ejde-637	430	21	p0	p0	NOUN
ejde-637	430	22	called	call	VERB
ejde-637	430	23	h2	h2	PROPN
ejde-637	430	24	as	as	ADP
ejde-637	430	25	x−	x−	PROPN
ejde-637	430	26	e	e	PROPN
ejde-637	430	27	=	=	PROPN
ejde-637	430	28	ξ1	ξ1	PROPN
ejde-637	430	29	and	and	CCONJ
ejde-637	430	30	x−	x−	PROPN
ejde-637	430	31	e	e	PROPN
ejde-637	430	32	=	=	PROPN
ejde-637	430	33	ξ2	ξ2	PROPN
ejde-637	430	34	,	,	PUNCT
ejde-637	430	35	respectively	respectively	ADV
ejde-637	430	36	.	.	PUNCT
ejde-637	431	1	apart	apart	ADV
ejde-637	431	2	from	from	ADP
ejde-637	431	3	this	this	PRON
ejde-637	431	4	,	,	PUNCT
ejde-637	431	5	one	one	NUM
ejde-637	431	6	the	the	DET
ejde-637	431	7	one	one	NUM
ejde-637	431	8	hand	hand	NOUN
ejde-637	431	9	,	,	PUNCT
ejde-637	431	10	if	if	SCONJ
ejde-637	431	11	µ6	µ6	PROPN
ejde-637	431	12	<	<	X
ejde-637	431	13	2µ2	2µ2	NUM
ejde-637	431	14	+	+	CCONJ
ejde-637	431	15	x+	x+	ADJ
ejde-637	431	16	e	e	X
ejde-637	431	17	<	<	X
ejde-637	431	18	µ2	µ2	PROPN
ejde-637	431	19	,	,	PUNCT
ejde-637	431	20	there	there	PRON
ejde-637	431	21	must	must	AUX
ejde-637	431	22	be	be	AUX
ejde-637	431	23	ξ11	ξ11	PROPN
ejde-637	431	24	<	<	X
ejde-637	431	25	ξ12	ξ12	VERB
ejde-637	431	26	<	<	X
ejde-637	431	27	ξ1	ξ1	NOUN
ejde-637	431	28	,	,	PUNCT
ejde-637	431	29	such	such	ADJ
ejde-637	431	30	that	that	SCONJ
ejde-637	431	31	y1	y1	NOUN
ejde-637	431	32	=	=	SYM
ejde-637	431	33	y+m2	y+m2	PROPN
ejde-637	431	34	,	,	PUNCT
ejde-637	431	35	if	if	SCONJ
ejde-637	431	36	x−	x−	PROPN
ejde-637	431	37	e	e	PROPN
ejde-637	431	38	=	=	PROPN
ejde-637	431	39	ξ11	ξ11	NOUN
ejde-637	431	40	;	;	PUNCT
ejde-637	431	41	y2	y2	PROPN
ejde-637	431	42	=	=	SYM
ejde-637	431	43	y+m2	y+m2	PROPN
ejde-637	431	44	,	,	PUNCT
ejde-637	431	45	if	if	SCONJ
ejde-637	431	46	x−	x−	PROPN
ejde-637	431	47	e	e	PROPN
ejde-637	431	48	=	=	PROPN
ejde-637	431	49	ξ12	ξ12	PROPN
ejde-637	431	50	,	,	PUNCT
ejde-637	431	51	which	which	PRON
ejde-637	431	52	mean	mean	VERB
ejde-637	431	53	there	there	PRON
ejde-637	431	54	both	both	PRON
ejde-637	431	55	appears	appear	VERB
ejde-637	431	56	a	a	DET
ejde-637	431	57	sliding	slide	VERB
ejde-637	431	58	heteroclinc	heteroclinc	NOUN
ejde-637	431	59	orbit	orbit	NOUN
ejde-637	431	60	h3	h3	NOUN
ejde-637	431	61	from	from	ADP
ejde-637	431	62	pey	pey	NOUN
ejde-637	431	63	to	to	ADP
ejde-637	431	64	x+	x+	PROPN
ejde-637	431	65	e	e	PROPN
ejde-637	431	66	as	as	ADP
ejde-637	431	67	x−	x−	PROPN
ejde-637	431	68	e	e	PROPN
ejde-637	431	69	=	=	PROPN
ejde-637	431	70	ξ11	ξ11	PROPN
ejde-637	431	71	and	and	CCONJ
ejde-637	432	1	x−	x−	PROPN
ejde-637	432	2	e	e	PROPN
ejde-637	432	3	=	=	PROPN
ejde-637	432	4	ξ12	ξ12	NOUN
ejde-637	432	5	,	,	PUNCT
ejde-637	432	6	that	that	PRON
ejde-637	432	7	is	be	AUX
ejde-637	432	8	h3	h3	NOUN
ejde-637	432	9	and	and	CCONJ
ejde-637	432	10	h1	h1	PROPN
ejde-637	432	11	will	will	AUX
ejde-637	432	12	appear	appear	VERB
ejde-637	432	13	in	in	ADP
ejde-637	432	14	turn	turn	NOUN
ejde-637	432	15	before	before	ADP
ejde-637	432	16	x−	x−	PROPN
ejde-637	432	17	e	e	PROPN
ejde-637	432	18	=	=	NOUN
ejde-637	432	19	µ6	µ6	PROPN
ejde-637	432	20	;	;	PUNCT
ejde-637	432	21	if	if	SCONJ
ejde-637	432	22	2µ2	2µ2	NUM
ejde-637	432	23	+	+	CCONJ
ejde-637	432	24	x+	x+	ADJ
ejde-637	432	25	e	e	X
ejde-637	432	26	<	<	X
ejde-637	432	27	µ6	µ6	PROPN
ejde-637	432	28	<	<	X
ejde-637	432	29	µ2	µ2	PROPN
ejde-637	432	30	,	,	PUNCT
ejde-637	432	31	it	it	PRON
ejde-637	432	32	is	be	AUX
ejde-637	432	33	easy	easy	ADJ
ejde-637	432	34	to	to	PART
ejde-637	432	35	see	see	VERB
ejde-637	432	36	only	only	ADV
ejde-637	432	37	h1	h1	PROPN
ejde-637	432	38	will	will	AUX
ejde-637	432	39	appear	appear	VERB
ejde-637	432	40	before	before	ADP
ejde-637	432	41	x−	x−	PROPN
ejde-637	432	42	e	e	PROPN
ejde-637	432	43	=	=	NOUN
ejde-637	432	44	µ6	µ6	PROPN
ejde-637	432	45	;	;	PUNCT
ejde-637	432	46	if	if	SCONJ
ejde-637	432	47	2µ2	2µ2	NUM
ejde-637	432	48	+	+	CCONJ
ejde-637	432	49	x+	x+	ADJ
ejde-637	432	50	e	e	X
ejde-637	432	51	<	<	X
ejde-637	432	52	µ2	µ2	PROPN
ejde-637	432	53	<	<	X
ejde-637	432	54	µ6	µ6	PROPN
ejde-637	432	55	,	,	PUNCT
ejde-637	432	56	neither	neither	CCONJ
ejde-637	432	57	h3	h3	NOUN
ejde-637	432	58	nor	nor	CCONJ
ejde-637	432	59	h1	h1	PROPN
ejde-637	432	60	will	will	AUX
ejde-637	432	61	appear	appear	VERB
ejde-637	432	62	before	before	ADP
ejde-637	432	63	x−	x−	PROPN
ejde-637	432	64	e	e	PROPN
ejde-637	432	65	=	=	PROPN
ejde-637	432	66	µ6	µ6	PROPN
ejde-637	432	67	since	since	SCONJ
ejde-637	432	68	p0	p0	PROPN
ejde-637	432	69	∈	∈	PROPN
ejde-637	432	70	σs	σs	PROPN
ejde-637	432	71	.	.	PROPN
ejde-637	433	1	on	on	ADP
ejde-637	433	2	the	the	DET
ejde-637	433	3	other	other	ADJ
ejde-637	433	4	hand	hand	NOUN
ejde-637	433	5	,	,	PUNCT
ejde-637	433	6	because	because	SCONJ
ejde-637	433	7	of	of	ADP
ejde-637	433	8	the	the	DET
ejde-637	433	9	sign	sign	NOUN
ejde-637	433	10	of	of	ADP
ejde-637	433	11	2µ2	2µ2	NUM
ejde-637	433	12	+	+	CCONJ
ejde-637	433	13	x+	x+	ADJ
ejde-637	433	14	e	e	PART
ejde-637	433	15	−	−	PROPN
ejde-637	433	16	µ6	µ6	NOUN
ejde-637	433	17	is	be	AUX
ejde-637	433	18	not	not	PART
ejde-637	433	19	sure	sure	ADJ
ejde-637	433	20	,	,	PUNCT
ejde-637	433	21	so	so	ADV
ejde-637	433	22	the	the	DET
ejde-637	433	23	size	size	NOUN
ejde-637	433	24	relationship	relationship	NOUN
ejde-637	433	25	of	of	ADP
ejde-637	433	26	ξ2	ξ2	NOUN
ejde-637	433	27	with	with	ADP
ejde-637	433	28	2µ2	2µ2	NUM
ejde-637	433	29	+	+	CCONJ
ejde-637	433	30	x+	x+	ADJ
ejde-637	433	31	e	e	NOUN
ejde-637	433	32	is	be	AUX
ejde-637	433	33	uncertain	uncertain	ADJ
ejde-637	433	34	.	.	PUNCT
ejde-637	434	1	then	then	ADV
ejde-637	434	2	there	there	PRON
ejde-637	434	3	may	may	AUX
ejde-637	434	4	exist	exist	VERB
ejde-637	434	5	some	some	DET
ejde-637	434	6	special	special	ADJ
ejde-637	434	7	separatrixes	separatrix	NOUN
ejde-637	434	8	,	,	PUNCT
ejde-637	434	9	which	which	PRON
ejde-637	434	10	will	will	AUX
ejde-637	434	11	be	be	AUX
ejde-637	434	12	discussed	discuss	VERB
ejde-637	434	13	as	as	SCONJ
ejde-637	434	14	follows	follow	VERB
ejde-637	434	15	:	:	PUNCT
ejde-637	434	16	if	if	SCONJ
ejde-637	434	17	y−	y−	NOUN
ejde-637	434	18	>	>	X
ejde-637	434	19	y+	y+	NUM
ejde-637	434	20	is	be	AUX
ejde-637	434	21	true	true	ADJ
ejde-637	434	22	for	for	ADP
ejde-637	434	23	x−	x−	PROPN
ejde-637	434	24	e	e	PROPN
ejde-637	434	25	<	<	X
ejde-637	434	26	2µ2+x+	2µ2+x+	NUM
ejde-637	434	27	e	e	NOUN
ejde-637	434	28	,	,	PUNCT
ejde-637	434	29	there	there	PRON
ejde-637	434	30	must	must	AUX
ejde-637	434	31	be	be	AUX
ejde-637	434	32	a	a	DET
ejde-637	434	33	sliding	slide	VERB
ejde-637	434	34	cycle	cycle	NOUN
ejde-637	434	35	h4	h4	NOUN
ejde-637	434	36	containing	contain	VERB
ejde-637	434	37	p0	p0	NOUN
ejde-637	434	38	before	before	ADP
ejde-637	434	39	y−	y−	NOUN
ejde-637	434	40	=	=	PUNCT
ejde-637	434	41	y+	y+	PROPN
ejde-637	434	42	since	since	SCONJ
ejde-637	434	43	the	the	DET
ejde-637	434	44	orbit	orbit	NOUN
ejde-637	434	45	of	of	ADP
ejde-637	434	46	⊕-system	⊕-system	NOUN
ejde-637	434	47	starting	start	VERB
ejde-637	434	48	from	from	ADP
ejde-637	434	49	y−	y−	NOUN
ejde-637	434	50	will	will	AUX
ejde-637	434	51	arrive	arrive	VERB
ejde-637	434	52	at	at	ADP
ejde-637	434	53	σx	σx	PROPN
ejde-637	434	54	s	s	PROPN
ejde-637	434	55	.	.	PUNCT
ejde-637	435	1	if	if	SCONJ
ejde-637	435	2	y−	y−	NOUN
ejde-637	435	3	>	>	X
ejde-637	435	4	y+	y+	NUM
ejde-637	435	5	is	be	AUX
ejde-637	435	6	true	true	ADJ
ejde-637	435	7	for	for	ADP
ejde-637	435	8	2µ2	2µ2	NUM
ejde-637	435	9	+	+	CCONJ
ejde-637	435	10	x+	x+	PROPN
ejde-637	435	11	e	e	X
ejde-637	435	12	<	<	X
ejde-637	435	13	x−	x−	PROPN
ejde-637	435	14	e	e	X
ejde-637	435	15	<	<	X
ejde-637	435	16	µ2	µ2	PROPN
ejde-637	435	17	,	,	PUNCT
ejde-637	435	18	h4	h4	PROPN
ejde-637	435	19	must	must	AUX
ejde-637	435	20	exist	exist	VERB
ejde-637	435	21	,	,	PUNCT
ejde-637	435	22	meanwhile	meanwhile	ADV
ejde-637	435	23	,	,	PUNCT
ejde-637	435	24	there	there	PRON
ejde-637	435	25	must	must	AUX
ejde-637	435	26	exist	exist	VERB
ejde-637	435	27	a	a	DET
ejde-637	435	28	repulsive	repulsive	ADJ
ejde-637	435	29	limit	limit	NOUN
ejde-637	435	30	cycle	cycle	NOUN
ejde-637	435	31	h5	h5	NOUN
ejde-637	435	32	before	before	ADP
ejde-637	435	33	x−	x−	PROPN
ejde-637	435	34	e	e	PROPN
ejde-637	435	35	=	=	PROPN
ejde-637	435	36	ξ2	ξ2	PROPN
ejde-637	435	37	.	.	PUNCT
ejde-637	436	1	to	to	PART
ejde-637	436	2	prove	prove	VERB
ejde-637	436	3	this	this	PRON
ejde-637	436	4	,	,	PUNCT
ejde-637	436	5	we	we	PRON
ejde-637	436	6	need	need	VERB
ejde-637	436	7	constructing	construct	VERB
ejde-637	436	8	the	the	DET
ejde-637	436	9	poincaré	poincaré	ADJ
ejde-637	436	10	map	map	NOUN
ejde-637	436	11	as	as	SCONJ
ejde-637	436	12	follows	follow	VERB
ejde-637	436	13	:	:	PUNCT
ejde-637	436	14	p2	p2	PROPN
ejde-637	436	15	:	:	PUNCT
ejde-637	436	16	dp2	dp2	PROPN
ejde-637	436	17	7→	7→	NUM
ejde-637	436	18	dp2	dp2	NOUN
ejde-637	436	19	,	,	PUNCT
ejde-637	436	20	p2(0	p2(0	NOUN
ejde-637	436	21	,	,	PUNCT
ejde-637	436	22	y0	y0	NOUN
ejde-637	436	23	)	)	PUNCT
ejde-637	436	24	=	=	SYM
ejde-637	436	25	(	(	PUNCT
ejde-637	436	26	0	0	NUM
ejde-637	436	27	,	,	PUNCT
ejde-637	436	28	y1	y1	NOUN
ejde-637	436	29	)	)	PUNCT
ejde-637	436	30	,	,	PUNCT
ejde-637	436	31	where	where	SCONJ
ejde-637	436	32	dp2	dp2	PROPN
ejde-637	436	33	=	=	PRON
ejde-637	436	34	{	{	PUNCT
ejde-637	436	35	(	(	PUNCT
ejde-637	436	36	0	0	NUM
ejde-637	436	37	,	,	PUNCT
ejde-637	436	38	y	y	PROPN
ejde-637	436	39	)	)	PUNCT
ejde-637	436	40	:	:	PUNCT
ejde-637	437	1	y	y	PROPN
ejde-637	437	2	∈	∈	PROPN
ejde-637	438	1	[	[	X
ejde-637	438	2	y−t	y−t	NOUN
ejde-637	438	3	,	,	PUNCT
ejde-637	438	4	y	y	PROPN
ejde-637	438	5	−	−	PROPN
ejde-637	438	6	]	]	PUNCT
ejde-637	438	7	}	}	PUNCT
ejde-637	438	8	,	,	PUNCT
ejde-637	438	9	and	and	CCONJ
ejde-637	438	10	(	(	PUNCT
ejde-637	438	11	0	0	NUM
ejde-637	438	12	,	,	PUNCT
ejde-637	438	13	y1	y1	NOUN
ejde-637	438	14	)	)	PUNCT
ejde-637	438	15	is	be	AUX
ejde-637	438	16	the	the	DET
ejde-637	438	17	first	first	ADJ
ejde-637	438	18	arriving	arriving	NOUN
ejde-637	438	19	point	point	NOUN
ejde-637	438	20	at	at	ADP
ejde-637	438	21	dp2	dp2	PROPN
ejde-637	438	22	of	of	ADP
ejde-637	438	23	the	the	DET
ejde-637	438	24	forward	forward	ADJ
ejde-637	438	25	orbit	orbit	NOUN
ejde-637	438	26	of	of	ADP
ejde-637	438	27	system	system	NOUN
ejde-637	438	28	(	(	PUNCT
ejde-637	438	29	1.1	1.1	NUM
ejde-637	438	30	)	)	PUNCT
ejde-637	438	31	starting	start	VERB
ejde-637	438	32	from	from	ADP
ejde-637	438	33	(	(	PUNCT
ejde-637	438	34	0	0	NUM
ejde-637	438	35	,	,	PUNCT
ejde-637	438	36	y0	y0	NOUN
ejde-637	438	37	)	)	PUNCT
ejde-637	438	38	.	.	PUNCT
ejde-637	439	1	then	then	ADV
ejde-637	439	2	we	we	PRON
ejde-637	439	3	must	must	AUX
ejde-637	439	4	have	have	VERB
ejde-637	439	5	p2((0	p2((0	NOUN
ejde-637	439	6	,	,	PUNCT
ejde-637	439	7	y	y	PROPN
ejde-637	439	8	+	+	PROPN
ejde-637	439	9	)	)	PUNCT
ejde-637	439	10	)	)	PUNCT
ejde-637	440	1	=	=	SYM
ejde-637	440	2	(	(	PUNCT
ejde-637	440	3	0	0	NUM
ejde-637	440	4	,	,	PUNCT
ejde-637	440	5	y−	y−	NOUN
ejde-637	440	6	)	)	PUNCT
ejde-637	440	7	.	.	PUNCT
ejde-637	441	1	and	and	CCONJ
ejde-637	441	2	there	there	PRON
ejde-637	441	3	must	must	AUX
ejde-637	441	4	be	be	AUX
ejde-637	441	5	(	(	PUNCT
ejde-637	441	6	0	0	NUM
ejde-637	441	7	,	,	PUNCT
ejde-637	441	8	y∗1	y∗1	NOUN
ejde-637	441	9	)	)	PUNCT
ejde-637	441	10	and	and	CCONJ
ejde-637	441	11	(	(	PUNCT
ejde-637	441	12	0	0	NUM
ejde-637	441	13	,	,	PUNCT
ejde-637	441	14	y∗2	y∗2	PROPN
ejde-637	441	15	)	)	PUNCT
ejde-637	441	16	,	,	PUNCT
ejde-637	441	17	which	which	PRON
ejde-637	441	18	satisfy	satisfy	VERB
ejde-637	441	19	16	16	NUM
ejde-637	441	20	q.-q	q.-q	PROPN
ejde-637	441	21	.	.	PUNCT
ejde-637	442	1	han	han	PROPN
ejde-637	442	2	,	,	PUNCT
ejde-637	442	3	s.-m	s.-m	PROPN
ejde-637	442	4	.	.	PUNCT
ejde-637	443	1	huan	huan	PROPN
ejde-637	443	2	ejde-2024/57	ejde-2024/57	PROPN
ejde-637	443	3	y+t	y+t	PROPN
ejde-637	443	4	<	<	X
ejde-637	443	5	y∗2	y∗2	PROPN
ejde-637	443	6	<	<	X
ejde-637	443	7	y∗1	y∗1	PROPN
ejde-637	443	8	<	<	X
ejde-637	443	9	y+	y+	PROPN
ejde-637	443	10	,	,	PUNCT
ejde-637	443	11	such	such	ADJ
ejde-637	443	12	that	that	DET
ejde-637	443	13	p2(0	p2(0	NOUN
ejde-637	443	14	,	,	PUNCT
ejde-637	443	15	y	y	PROPN
ejde-637	443	16	∗	∗	NOUN
ejde-637	443	17	1	1	NUM
ejde-637	443	18	)	)	PUNCT
ejde-637	443	19	=	=	SYM
ejde-637	443	20	(	(	PUNCT
ejde-637	443	21	0	0	NUM
ejde-637	443	22	,	,	PUNCT
ejde-637	443	23	y∗2	y∗2	PROPN
ejde-637	443	24	)	)	PUNCT
ejde-637	443	25	since	since	SCONJ
ejde-637	443	26	pey	pey	NOUN
ejde-637	443	27	is	be	AUX
ejde-637	443	28	atable	atable	ADJ
ejde-637	443	29	.	.	PUNCT
ejde-637	444	1	so	so	ADV
ejde-637	444	2	there	there	PRON
ejde-637	444	3	must	must	AUX
ejde-637	444	4	exist	exist	VERB
ejde-637	444	5	y∗1	y∗1	NOUN
ejde-637	444	6	<	<	X
ejde-637	444	7	y∗p	y∗p	PROPN
ejde-637	444	8	<	<	X
ejde-637	444	9	y+	y+	NOUN
ejde-637	444	10	,	,	PUNCT
ejde-637	444	11	such	such	ADJ
ejde-637	444	12	that	that	DET
ejde-637	444	13	p2(0	p2(0	NOUN
ejde-637	444	14	,	,	PUNCT
ejde-637	444	15	y	y	PROPN
ejde-637	444	16	∗	∗	NOUN
ejde-637	444	17	p	p	NOUN
ejde-637	444	18	)	)	PUNCT
ejde-637	444	19	=	=	SYM
ejde-637	444	20	(	(	PUNCT
ejde-637	444	21	0	0	NUM
ejde-637	444	22	,	,	PUNCT
ejde-637	444	23	y∗p	y∗p	NUM
ejde-637	444	24	)	)	PUNCT
ejde-637	444	25	.	.	PUNCT
ejde-637	445	1	which	which	PRON
ejde-637	445	2	implies	imply	VERB
ejde-637	445	3	the	the	DET
ejde-637	445	4	existence	existence	NOUN
ejde-637	445	5	of	of	ADP
ejde-637	445	6	the	the	DET
ejde-637	445	7	repulsive	repulsive	ADJ
ejde-637	445	8	h5	h5	NOUN
ejde-637	445	9	.	.	PUNCT
ejde-637	446	1	whether	whether	SCONJ
ejde-637	446	2	y−	y−	NOUN
ejde-637	446	3	=	=	SYM
ejde-637	446	4	y+	y+	X
ejde-637	446	5	is	be	AUX
ejde-637	446	6	true	true	ADJ
ejde-637	446	7	for	for	ADP
ejde-637	446	8	x−	x−	PROPN
ejde-637	446	9	e	e	PROPN
ejde-637	446	10	<	<	X
ejde-637	446	11	2µ2+x+	2µ2+x+	NUM
ejde-637	446	12	e	e	NOUN
ejde-637	446	13	or	or	CCONJ
ejde-637	446	14	2µ2+x+	2µ2+x+	NUM
ejde-637	446	15	e	e	NOUN
ejde-637	446	16	<	<	X
ejde-637	446	17	x−	x−	PROPN
ejde-637	446	18	e	e	X
ejde-637	446	19	<	<	X
ejde-637	446	20	µ2	µ2	PROPN
ejde-637	446	21	,	,	PUNCT
ejde-637	446	22	it	it	PRON
ejde-637	446	23	is	be	AUX
ejde-637	446	24	obvious	obvious	ADJ
ejde-637	446	25	that	that	SCONJ
ejde-637	446	26	there	there	PRON
ejde-637	446	27	must	must	AUX
ejde-637	446	28	arise	arise	VERB
ejde-637	446	29	a	a	DET
ejde-637	446	30	sliding	slide	VERB
ejde-637	446	31	-	-	PUNCT
ejde-637	446	32	zero	zero	NUM
ejde-637	446	33	cycle	cycle	NOUN
ejde-637	446	34	h2	h2	NOUN
ejde-637	446	35	.	.	PUNCT
ejde-637	447	1	if	if	SCONJ
ejde-637	447	2	y−	y−	NOUN
ejde-637	447	3	<	<	X
ejde-637	447	4	y+	y+	X
ejde-637	447	5	is	be	AUX
ejde-637	447	6	true	true	ADJ
ejde-637	447	7	for	for	ADP
ejde-637	447	8	x−	x−	PROPN
ejde-637	447	9	e	e	PROPN
ejde-637	447	10	<	<	X
ejde-637	447	11	2µ2	2µ2	NUM
ejde-637	447	12	+	+	CCONJ
ejde-637	447	13	x+	x+	ADJ
ejde-637	447	14	e	e	X
ejde-637	447	15	,	,	PUNCT
ejde-637	447	16	we	we	PRON
ejde-637	447	17	obtain	obtain	VERB
ejde-637	447	18	a	a	DET
ejde-637	447	19	attractive	attractive	ADJ
ejde-637	447	20	limit	limit	NOUN
ejde-637	447	21	cycle	cycle	NOUN
ejde-637	447	22	h6	h6	PROPN
ejde-637	447	23	before	before	ADP
ejde-637	447	24	x−	x−	PROPN
ejde-637	447	25	e	e	PROPN
ejde-637	447	26	=	=	PROPN
ejde-637	447	27	2µ2	2µ2	NUM
ejde-637	447	28	+	+	CCONJ
ejde-637	447	29	x+	x+	ADJ
ejde-637	447	30	e	e	X
ejde-637	447	31	.	.	PUNCT
ejde-637	448	1	to	to	PART
ejde-637	448	2	prove	prove	VERB
ejde-637	448	3	this	this	PRON
ejde-637	448	4	,	,	PUNCT
ejde-637	448	5	we	we	PRON
ejde-637	448	6	need	need	VERB
ejde-637	448	7	constructing	construct	VERB
ejde-637	448	8	the	the	DET
ejde-637	448	9	poincaré	poincaré	ADJ
ejde-637	448	10	map	map	NOUN
ejde-637	448	11	as	as	SCONJ
ejde-637	448	12	follows	follow	VERB
ejde-637	448	13	:	:	PUNCT
ejde-637	448	14	p3	p3	NOUN
ejde-637	448	15	:	:	PUNCT
ejde-637	448	16	dp3	dp3	PROPN
ejde-637	448	17	7→	7→	PROPN
ejde-637	448	18	dp3	dp3	PROPN
ejde-637	448	19	,	,	PUNCT
ejde-637	448	20	p3(0	p3(0	PROPN
ejde-637	448	21	,	,	PUNCT
ejde-637	448	22	y0	y0	PROPN
ejde-637	448	23	)	)	PUNCT
ejde-637	448	24	=	=	SYM
ejde-637	448	25	(	(	PUNCT
ejde-637	448	26	0	0	NUM
ejde-637	448	27	,	,	PUNCT
ejde-637	448	28	y1	y1	PROPN
ejde-637	448	29	)	)	PUNCT
ejde-637	448	30	,	,	PUNCT
ejde-637	448	31	where	where	SCONJ
ejde-637	448	32	dp3	dp3	PROPN
ejde-637	448	33	=	=	PRON
ejde-637	448	34	{	{	PUNCT
ejde-637	448	35	(	(	PUNCT
ejde-637	448	36	0	0	NUM
ejde-637	448	37	,	,	PUNCT
ejde-637	448	38	y	y	PROPN
ejde-637	448	39	)	)	PUNCT
ejde-637	448	40	:	:	PUNCT
ejde-637	448	41	y	y	PROPN
ejde-637	448	42	∈	∈	PROPN
ejde-637	449	1	[	[	X
ejde-637	449	2	0	0	NUM
ejde-637	449	3	,	,	PUNCT
ejde-637	449	4	y+t	y+t	X
ejde-637	449	5	]	]	PUNCT
ejde-637	449	6	}	}	PUNCT
ejde-637	449	7	,	,	PUNCT
ejde-637	449	8	and	and	CCONJ
ejde-637	449	9	(	(	PUNCT
ejde-637	449	10	0	0	NUM
ejde-637	449	11	,	,	PUNCT
ejde-637	449	12	y1	y1	NOUN
ejde-637	449	13	)	)	PUNCT
ejde-637	449	14	is	be	AUX
ejde-637	449	15	the	the	DET
ejde-637	449	16	first	first	ADJ
ejde-637	449	17	arriving	arriving	NOUN
ejde-637	449	18	point	point	NOUN
ejde-637	449	19	at	at	ADP
ejde-637	449	20	dp3	dp3	PROPN
ejde-637	449	21	of	of	ADP
ejde-637	449	22	the	the	DET
ejde-637	449	23	forward	forward	ADJ
ejde-637	449	24	orbit	orbit	NOUN
ejde-637	449	25	of	of	ADP
ejde-637	449	26	system	system	NOUN
ejde-637	449	27	(	(	PUNCT
ejde-637	449	28	1.1	1.1	NUM
ejde-637	449	29	)	)	PUNCT
ejde-637	449	30	starting	start	VERB
ejde-637	449	31	from	from	ADP
ejde-637	449	32	(	(	PUNCT
ejde-637	449	33	0	0	NUM
ejde-637	449	34	,	,	PUNCT
ejde-637	449	35	y0	y0	NOUN
ejde-637	449	36	)	)	PUNCT
ejde-637	449	37	.	.	PUNCT
ejde-637	450	1	thus	thus	ADV
ejde-637	450	2	there	there	PRON
ejde-637	450	3	must	must	AUX
ejde-637	450	4	be	be	AUX
ejde-637	450	5	(	(	PUNCT
ejde-637	450	6	0	0	NUM
ejde-637	450	7	,	,	PUNCT
ejde-637	450	8	y⋄1	y⋄1	PROPN
ejde-637	450	9	)	)	PUNCT
ejde-637	450	10	and	and	CCONJ
ejde-637	450	11	(	(	PUNCT
ejde-637	450	12	0	0	NUM
ejde-637	450	13	,	,	PUNCT
ejde-637	450	14	y⋄2	y⋄2	PRON
ejde-637	450	15	)	)	PUNCT
ejde-637	450	16	,	,	PUNCT
ejde-637	450	17	0	0	PUNCT
ejde-637	450	18	<	<	X
ejde-637	450	19	y⋄1	y⋄1	X
ejde-637	450	20	<	<	X
ejde-637	450	21	y⋄2	y⋄2	PROPN
ejde-637	450	22	<	<	X
ejde-637	450	23	y+t	y+t	PROPN
ejde-637	450	24	,	,	PUNCT
ejde-637	450	25	such	such	ADJ
ejde-637	450	26	that	that	SCONJ
ejde-637	450	27	p3(0	p3(0	PROPN
ejde-637	450	28	,	,	PUNCT
ejde-637	450	29	0	0	NUM
ejde-637	450	30	)	)	PUNCT
ejde-637	450	31	=	=	SYM
ejde-637	450	32	(	(	PUNCT
ejde-637	450	33	0	0	NUM
ejde-637	450	34	,	,	PUNCT
ejde-637	450	35	y⋄1	y⋄1	PROPN
ejde-637	450	36	)	)	PUNCT
ejde-637	450	37	,	,	PUNCT
ejde-637	450	38	p3((0	p3((0	PROPN
ejde-637	450	39	,	,	PUNCT
ejde-637	450	40	y	y	PROPN
ejde-637	450	41	+	+	PROPN
ejde-637	450	42	t	t	PROPN
ejde-637	450	43	)	)	PUNCT
ejde-637	450	44	)	)	PUNCT
ejde-637	451	1	=	=	PUNCT
ejde-637	451	2	(	(	PUNCT
ejde-637	451	3	0	0	NUM
ejde-637	451	4	,	,	PUNCT
ejde-637	451	5	y⋄2	y⋄2	PRON
ejde-637	451	6	)	)	PUNCT
ejde-637	451	7	,	,	PUNCT
ejde-637	451	8	since	since	SCONJ
ejde-637	451	9	y−	y−	NOUN
ejde-637	451	10	<	<	X
ejde-637	451	11	y+	y+	PROPN
ejde-637	451	12	and	and	CCONJ
ejde-637	451	13	0	0	NUM
ejde-637	451	14	<	<	X
ejde-637	451	15	y+t	y+t	X
ejde-637	451	16	<	<	X
ejde-637	451	17	y−t	y−t	PROPN
ejde-637	451	18	,	,	PUNCT
ejde-637	451	19	respectively	respectively	ADV
ejde-637	451	20	.	.	PUNCT
ejde-637	452	1	so	so	ADV
ejde-637	452	2	there	there	PRON
ejde-637	452	3	must	must	AUX
ejde-637	452	4	be	be	AUX
ejde-637	452	5	(	(	PUNCT
ejde-637	452	6	0	0	NUM
ejde-637	452	7	,	,	PUNCT
ejde-637	452	8	y∗p	y∗p	NUM
ejde-637	452	9	)	)	PUNCT
ejde-637	452	10	,	,	PUNCT
ejde-637	452	11	such	such	ADJ
ejde-637	452	12	that	that	SCONJ
ejde-637	452	13	y⋄1	y⋄1	PROPN
ejde-637	452	14	<	<	X
ejde-637	452	15	y⋄p	y⋄p	X
ejde-637	452	16	<	<	X
ejde-637	452	17	y⋄2	y⋄2	PROPN
ejde-637	452	18	p3(0	p3(0	PROPN
ejde-637	452	19	,	,	PUNCT
ejde-637	452	20	y	y	PROPN
ejde-637	452	21	⋄	⋄	PROPN
ejde-637	452	22	p	p	X
ejde-637	452	23	)	)	PUNCT
ejde-637	452	24	=	=	SYM
ejde-637	452	25	(	(	PUNCT
ejde-637	452	26	0	0	NUM
ejde-637	452	27	,	,	PUNCT
ejde-637	452	28	y⋄p	y⋄p	NUM
ejde-637	452	29	)	)	PUNCT
ejde-637	452	30	.	.	PUNCT
ejde-637	453	1	which	which	PRON
ejde-637	453	2	implies	imply	VERB
ejde-637	453	3	the	the	DET
ejde-637	453	4	existence	existence	NOUN
ejde-637	453	5	of	of	ADP
ejde-637	453	6	the	the	DET
ejde-637	453	7	attractive	attractive	ADJ
ejde-637	453	8	h6	h6	PROPN
ejde-637	453	9	.	.	PUNCT
ejde-637	454	1	if	if	SCONJ
ejde-637	454	2	y	y	PROPN
ejde-637	454	3	−	−	PROPN
ejde-637	454	4	<	<	X
ejde-637	454	5	y+	y+	X
ejde-637	454	6	is	be	AUX
ejde-637	454	7	true	true	ADJ
ejde-637	454	8	for	for	ADP
ejde-637	454	9	2µ2	2µ2	NUM
ejde-637	455	1	+	+	PROPN
ejde-637	455	2	x+	x+	ADJ
ejde-637	455	3	e	e	X
ejde-637	455	4	<	<	X
ejde-637	455	5	x−	x−	PROPN
ejde-637	455	6	e	e	X
ejde-637	455	7	<	<	X
ejde-637	455	8	µ2	µ2	PROPN
ejde-637	455	9	,	,	PUNCT
ejde-637	455	10	there	there	PRON
ejde-637	455	11	must	must	AUX
ejde-637	455	12	exist	exist	VERB
ejde-637	455	13	a	a	DET
ejde-637	455	14	sliding	slide	VERB
ejde-637	455	15	heteroclinic	heteroclinic	ADJ
ejde-637	455	16	orbit	orbit	NOUN
ejde-637	455	17	h71	h71	PROPN
ejde-637	455	18	from	from	ADP
ejde-637	455	19	x+	x+	PROPN
ejde-637	455	20	e	e	NOUN
ejde-637	455	21	to	to	AUX
ejde-637	455	22	pey	pey	VERB
ejde-637	455	23	until	until	SCONJ
ejde-637	455	24	x−	x−	PROPN
ejde-637	455	25	e	e	PROPN
ejde-637	455	26	=	=	PUNCT
ejde-637	455	27	−x+	−x+	X
ejde-637	455	28	e	e	NOUN
ejde-637	455	29	since	since	SCONJ
ejde-637	455	30	σy	σy	PROPN
ejde-637	455	31	s	s	PROPN
ejde-637	455	32	is	be	AUX
ejde-637	455	33	attractive	attractive	ADJ
ejde-637	455	34	.	.	PUNCT
ejde-637	456	1	then	then	ADV
ejde-637	456	2	h71	h71	PROPN
ejde-637	456	3	turns	turn	VERB
ejde-637	456	4	into	into	ADP
ejde-637	456	5	a	a	DET
ejde-637	456	6	sliding	slide	VERB
ejde-637	456	7	heteroclinic	heteroclinic	ADJ
ejde-637	456	8	orbit	orbit	NOUN
ejde-637	456	9	h72	h72	NOUN
ejde-637	456	10	from	from	ADP
ejde-637	456	11	x+	x+	ADJ
ejde-637	456	12	e	e	NOUN
ejde-637	456	13	to	to	ADP
ejde-637	456	14	pex	pex	PROPN
ejde-637	456	15	until	until	ADP
ejde-637	456	16	x−	x−	PROPN
ejde-637	456	17	e	e	PROPN
ejde-637	456	18	=	=	PROPN
ejde-637	456	19	min{2µ1	min{2µ1	PROPN
ejde-637	456	20	+	+	CCONJ
ejde-637	456	21	x+	x+	PROPN
ejde-637	456	22	e	e	X
ejde-637	456	23	,	,	PUNCT
ejde-637	456	24	µ3	µ3	NUM
ejde-637	456	25	}	}	PUNCT
ejde-637	456	26	.	.	PUNCT
ejde-637	457	1	thus	thus	ADV
ejde-637	457	2	according	accord	VERB
ejde-637	457	3	to	to	ADP
ejde-637	457	4	the	the	DET
ejde-637	457	5	above	above	ADJ
ejde-637	457	6	analysis	analysis	NOUN
ejde-637	457	7	,	,	PUNCT
ejde-637	457	8	we	we	PRON
ejde-637	457	9	obtain	obtain	VERB
ejde-637	457	10	h4	h4	NOUN
ejde-637	457	11	,	,	PUNCT
ejde-637	457	12	h2	h2	PROPN
ejde-637	457	13	and	and	CCONJ
ejde-637	457	14	h6	h6	PROPN
ejde-637	457	15	will	will	AUX
ejde-637	457	16	appears	appear	VERB
ejde-637	457	17	in	in	ADP
ejde-637	457	18	turn	turn	NOUN
ejde-637	457	19	if	if	SCONJ
ejde-637	457	20	y−	y−	NOUN
ejde-637	457	21	<	<	X
ejde-637	457	22	y+	y+	X
ejde-637	457	23	is	be	AUX
ejde-637	457	24	true	true	ADJ
ejde-637	457	25	for	for	ADP
ejde-637	457	26	x−	x−	PROPN
ejde-637	457	27	e	e	PROPN
ejde-637	457	28	<	<	X
ejde-637	457	29	2µ2+x+	2µ2+x+	NUM
ejde-637	457	30	e	e	NOUN
ejde-637	457	31	,	,	PUNCT
ejde-637	457	32	which	which	PRON
ejde-637	457	33	implies	imply	VERB
ejde-637	457	34	that	that	SCONJ
ejde-637	457	35	there	there	PRON
ejde-637	457	36	is	be	VERB
ejde-637	457	37	a	a	DET
ejde-637	457	38	sliding	slide	VERB
ejde-637	457	39	cycle	cycle	NOUN
ejde-637	457	40	bifurcation	bifurcation	NOUN
ejde-637	457	41	as	as	ADP
ejde-637	457	42	x−	x−	PROPN
ejde-637	457	43	e	e	PROPN
ejde-637	457	44	=	=	PROPN
ejde-637	457	45	ξ2	ξ2	PROPN
ejde-637	457	46	.	.	PUNCT
ejde-637	458	1	in	in	ADP
ejde-637	458	2	addition	addition	NOUN
ejde-637	458	3	,	,	PUNCT
ejde-637	458	4	h1	h1	PROPN
ejde-637	458	5	and	and	CCONJ
ejde-637	458	6	h4	h4	PROPN
ejde-637	458	7	will	will	AUX
ejde-637	458	8	appear	appear	VERB
ejde-637	458	9	in	in	ADP
ejde-637	458	10	turn	turn	NOUN
ejde-637	458	11	if	if	SCONJ
ejde-637	458	12	y−	y−	NOUN
ejde-637	458	13	>	>	X
ejde-637	458	14	y+	y+	NUM
ejde-637	458	15	is	be	AUX
ejde-637	458	16	true	true	ADJ
ejde-637	458	17	for	for	ADP
ejde-637	458	18	x−	x−	PROPN
ejde-637	458	19	e	e	PROPN
ejde-637	458	20	<	<	X
ejde-637	458	21	2µ2+x+	2µ2+x+	NUM
ejde-637	458	22	e	e	NOUN
ejde-637	458	23	,	,	PUNCT
ejde-637	458	24	which	which	PRON
ejde-637	458	25	implies	imply	VERB
ejde-637	458	26	that	that	SCONJ
ejde-637	458	27	there	there	PRON
ejde-637	458	28	is	be	VERB
ejde-637	458	29	a	a	DET
ejde-637	458	30	sliding	slide	VERB
ejde-637	458	31	homoclinic	homoclinic	ADJ
ejde-637	458	32	bifurcation	bifurcation	NOUN
ejde-637	458	33	as	as	ADP
ejde-637	458	34	x−	x−	PROPN
ejde-637	458	35	e	e	PROPN
ejde-637	458	36	=	=	PROPN
ejde-637	458	37	ξ1	ξ1	PROPN
ejde-637	458	38	.	.	PUNCT
ejde-637	459	1	the	the	DET
ejde-637	459	2	proof	proof	NOUN
ejde-637	459	3	is	be	AUX
ejde-637	459	4	complete	complete	ADJ
ejde-637	459	5	.	.	PUNCT
ejde-637	460	1	□	□	PUNCT
ejde-637	460	2	5	5	X
ejde-637	460	3	.	.	PUNCT
ejde-637	460	4	examples	example	NOUN
ejde-637	460	5	in	in	ADP
ejde-637	460	6	this	this	DET
ejde-637	460	7	section	section	NOUN
ejde-637	460	8	,	,	PUNCT
ejde-637	460	9	three	three	NUM
ejde-637	460	10	examples	example	NOUN
ejde-637	460	11	are	be	AUX
ejde-637	460	12	provided	provide	VERB
ejde-637	460	13	to	to	PART
ejde-637	460	14	illustrate	illustrate	VERB
ejde-637	460	15	some	some	DET
ejde-637	460	16	separatrixes	separatrix	NOUN
ejde-637	460	17	in	in	ADP
ejde-637	460	18	the	the	DET
ejde-637	460	19	theorems	theorem	NOUN
ejde-637	460	20	in	in	ADP
ejde-637	460	21	section	section	NOUN
ejde-637	460	22	3	3	NUM
ejde-637	460	23	.	.	PUNCT
ejde-637	461	1	it	it	PRON
ejde-637	461	2	should	should	AUX
ejde-637	461	3	be	be	AUX
ejde-637	461	4	noted	note	VERB
ejde-637	461	5	that	that	SCONJ
ejde-637	461	6	the	the	DET
ejde-637	461	7	red	red	NOUN
ejde-637	461	8	and	and	CCONJ
ejde-637	461	9	the	the	DET
ejde-637	461	10	blue	blue	ADJ
ejde-637	461	11	curves	curve	NOUN
ejde-637	461	12	in	in	ADP
ejde-637	461	13	the	the	DET
ejde-637	461	14	following	follow	VERB
ejde-637	461	15	figures	figure	NOUN
ejde-637	461	16	represent	represent	VERB
ejde-637	461	17	the	the	DET
ejde-637	461	18	orbits	orbit	NOUN
ejde-637	461	19	of	of	ADP
ejde-637	461	20	the	the	DET
ejde-637	461	21	⊕-system	⊕-system	NOUN
ejde-637	461	22	and	and	CCONJ
ejde-637	461	23	the	the	DET
ejde-637	461	24	⊖-system	⊖-system	NOUN
ejde-637	461	25	,	,	PUNCT
ejde-637	461	26	respectively	respectively	ADV
ejde-637	461	27	.	.	PUNCT
ejde-637	462	1	and	and	CCONJ
ejde-637	462	2	the	the	DET
ejde-637	462	3	arrows	arrow	NOUN
ejde-637	462	4	represents	represent	VERB
ejde-637	462	5	the	the	DET
ejde-637	462	6	directions	direction	NOUN
ejde-637	462	7	of	of	ADP
ejde-637	462	8	the	the	DET
ejde-637	462	9	orbits	orbit	NOUN
ejde-637	462	10	on	on	ADP
ejde-637	462	11	the	the	DET
ejde-637	462	12	forward	forward	ADJ
ejde-637	462	13	time	time	NOUN
ejde-637	462	14	.	.	PUNCT
ejde-637	463	1	example	example	NOUN
ejde-637	463	2	5.1	5.1	NUM
ejde-637	463	3	.	.	PUNCT
ejde-637	464	1	let	let	VERB
ejde-637	464	2	a	a	DET
ejde-637	464	3	=	=	X
ejde-637	464	4	(	(	PUNCT
ejde-637	464	5	−4	−4	PROPN
ejde-637	464	6	2	2	NUM
ejde-637	464	7	3	3	NUM
ejde-637	464	8	1	1	NUM
ejde-637	464	9	)	)	PUNCT
ejde-637	464	10	,	,	PUNCT
ejde-637	464	11	x−	x−	PROPN
ejde-637	464	12	e	e	PROPN
ejde-637	464	13	=	=	PRON
ejde-637	464	14	(	(	PUNCT
ejde-637	464	15	5	5	NUM
ejde-637	464	16	−3	−3	ADV
ejde-637	464	17	)	)	PUNCT
ejde-637	464	18	,	,	PUNCT
ejde-637	464	19	x+	x+	X
ejde-637	464	20	e	e	X
ejde-637	464	21	=	=	SYM
ejde-637	464	22	(	(	PUNCT
ejde-637	464	23	2	2	NUM
ejde-637	464	24	3	3	NUM
ejde-637	464	25	)	)	PUNCT
ejde-637	464	26	.	.	PUNCT
ejde-637	465	1	(	(	PUNCT
ejde-637	465	2	5.1	5.1	NUM
ejde-637	465	3	)	)	PUNCT
ejde-637	465	4	by	by	ADP
ejde-637	465	5	simple	simple	ADJ
ejde-637	465	6	calculations	calculation	NOUN
ejde-637	465	7	,	,	PUNCT
ejde-637	465	8	we	we	PRON
ejde-637	465	9	have	have	VERB
ejde-637	465	10	x+	x+	ADJ
ejde-637	465	11	t	t	NOUN
ejde-637	465	12	=	=	SYM
ejde-637	465	13	3	3	NUM
ejde-637	465	14	,	,	PUNCT
ejde-637	465	15	x+	x+	ADJ
ejde-637	465	16	m1	m1	NOUN
ejde-637	465	17	=	=	SYM
ejde-637	465	18	1	1	NUM
ejde-637	465	19	,	,	PUNCT
ejde-637	465	20	x+	x+	NUM
ejde-637	465	21	m2	m2	PROPN
ejde-637	465	22	=	=	PROPN
ejde-637	465	23	8	8	NUM
ejde-637	465	24	,	,	PUNCT
ejde-637	465	25	x−	x−	PROPN
ejde-637	465	26	t	t	PROPN
ejde-637	465	27	=	=	SYM
ejde-637	465	28	4	4	NUM
ejde-637	465	29	,	,	PUNCT
ejde-637	465	30	x−	x−	PROPN
ejde-637	465	31	m1	m1	PROPN
ejde-637	465	32	=	=	PUNCT
ejde-637	465	33	6	6	NUM
ejde-637	465	34	,	,	PUNCT
ejde-637	465	35	x−	x−	PROPN
ejde-637	465	36	m2	m2	PROPN
ejde-637	465	37	=	=	PROPN
ejde-637	465	38	−1	−1	PROPN
ejde-637	465	39	,	,	PUNCT
ejde-637	465	40	2µ1	2µ1	NUM
ejde-637	466	1	+	+	CCONJ
ejde-637	466	2	x+	x+	ADJ
ejde-637	466	3	e	e	X
ejde-637	466	4	=	=	SYM
ejde-637	466	5	4	4	NUM
ejde-637	466	6	<	<	X
ejde-637	466	7	µ3	µ3	NOUN
ejde-637	466	8	=	=	NOUN
ejde-637	466	9	7	7	X
ejde-637	466	10	.	.	NOUN
ejde-637	466	11	through	through	ADP
ejde-637	466	12	numerical	numerical	PROPN
ejde-637	466	13	simulation	simulation	PROPN
ejde-637	466	14	,	,	PUNCT
ejde-637	466	15	there	there	PRON
ejde-637	466	16	exists	exist	VERB
ejde-637	466	17	an	an	DET
ejde-637	466	18	attractive	attractive	ADJ
ejde-637	466	19	limit	limit	NOUN
ejde-637	466	20	cycle	cycle	NOUN
ejde-637	466	21	illustrated	illustrate	VERB
ejde-637	466	22	in	in	ADP
ejde-637	466	23	figure	figure	NOUN
ejde-637	466	24	2	2	NUM
ejde-637	466	25	,	,	PUNCT
ejde-637	466	26	which	which	PRON
ejde-637	466	27	supported	support	VERB
ejde-637	466	28	the	the	DET
ejde-637	466	29	conclusion	conclusion	NOUN
ejde-637	466	30	about	about	ADP
ejde-637	466	31	l2	l2	NOUN
ejde-637	466	32	in	in	ADP
ejde-637	466	33	theorem	theorem	ADJ
ejde-637	466	34	3.4	3.4	NUM
ejde-637	466	35	.	.	PUNCT
ejde-637	467	1	ejde-2024/57	ejde-2024/57	NOUN
ejde-637	467	2	planar	planar	ADJ
ejde-637	467	3	sector	sector	NOUN
ejde-637	467	4	-	-	PUNCT
ejde-637	467	5	wise	wise	ADJ
ejde-637	467	6	linear	linear	ADJ
ejde-637	467	7	systems	system	NOUN
ejde-637	467	8	17	17	NUM
ejde-637	467	9	figure	figure	NOUN
ejde-637	467	10	2	2	NUM
ejde-637	467	11	.	.	NOUN
ejde-637	467	12	existence	existence	NOUN
ejde-637	467	13	of	of	ADP
ejde-637	467	14	the	the	DET
ejde-637	467	15	attractive	attractive	ADJ
ejde-637	467	16	limit	limit	NOUN
ejde-637	467	17	cycle	cycle	NOUN
ejde-637	467	18	of	of	ADP
ejde-637	467	19	equation	equation	NOUN
ejde-637	467	20	(	(	PUNCT
ejde-637	467	21	5.1	5.1	NUM
ejde-637	467	22	)	)	PUNCT
ejde-637	467	23	example	example	NOUN
ejde-637	467	24	5.2	5.2	NUM
ejde-637	467	25	.	.	PUNCT
ejde-637	468	1	let	let	VERB
ejde-637	468	2	a	a	PRON
ejde-637	468	3	=	=	NOUN
ejde-637	468	4	(	(	PUNCT
ejde-637	468	5	−1	−1	NOUN
ejde-637	468	6	2	2	NUM
ejde-637	468	7	3	3	NUM
ejde-637	468	8	4	4	NUM
ejde-637	468	9	)	)	PUNCT
ejde-637	468	10	,	,	PUNCT
ejde-637	469	1	x−	x−	PROPN
ejde-637	469	2	e	e	PROPN
ejde-637	469	3	=	=	PRON
ejde-637	469	4	(	(	PUNCT
ejde-637	469	5	9	9	NUM
ejde-637	469	6	−3	−3	NOUN
ejde-637	469	7	)	)	PUNCT
ejde-637	469	8	,	,	PUNCT
ejde-637	469	9	x+	x+	X
ejde-637	469	10	e	e	X
ejde-637	469	11	=	=	SYM
ejde-637	469	12	(	(	PUNCT
ejde-637	469	13	2	2	NUM
ejde-637	469	14	3	3	NUM
ejde-637	469	15	)	)	PUNCT
ejde-637	469	16	.	.	PUNCT
ejde-637	470	1	(	(	PUNCT
ejde-637	470	2	5.2	5.2	NUM
ejde-637	470	3	)	)	PUNCT
ejde-637	470	4	by	by	ADP
ejde-637	470	5	simple	simple	ADJ
ejde-637	470	6	calculations	calculation	NOUN
ejde-637	470	7	,	,	PUNCT
ejde-637	470	8	we	we	PRON
ejde-637	470	9	have	have	VERB
ejde-637	470	10	x+	x+	ADJ
ejde-637	470	11	t	t	NOUN
ejde-637	470	12	=	=	SYM
ejde-637	470	13	6	6	NUM
ejde-637	470	14	,	,	PUNCT
ejde-637	470	15	x+	x+	ADJ
ejde-637	470	16	m1	m1	NOUN
ejde-637	470	17	=	=	SYM
ejde-637	470	18	1	1	NUM
ejde-637	470	19	,	,	PUNCT
ejde-637	470	20	x+	x+	NUM
ejde-637	470	21	m2	m2	PROPN
ejde-637	470	22	=	=	PROPN
ejde-637	470	23	8	8	NUM
ejde-637	470	24	,	,	PUNCT
ejde-637	470	25	x−	x−	PROPN
ejde-637	470	26	t	t	PROPN
ejde-637	470	27	=	=	SYM
ejde-637	470	28	5	5	NUM
ejde-637	470	29	,	,	PUNCT
ejde-637	470	30	x−	x−	PROPN
ejde-637	470	31	m1	m1	PROPN
ejde-637	470	32	=	=	PROPN
ejde-637	470	33	10	10	NUM
ejde-637	470	34	,	,	PUNCT
ejde-637	470	35	x−	x−	PROPN
ejde-637	470	36	m2	m2	PROPN
ejde-637	470	37	=	=	PROPN
ejde-637	470	38	3	3	NUM
ejde-637	470	39	,	,	PUNCT
ejde-637	470	40	2µ1	2µ1	NUM
ejde-637	470	41	+	+	CCONJ
ejde-637	470	42	x+	x+	ADJ
ejde-637	470	43	e	e	X
ejde-637	470	44	=	=	SYM
ejde-637	470	45	10	10	NUM
ejde-637	470	46	>	>	SYM
ejde-637	470	47	µ3	µ3	NOUN
ejde-637	470	48	=	=	PUNCT
ejde-637	470	49	7	7	X
ejde-637	470	50	.	.	NOUN
ejde-637	470	51	through	through	ADP
ejde-637	470	52	numerical	numerical	PROPN
ejde-637	470	53	simulation	simulation	PROPN
ejde-637	470	54	,	,	PUNCT
ejde-637	470	55	there	there	PRON
ejde-637	470	56	exists	exist	VERB
ejde-637	470	57	a	a	DET
ejde-637	470	58	repulsive	repulsive	ADJ
ejde-637	470	59	limit	limit	NOUN
ejde-637	470	60	cycle	cycle	NOUN
ejde-637	470	61	illustrated	illustrate	VERB
ejde-637	470	62	in	in	ADP
ejde-637	470	63	figure	figure	NOUN
ejde-637	470	64	3	3	NUM
ejde-637	470	65	,	,	PUNCT
ejde-637	470	66	which	which	PRON
ejde-637	470	67	supported	support	VERB
ejde-637	470	68	the	the	DET
ejde-637	470	69	conclusion	conclusion	NOUN
ejde-637	470	70	about	about	ADP
ejde-637	470	71	l1	l1	PROPN
ejde-637	470	72	in	in	ADP
ejde-637	470	73	theorem	theorem	PROPN
ejde-637	470	74	3.4	3.4	NUM
ejde-637	470	75	.	.	PUNCT
ejde-637	471	1	figure	figure	NOUN
ejde-637	471	2	3	3	NUM
ejde-637	471	3	.	.	PUNCT
ejde-637	472	1	existence	existence	NOUN
ejde-637	472	2	of	of	ADP
ejde-637	472	3	the	the	DET
ejde-637	472	4	repulsive	repulsive	ADJ
ejde-637	472	5	limit	limit	NOUN
ejde-637	472	6	cycle	cycle	NOUN
ejde-637	472	7	of	of	ADP
ejde-637	472	8	equation	equation	NOUN
ejde-637	472	9	(	(	PUNCT
ejde-637	472	10	5.2	5.2	NUM
ejde-637	472	11	)	)	PUNCT
ejde-637	472	12	example	example	NOUN
ejde-637	473	1	5.3	5.3	NUM
ejde-637	473	2	.	.	PUNCT
ejde-637	474	1	let	let	VERB
ejde-637	474	2	a	a	PRON
ejde-637	474	3	=	=	X
ejde-637	474	4	(	(	PUNCT
ejde-637	474	5	−4	−4	PROPN
ejde-637	474	6	2	2	NUM
ejde-637	474	7	3	3	NUM
ejde-637	474	8	1	1	NUM
ejde-637	474	9	)	)	PUNCT
ejde-637	474	10	,	,	PUNCT
ejde-637	474	11	x−	x−	PROPN
ejde-637	474	12	e	e	PROPN
ejde-637	474	13	=	=	PRON
ejde-637	474	14	(	(	PUNCT
ejde-637	474	15	µ	µ	X
ejde-637	474	16	−10	−10	X
ejde-637	474	17	)	)	PUNCT
ejde-637	474	18	,	,	PUNCT
ejde-637	475	1	x+	x+	X
ejde-637	475	2	e	e	X
ejde-637	475	3	=	=	SYM
ejde-637	475	4	(	(	PUNCT
ejde-637	475	5	4	4	NUM
ejde-637	475	6	10	10	NUM
ejde-637	475	7	)	)	PUNCT
ejde-637	475	8	.	.	PUNCT
ejde-637	476	1	(	(	PUNCT
ejde-637	476	2	5.3	5.3	NUM
ejde-637	476	3	)	)	PUNCT
ejde-637	476	4	18	18	NUM
ejde-637	476	5	q.-q	q.-q	PROPN
ejde-637	476	6	.	.	PUNCT
ejde-637	477	1	han	han	PROPN
ejde-637	477	2	,	,	PUNCT
ejde-637	477	3	s.-m	s.-m	PROPN
ejde-637	477	4	.	.	PUNCT
ejde-637	478	1	huan	huan	PROPN
ejde-637	478	2	ejde-2024/57	ejde-2024/57	PROPN
ejde-637	478	3	for	for	ADP
ejde-637	478	4	−9	−9	X
ejde-637	478	5	<	<	X
ejde-637	478	6	µ	µ	X
ejde-637	478	7	<	<	X
ejde-637	478	8	−6	−6	PROPN
ejde-637	478	9	,	,	PUNCT
ejde-637	478	10	we	we	PRON
ejde-637	478	11	will	will	AUX
ejde-637	478	12	show	show	VERB
ejde-637	478	13	there	there	ADV
ejde-637	478	14	exist	exist	VERB
ejde-637	478	15	a	a	DET
ejde-637	478	16	sliding	slide	VERB
ejde-637	478	17	homoclinic	homoclinic	ADJ
ejde-637	478	18	bifurcation	bifurcation	NOUN
ejde-637	478	19	and	and	CCONJ
ejde-637	478	20	a	a	DET
ejde-637	478	21	sliding	slide	VERB
ejde-637	478	22	cycle	cycle	NOUN
ejde-637	478	23	bifurcation	bifurcation	NOUN
ejde-637	478	24	.	.	PUNCT
ejde-637	479	1	by	by	ADP
ejde-637	479	2	easy	easy	ADJ
ejde-637	479	3	calculations	calculation	NOUN
ejde-637	479	4	,	,	PUNCT
ejde-637	479	5	it	it	PRON
ejde-637	479	6	follows	follow	VERB
ejde-637	479	7	that	that	SCONJ
ejde-637	479	8	x+	x+	PROPN
ejde-637	479	9	t	t	X
ejde-637	479	10	=	=	SYM
ejde-637	479	11	22/3	22/3	NUM
ejde-637	479	12	,	,	PUNCT
ejde-637	479	13	y+t	y+t	X
ejde-637	479	14	=	=	SYM
ejde-637	479	15	2	2	NUM
ejde-637	479	16	,	,	PUNCT
ejde-637	479	17	y+m1	y+m1	NOUN
ejde-637	479	18	=	=	PUNCT
ejde-637	479	19	−2	−2	NOUN
ejde-637	479	20	,	,	PUNCT
ejde-637	479	21	y+m2	y+m2	PROPN
ejde-637	479	22	=	=	NOUN
ejde-637	479	23	12	12	NUM
ejde-637	479	24	.	.	PUNCT
ejde-637	480	1	in	in	ADP
ejde-637	480	2	addition	addition	NOUN
ejde-637	480	3	,	,	PUNCT
ejde-637	480	4	we	we	PRON
ejde-637	480	5	obtain	obtain	VERB
ejde-637	480	6	the	the	DET
ejde-637	480	7	following	following	ADJ
ejde-637	480	8	statements	statement	NOUN
ejde-637	480	9	:	:	PUNCT
ejde-637	480	10	(	(	PUNCT
ejde-637	480	11	1	1	X
ejde-637	480	12	)	)	PUNCT
ejde-637	480	13	as	as	ADP
ejde-637	480	14	µ	µ	NOUN
ejde-637	480	15	=	=	SYM
ejde-637	480	16	−8.4	−8.4	PROPN
ejde-637	480	17	,	,	PUNCT
ejde-637	480	18	we	we	PRON
ejde-637	480	19	have	have	VERB
ejde-637	480	20	x−	x−	PROPN
ejde-637	480	21	t	t	PROPN
ejde-637	480	22	=	=	PUNCT
ejde-637	480	23	−176/15	−176/15	PROPN
ejde-637	480	24	,	,	PUNCT
ejde-637	480	25	y−t	y−t	VERB
ejde-637	480	26	=	=	NUM
ejde-637	480	27	6.8	6.8	NUM
ejde-637	480	28	,	,	PUNCT
ejde-637	480	29	y−m1	y−m1	NOUN
ejde-637	480	30	=	=	SYM
ejde-637	480	31	15.2	15.2	NUM
ejde-637	480	32	,	,	PUNCT
ejde-637	480	33	y−m2	y−m2	NOUN
ejde-637	480	34	=	=	SYM
ejde-637	480	35	−14.2	−14.2	NOUN
ejde-637	480	36	.	.	PUNCT
ejde-637	480	37	by	by	ADP
ejde-637	480	38	numerical	numerical	PROPN
ejde-637	480	39	simulation	simulation	PROPN
ejde-637	480	40	,	,	PUNCT
ejde-637	480	41	we	we	PRON
ejde-637	480	42	have	have	VERB
ejde-637	480	43	y−	y−	NOUN
ejde-637	480	44	=	=	SYM
ejde-637	480	45	y+m2	y+m2	PROPN
ejde-637	480	46	,	,	PUNCT
ejde-637	480	47	and	and	CCONJ
ejde-637	480	48	there	there	PRON
ejde-637	480	49	exists	exist	VERB
ejde-637	480	50	a	a	DET
ejde-637	480	51	sliding	slide	VERB
ejde-637	480	52	homoclinic	homoclinic	ADJ
ejde-637	480	53	cycle	cycle	NOUN
ejde-637	480	54	illustrated	illustrate	VERB
ejde-637	480	55	in	in	ADP
ejde-637	480	56	figure	figure	NOUN
ejde-637	480	57	4	4	NUM
ejde-637	480	58	,	,	PUNCT
ejde-637	480	59	which	which	PRON
ejde-637	480	60	is	be	AUX
ejde-637	480	61	in	in	ADP
ejde-637	480	62	agreement	agreement	NOUN
ejde-637	480	63	with	with	ADP
ejde-637	480	64	the	the	DET
ejde-637	480	65	orbit	orbit	NOUN
ejde-637	480	66	h1	h1	NOUN
ejde-637	480	67	in	in	ADP
ejde-637	480	68	theorem	theorem	ADJ
ejde-637	480	69	3.6	3.6	NUM
ejde-637	480	70	.	.	PUNCT
ejde-637	480	71	figure	figure	NOUN
ejde-637	480	72	4	4	NUM
ejde-637	480	73	.	.	PUNCT
ejde-637	481	1	existence	existence	NOUN
ejde-637	481	2	of	of	ADP
ejde-637	481	3	the	the	DET
ejde-637	481	4	sliding	slide	VERB
ejde-637	481	5	homoclinic	homoclinic	ADJ
ejde-637	481	6	cycle	cycle	NOUN
ejde-637	481	7	of	of	ADP
ejde-637	481	8	equation	equation	NOUN
ejde-637	481	9	(	(	PUNCT
ejde-637	481	10	5.3	5.3	NUM
ejde-637	481	11	)	)	PUNCT
ejde-637	481	12	with	with	ADP
ejde-637	481	13	µ	µ	X
ejde-637	481	14	=	=	SYM
ejde-637	481	15	−8.4	−8.4	X
ejde-637	481	16	(	(	PUNCT
ejde-637	481	17	2	2	NUM
ejde-637	481	18	)	)	PUNCT
ejde-637	481	19	as	as	ADP
ejde-637	481	20	µ	µ	NOUN
ejde-637	481	21	=	=	SYM
ejde-637	481	22	−7	−7	PROPN
ejde-637	481	23	,	,	PUNCT
ejde-637	481	24	we	we	PRON
ejde-637	481	25	have	have	VERB
ejde-637	481	26	x−	x−	PROPN
ejde-637	481	27	t	t	PROPN
ejde-637	482	1	=	=	SYM
ejde-637	482	2	−31/3	−31/3	PROPN
ejde-637	482	3	,	,	PUNCT
ejde-637	482	4	y−t	y−t	VERB
ejde-637	482	5	=	=	SYM
ejde-637	482	6	4	4	NUM
ejde-637	482	7	,	,	PUNCT
ejde-637	482	8	y−m1	y−m1	NOUN
ejde-637	482	9	=	=	SYM
ejde-637	482	10	11	11	NUM
ejde-637	482	11	,	,	PUNCT
ejde-637	482	12	y−m2	y−m2	NOUN
ejde-637	482	13	=	=	SYM
ejde-637	482	14	−27/2	−27/2	X
ejde-637	482	15	.	.	PROPN
ejde-637	482	16	by	by	ADP
ejde-637	482	17	numerical	numerical	PROPN
ejde-637	482	18	simulation	simulation	PROPN
ejde-637	482	19	,	,	PUNCT
ejde-637	482	20	we	we	PRON
ejde-637	482	21	have	have	VERB
ejde-637	482	22	y−	y−	NOUN
ejde-637	482	23	<	<	X
ejde-637	482	24	y+m2	y+m2	PROPN
ejde-637	482	25	,	,	PUNCT
ejde-637	482	26	and	and	CCONJ
ejde-637	482	27	there	there	PRON
ejde-637	482	28	exists	exist	VERB
ejde-637	482	29	a	a	DET
ejde-637	482	30	sliding	slide	VERB
ejde-637	482	31	cycle	cycle	NOUN
ejde-637	482	32	illustrated	illustrate	VERB
ejde-637	482	33	in	in	ADP
ejde-637	482	34	figure	figure	NOUN
ejde-637	482	35	5	5	NUM
ejde-637	482	36	,	,	PUNCT
ejde-637	482	37	which	which	PRON
ejde-637	482	38	is	be	AUX
ejde-637	482	39	in	in	ADP
ejde-637	482	40	agreement	agreement	NOUN
ejde-637	482	41	with	with	ADP
ejde-637	482	42	the	the	DET
ejde-637	482	43	orbit	orbit	NOUN
ejde-637	482	44	h4	h4	PROPN
ejde-637	482	45	in	in	ADP
ejde-637	482	46	theorem	theorem	PROPN
ejde-637	482	47	3.6	3.6	NUM
ejde-637	482	48	.	.	PUNCT
ejde-637	483	1	(	(	PUNCT
ejde-637	483	2	3	3	NUM
ejde-637	483	3	)	)	PUNCT
ejde-637	483	4	as	as	ADP
ejde-637	483	5	µ	µ	NOUN
ejde-637	483	6	=	=	SYM
ejde-637	483	7	−6.2	−6.2	PROPN
ejde-637	483	8	,	,	PUNCT
ejde-637	483	9	we	we	PRON
ejde-637	483	10	have	have	VERB
ejde-637	483	11	x−	x−	PROPN
ejde-637	483	12	t	t	PROPN
ejde-637	483	13	=	=	SYM
ejde-637	483	14	−143/15	−143/15	PROPN
ejde-637	483	15	,	,	PUNCT
ejde-637	483	16	y−t	y−t	VERB
ejde-637	483	17	=	=	VERB
ejde-637	483	18	2.4	2.4	NUM
ejde-637	483	19	,	,	PUNCT
ejde-637	483	20	y−m1	y−m1	NOUN
ejde-637	483	21	=	=	SYM
ejde-637	483	22	8.6	8.6	NUM
ejde-637	483	23	,	,	PUNCT
ejde-637	483	24	y−m2	y−m2	NOUN
ejde-637	483	25	=	=	SYM
ejde-637	483	26	−13.1	−13.1	NOUN
ejde-637	483	27	.	.	PUNCT
ejde-637	484	1	by	by	ADP
ejde-637	484	2	numerical	numerical	PROPN
ejde-637	484	3	simulation	simulation	PROPN
ejde-637	484	4	,	,	PUNCT
ejde-637	484	5	we	we	PRON
ejde-637	484	6	have	have	VERB
ejde-637	484	7	y−	y−	NOUN
ejde-637	484	8	=	=	SYM
ejde-637	484	9	y+	y+	NOUN
ejde-637	484	10	,	,	PUNCT
ejde-637	484	11	and	and	CCONJ
ejde-637	484	12	there	there	PRON
ejde-637	484	13	exists	exist	VERB
ejde-637	484	14	a	a	DET
ejde-637	484	15	sliding	slide	VERB
ejde-637	484	16	-	-	PUNCT
ejde-637	484	17	zero	zero	NUM
ejde-637	484	18	cycle	cycle	NOUN
ejde-637	484	19	illustrated	illustrate	VERB
ejde-637	484	20	in	in	ADP
ejde-637	484	21	figures	figure	NOUN
ejde-637	484	22	6	6	NUM
ejde-637	484	23	and	and	CCONJ
ejde-637	484	24	7	7	NUM
ejde-637	484	25	,	,	PUNCT
ejde-637	484	26	which	which	PRON
ejde-637	484	27	is	be	AUX
ejde-637	484	28	in	in	ADP
ejde-637	484	29	agreement	agreement	NOUN
ejde-637	484	30	with	with	ADP
ejde-637	484	31	the	the	DET
ejde-637	484	32	orbit	orbit	NOUN
ejde-637	484	33	h2	h2	PROPN
ejde-637	484	34	in	in	ADP
ejde-637	484	35	theorem	theorem	PROPN
ejde-637	484	36	3.6	3.6	NUM
ejde-637	484	37	.	.	PUNCT
ejde-637	485	1	(	(	PUNCT
ejde-637	485	2	4	4	NUM
ejde-637	485	3	)	)	PUNCT
ejde-637	485	4	as	as	ADP
ejde-637	485	5	µ	µ	NOUN
ejde-637	485	6	=	=	SYM
ejde-637	485	7	−6.15	−6.15	NOUN
ejde-637	485	8	,	,	PUNCT
ejde-637	485	9	we	we	PRON
ejde-637	485	10	have	have	VERB
ejde-637	485	11	x−	x−	PROPN
ejde-637	485	12	t	t	PROPN
ejde-637	485	13	=	=	SYM
ejde-637	485	14	−123/20	−123/20	PROPN
ejde-637	485	15	,	,	PUNCT
ejde-637	485	16	y−t	y−t	VERB
ejde-637	485	17	=	=	NOUN
ejde-637	485	18	2.3	2.3	NUM
ejde-637	485	19	,	,	PUNCT
ejde-637	485	20	y−m1	y−m1	NOUN
ejde-637	485	21	=	=	SYM
ejde-637	485	22	8.45	8.45	NUM
ejde-637	485	23	,	,	PUNCT
ejde-637	485	24	y−m2	y−m2	NOUN
ejde-637	486	1	=	=	PUNCT
ejde-637	486	2	−523/40	−523/40	NOUN
ejde-637	486	3	.	.	PUNCT
ejde-637	486	4	by	by	ADP
ejde-637	486	5	numerical	numerical	PROPN
ejde-637	486	6	simulation	simulation	PROPN
ejde-637	486	7	,	,	PUNCT
ejde-637	486	8	we	we	PRON
ejde-637	486	9	have	have	VERB
ejde-637	486	10	y−	y−	NOUN
ejde-637	486	11	<	<	X
ejde-637	486	12	y+	y+	X
ejde-637	486	13	,	,	PUNCT
ejde-637	486	14	and	and	CCONJ
ejde-637	486	15	there	there	PRON
ejde-637	486	16	exists	exist	VERB
ejde-637	486	17	the	the	DET
ejde-637	486	18	attractive	attractive	ADJ
ejde-637	486	19	limit	limit	NOUN
ejde-637	486	20	cycle	cycle	NOUN
ejde-637	486	21	illustrated	illustrate	VERB
ejde-637	486	22	in	in	ADP
ejde-637	486	23	figures	figure	NOUN
ejde-637	486	24	8	8	NUM
ejde-637	486	25	and	and	CCONJ
ejde-637	486	26	9	9	NUM
ejde-637	486	27	,	,	PUNCT
ejde-637	486	28	which	which	PRON
ejde-637	486	29	is	be	AUX
ejde-637	486	30	in	in	ADP
ejde-637	486	31	agreement	agreement	NOUN
ejde-637	486	32	with	with	ADP
ejde-637	486	33	the	the	DET
ejde-637	486	34	orbit	orbit	NOUN
ejde-637	486	35	h6	h6	PROPN
ejde-637	486	36	in	in	ADP
ejde-637	486	37	theorem	theorem	PROPN
ejde-637	486	38	3.6	3.6	NUM
ejde-637	486	39	.	.	PUNCT
ejde-637	487	1	it	it	PRON
ejde-637	487	2	follows	follow	VERB
ejde-637	487	3	that	that	SCONJ
ejde-637	487	4	there	there	PRON
ejde-637	487	5	is	be	VERB
ejde-637	487	6	a	a	DET
ejde-637	487	7	sliding	slide	VERB
ejde-637	487	8	homoclinic	homoclinic	ADJ
ejde-637	487	9	bifurcation	bifurcation	NOUN
ejde-637	487	10	at	at	ADP
ejde-637	487	11	µ	µ	NOUN
ejde-637	487	12	=	=	SYM
ejde-637	487	13	−8.4	−8.4	NOUN
ejde-637	487	14	and	and	CCONJ
ejde-637	487	15	a	a	DET
ejde-637	487	16	sliding	slide	VERB
ejde-637	487	17	cycle	cycle	NOUN
ejde-637	487	18	bifurcation	bifurcation	NOUN
ejde-637	487	19	at	at	ADP
ejde-637	487	20	µ	µ	NOUN
ejde-637	487	21	=	=	SYM
ejde-637	487	22	−6.2	−6.2	PROPN
ejde-637	487	23	.	.	PUNCT
ejde-637	488	1	ejde-2024/57	ejde-2024/57	NOUN
ejde-637	488	2	planar	planar	ADJ
ejde-637	488	3	sector	sector	NOUN
ejde-637	488	4	-	-	PUNCT
ejde-637	488	5	wise	wise	ADJ
ejde-637	488	6	linear	linear	PROPN
ejde-637	488	7	systems	system	NOUN
ejde-637	488	8	19	19	NUM
ejde-637	488	9	figure	figure	NOUN
ejde-637	488	10	5	5	NUM
ejde-637	488	11	.	.	PUNCT
ejde-637	488	12	existence	existence	NOUN
ejde-637	488	13	of	of	ADP
ejde-637	488	14	the	the	DET
ejde-637	488	15	sliding	slide	VERB
ejde-637	488	16	cycle	cycle	NOUN
ejde-637	488	17	of	of	ADP
ejde-637	488	18	equation	equation	NOUN
ejde-637	488	19	(	(	PUNCT
ejde-637	488	20	5.3	5.3	NUM
ejde-637	488	21	)	)	PUNCT
ejde-637	488	22	with	with	ADP
ejde-637	488	23	µ	µ	NOUN
ejde-637	488	24	=	=	PUNCT
ejde-637	488	25	−7	−7	NOUN
ejde-637	488	26	figure	figure	VERB
ejde-637	488	27	6	6	NUM
ejde-637	488	28	.	.	PUNCT
ejde-637	489	1	existence	existence	NOUN
ejde-637	489	2	of	of	ADP
ejde-637	489	3	the	the	DET
ejde-637	489	4	sliding	sliding	ADJ
ejde-637	489	5	-	-	PUNCT
ejde-637	489	6	zero	zero	NUM
ejde-637	489	7	cycle	cycle	NOUN
ejde-637	489	8	of	of	ADP
ejde-637	489	9	equation	equation	NOUN
ejde-637	489	10	(	(	PUNCT
ejde-637	489	11	5.3	5.3	NUM
ejde-637	489	12	)	)	PUNCT
ejde-637	489	13	with	with	ADP
ejde-637	489	14	µ	µ	NOUN
ejde-637	489	15	=	=	SYM
ejde-637	489	16	−6.2	−6.2	PROPN
ejde-637	489	17	6	6	NUM
ejde-637	489	18	.	.	PUNCT
ejde-637	490	1	conclusions	conclusion	NOUN
ejde-637	490	2	in	in	ADP
ejde-637	490	3	this	this	DET
ejde-637	490	4	article	article	NOUN
ejde-637	490	5	,	,	PUNCT
ejde-637	490	6	taking	take	VERB
ejde-637	490	7	the	the	DET
ejde-637	490	8	perturbations	perturbation	NOUN
ejde-637	490	9	to	to	ADP
ejde-637	490	10	the	the	DET
ejde-637	490	11	separation	separation	NOUN
ejde-637	490	12	boundary	boundary	ADJ
ejde-637	490	13	into	into	ADP
ejde-637	490	14	consideration	consideration	NOUN
ejde-637	491	1	,	,	PUNCT
ejde-637	491	2	we	we	PRON
ejde-637	491	3	studied	study	VERB
ejde-637	491	4	a	a	DET
ejde-637	491	5	special	special	ADJ
ejde-637	491	6	class	class	NOUN
ejde-637	491	7	of	of	ADP
ejde-637	491	8	planar	planar	ADJ
ejde-637	491	9	sector	sector	NOUN
ejde-637	491	10	-	-	PUNCT
ejde-637	491	11	wise	wise	ADJ
ejde-637	491	12	linear	linear	NOUN
ejde-637	491	13	systems	system	NOUN
ejde-637	491	14	,	,	PUNCT
ejde-637	491	15	which	which	PRON
ejde-637	491	16	are	be	AUX
ejde-637	491	17	separated	separate	VERB
ejde-637	491	18	by	by	ADP
ejde-637	491	19	two	two	NUM
ejde-637	491	20	rays	ray	NOUN
ejde-637	491	21	starting	start	VERB
ejde-637	491	22	from	from	ADP
ejde-637	491	23	the	the	DET
ejde-637	491	24	same	same	ADJ
ejde-637	491	25	point	point	NOUN
ejde-637	491	26	.	.	PUNCT
ejde-637	492	1	more	more	ADV
ejde-637	492	2	precisely	precisely	ADV
ejde-637	492	3	,	,	PUNCT
ejde-637	492	4	the	the	DET
ejde-637	492	5	two	two	NUM
ejde-637	492	6	subsystems	subsystem	NOUN
ejde-637	492	7	of	of	ADP
ejde-637	492	8	this	this	DET
ejde-637	492	9	planar	planar	ADJ
ejde-637	492	10	sector	sector	NOUN
ejde-637	492	11	-	-	PUNCT
ejde-637	492	12	wise	wise	ADJ
ejde-637	492	13	linear	linear	NOUN
ejde-637	492	14	systems	system	NOUN
ejde-637	492	15	are	be	AUX
ejde-637	492	16	the	the	DET
ejde-637	492	17	same	same	ADJ
ejde-637	492	18	except	except	SCONJ
ejde-637	492	19	for	for	ADP
ejde-637	492	20	the	the	DET
ejde-637	492	21	positions	position	NOUN
ejde-637	492	22	of	of	ADP
ejde-637	492	23	x±	x±	PROPN
ejde-637	492	24	e	e	X
ejde-637	492	25	.	.	PUNCT
ejde-637	493	1	we	we	PRON
ejde-637	493	2	mainly	mainly	ADV
ejde-637	493	3	discussed	discuss	VERB
ejde-637	493	4	the	the	DET
ejde-637	493	5	global	global	ADJ
ejde-637	493	6	qualitative	qualitative	ADJ
ejde-637	493	7	dynamics	dynamic	NOUN
ejde-637	493	8	of	of	ADP
ejde-637	493	9	the	the	DET
ejde-637	493	10	system	system	NOUN
ejde-637	493	11	above	above	ADP
ejde-637	493	12	with	with	ADP
ejde-637	493	13	x±	x±	PROPN
ejde-637	493	14	e	e	NOUN
ejde-637	493	15	being	be	AUX
ejde-637	493	16	saddles	saddle	NOUN
ejde-637	493	17	,	,	PUNCT
ejde-637	493	18	since	since	SCONJ
ejde-637	493	19	the	the	DET
ejde-637	493	20	analysis	analysis	NOUN
ejde-637	493	21	of	of	ADP
ejde-637	493	22	dynamics	dynamic	NOUN
ejde-637	493	23	with	with	ADP
ejde-637	493	24	x±	x±	PROPN
ejde-637	493	25	e	e	NOUN
ejde-637	493	26	being	be	AUX
ejde-637	493	27	sink	sink	NOUN
ejde-637	493	28	or	or	CCONJ
ejde-637	493	29	source	source	NOUN
ejde-637	493	30	points	point	NOUN
ejde-637	493	31	is	be	AUX
ejde-637	493	32	similar	similar	ADJ
ejde-637	493	33	.	.	PUNCT
ejde-637	494	1	because	because	SCONJ
ejde-637	494	2	the	the	DET
ejde-637	494	3	global	global	ADJ
ejde-637	494	4	dynamics	dynamic	NOUN
ejde-637	494	5	of	of	ADP
ejde-637	494	6	piecewise	piecewise	NOUN
ejde-637	494	7	smooth	smooth	ADJ
ejde-637	494	8	systems	system	NOUN
ejde-637	494	9	is	be	AUX
ejde-637	494	10	so	so	ADV
ejde-637	494	11	complex	complex	ADJ
ejde-637	494	12	we	we	PRON
ejde-637	494	13	put	put	VERB
ejde-637	494	14	x+	x+	ADJ
ejde-637	494	15	e	e	X
ejde-637	494	16	>	>	X
ejde-637	494	17	0	0	NUM
ejde-637	494	18	,	,	PUNCT
ejde-637	494	19	y+e	y+e	NUM
ejde-637	495	1	=	=	SYM
ejde-637	496	1	−y−e	−y−e	VERB
ejde-637	496	2	>	>	X
ejde-637	496	3	0	0	PUNCT
ejde-637	497	1	and	and	CCONJ
ejde-637	497	2	only	only	ADV
ejde-637	497	3	left	leave	VERB
ejde-637	497	4	x−	x−	PROPN
ejde-637	497	5	e	e	PROPN
ejde-637	497	6	as	as	ADP
ejde-637	497	7	a	a	DET
ejde-637	497	8	bifurcation	bifurcation	NOUN
ejde-637	497	9	parameter	parameter	NOUN
ejde-637	497	10	.	.	PUNCT
ejde-637	498	1	based	base	VERB
ejde-637	498	2	on	on	ADP
ejde-637	498	3	our	our	PRON
ejde-637	498	4	results	result	NOUN
ejde-637	498	5	of	of	ADP
ejde-637	498	6	the	the	DET
ejde-637	498	7	existence	existence	NOUN
ejde-637	498	8	of	of	ADP
ejde-637	498	9	sliding	slide	VERB
ejde-637	498	10	set	set	VERB
ejde-637	498	11	and	and	CCONJ
ejde-637	498	12	pseudo	pseudo	NOUN
ejde-637	498	13	-	-	NOUN
ejde-637	498	14	equilibrium	equilibrium	NOUN
ejde-637	498	15	points	point	NOUN
ejde-637	498	16	,	,	PUNCT
ejde-637	498	17	and	and	CCONJ
ejde-637	498	18	the	the	DET
ejde-637	498	19	properties	property	NOUN
ejde-637	498	20	of	of	ADP
ejde-637	498	21	the	the	DET
ejde-637	498	22	unique	unique	ADJ
ejde-637	498	23	non	non	ADJ
ejde-637	498	24	-	-	ADJ
ejde-637	498	25	regular	regular	ADJ
ejde-637	498	26	point	point	NOUN
ejde-637	498	27	p0	p0	NOUN
ejde-637	498	28	=	=	SYM
ejde-637	498	29	(	(	PUNCT
ejde-637	498	30	0	0	NUM
ejde-637	498	31	,	,	PUNCT
ejde-637	498	32	0	0	NUM
ejde-637	498	33	)	)	PUNCT
ejde-637	498	34	,	,	PUNCT
ejde-637	498	35	we	we	PRON
ejde-637	498	36	obtained	obtain	VERB
ejde-637	498	37	that	that	SCONJ
ejde-637	498	38	there	there	PRON
ejde-637	498	39	exist	exist	VERB
ejde-637	498	40	sliding	slide	VERB
ejde-637	498	41	cycle	cycle	NOUN
ejde-637	498	42	bifurcation	bifurcation	NOUN
ejde-637	498	43	and	and	CCONJ
ejde-637	498	44	sliding	slide	VERB
ejde-637	498	45	homoclinic	homoclinic	ADJ
ejde-637	498	46	bifurcation	bifurcation	NOUN
ejde-637	498	47	in	in	ADP
ejde-637	498	48	the	the	DET
ejde-637	498	49	above	above	ADJ
ejde-637	498	50	system	system	NOUN
ejde-637	498	51	.	.	PUNCT
ejde-637	499	1	moreover	moreover	ADV
ejde-637	499	2	,	,	PUNCT
ejde-637	499	3	we	we	PRON
ejde-637	499	4	also	also	ADV
ejde-637	499	5	got	get	VERB
ejde-637	499	6	the	the	DET
ejde-637	499	7	existence	existence	NOUN
ejde-637	499	8	of	of	ADP
ejde-637	499	9	all	all	DET
ejde-637	499	10	important	important	ADJ
ejde-637	499	11	separatrixes	separatrix	NOUN
ejde-637	499	12	20	20	NUM
ejde-637	499	13	q.-q	q.-q	PROPN
ejde-637	499	14	.	.	PUNCT
ejde-637	500	1	han	han	PROPN
ejde-637	500	2	,	,	PUNCT
ejde-637	500	3	s.-m	s.-m	PROPN
ejde-637	500	4	.	.	PUNCT
ejde-637	501	1	huan	huan	PROPN
ejde-637	501	2	ejde-2024/57	ejde-2024/57	PROPN
ejde-637	501	3	figure	figure	VERB
ejde-637	501	4	7	7	NUM
ejde-637	501	5	.	.	PUNCT
ejde-637	501	6	expansion	expansion	NOUN
ejde-637	501	7	of	of	ADP
ejde-637	501	8	the	the	DET
ejde-637	501	9	sliding	sliding	ADJ
ejde-637	501	10	-	-	PUNCT
ejde-637	501	11	zero	zero	NUM
ejde-637	501	12	cycle	cycle	NOUN
ejde-637	501	13	in	in	ADP
ejde-637	501	14	figure	figure	NOUN
ejde-637	501	15	6	6	NUM
ejde-637	501	16	figure	figure	NOUN
ejde-637	501	17	8	8	NUM
ejde-637	501	18	.	.	PUNCT
ejde-637	502	1	existence	existence	NOUN
ejde-637	502	2	of	of	ADP
ejde-637	502	3	the	the	DET
ejde-637	502	4	attractive	attractive	ADJ
ejde-637	502	5	limit	limit	NOUN
ejde-637	502	6	cycle	cycle	NOUN
ejde-637	502	7	of	of	ADP
ejde-637	502	8	equation	equation	NOUN
ejde-637	502	9	(	(	PUNCT
ejde-637	502	10	5.3	5.3	NUM
ejde-637	502	11	)	)	PUNCT
ejde-637	502	12	with	with	ADP
ejde-637	502	13	µ	µ	NOUN
ejde-637	502	14	=	=	SYM
ejde-637	502	15	−6.15	−6.15	NOUN
ejde-637	502	16	and	and	CCONJ
ejde-637	502	17	their	their	PRON
ejde-637	502	18	dependence	dependence	NOUN
ejde-637	502	19	on	on	ADP
ejde-637	502	20	the	the	DET
ejde-637	502	21	bifurcation	bifurcation	NOUN
ejde-637	502	22	parameter	parameter	NOUN
ejde-637	502	23	x−	x−	PROPN
ejde-637	502	24	e	e	PROPN
ejde-637	502	25	.	.	PUNCT
ejde-637	503	1	for	for	ADP
ejde-637	503	2	example	example	NOUN
ejde-637	503	3	,	,	PUNCT
ejde-637	503	4	there	there	PRON
ejde-637	503	5	is	be	VERB
ejde-637	503	6	a	a	DET
ejde-637	503	7	sliding	slide	VERB
ejde-637	503	8	heteroclinic	heteroclinic	ADJ
ejde-637	503	9	orbit	orbit	NOUN
ejde-637	503	10	,	,	PUNCT
ejde-637	503	11	which	which	PRON
ejde-637	503	12	first	first	ADV
ejde-637	503	13	turns	turn	VERB
ejde-637	503	14	a	a	DET
ejde-637	503	15	heteroclinic	heteroclinic	ADJ
ejde-637	503	16	cycle	cycle	NOUN
ejde-637	503	17	and	and	CCONJ
ejde-637	503	18	then	then	ADV
ejde-637	503	19	a	a	DET
ejde-637	503	20	limit	limit	NOUN
ejde-637	503	21	cycle	cycle	NOUN
ejde-637	503	22	,	,	PUNCT
ejde-637	503	23	meanwhile	meanwhile	ADV
ejde-637	503	24	,	,	PUNCT
ejde-637	503	25	there	there	PRON
ejde-637	503	26	exists	exist	VERB
ejde-637	503	27	a	a	DET
ejde-637	503	28	sliding	slide	VERB
ejde-637	503	29	heteroclinic	heteroclinic	ADJ
ejde-637	503	30	orbit	orbit	NOUN
ejde-637	503	31	which	which	PRON
ejde-637	503	32	first	first	ADV
ejde-637	503	33	turns	turn	VERB
ejde-637	503	34	a	a	DET
ejde-637	503	35	limit	limit	NOUN
ejde-637	503	36	cycle	cycle	NOUN
ejde-637	503	37	and	and	CCONJ
ejde-637	503	38	then	then	ADV
ejde-637	503	39	a	a	DET
ejde-637	503	40	heteroclinic	heteroclinic	ADJ
ejde-637	503	41	cycle	cycle	NOUN
ejde-637	503	42	.	.	PUNCT
ejde-637	504	1	in	in	ADP
ejde-637	504	2	addition	addition	NOUN
ejde-637	504	3	,	,	PUNCT
ejde-637	504	4	we	we	PRON
ejde-637	504	5	found	find	VERB
ejde-637	504	6	the	the	DET
ejde-637	504	7	coexistence	coexistence	NOUN
ejde-637	504	8	of	of	ADP
ejde-637	504	9	a	a	DET
ejde-637	504	10	sliding	slide	VERB
ejde-637	504	11	homoclinic	homoclinic	ADJ
ejde-637	504	12	cycle	cycle	NOUN
ejde-637	504	13	and	and	CCONJ
ejde-637	504	14	a	a	DET
ejde-637	504	15	sliding	slide	VERB
ejde-637	504	16	heteroclinic	heteroclinic	ADJ
ejde-637	504	17	orbit	orbit	NOUN
ejde-637	504	18	,	,	PUNCT
ejde-637	504	19	while	while	SCONJ
ejde-637	504	20	we	we	PRON
ejde-637	504	21	also	also	ADV
ejde-637	504	22	found	find	VERB
ejde-637	504	23	the	the	DET
ejde-637	504	24	coexistence	coexistence	NOUN
ejde-637	504	25	of	of	ADP
ejde-637	504	26	a	a	DET
ejde-637	504	27	sliding	slide	VERB
ejde-637	504	28	cycle	cycle	NOUN
ejde-637	504	29	and	and	CCONJ
ejde-637	504	30	a	a	DET
ejde-637	504	31	limit	limit	NOUN
ejde-637	504	32	cycle	cycle	NOUN
ejde-637	504	33	.	.	PUNCT
ejde-637	505	1	acknowledgments	acknowledgment	NOUN
ejde-637	505	2	.	.	PUNCT
ejde-637	506	1	this	this	DET
ejde-637	506	2	work	work	NOUN
ejde-637	506	3	is	be	AUX
ejde-637	506	4	supported	support	VERB
ejde-637	506	5	by	by	ADP
ejde-637	506	6	national	national	ADJ
ejde-637	506	7	natural	natural	PROPN
ejde-637	506	8	science	science	PROPN
ejde-637	506	9	foundation	foundation	PROPN
ejde-637	506	10	of	of	ADP
ejde-637	506	11	china	china	PROPN
ejde-637	506	12	(	(	PUNCT
ejde-637	506	13	11301196	11301196	NUM
ejde-637	506	14	)	)	PUNCT
ejde-637	506	15	and	and	CCONJ
ejde-637	506	16	by	by	ADP
ejde-637	506	17	the	the	DET
ejde-637	506	18	fundamental	fundamental	ADJ
ejde-637	506	19	research	research	NOUN
ejde-637	506	20	funds	fund	NOUN
ejde-637	506	21	for	for	ADP
ejde-637	506	22	the	the	DET
ejde-637	506	23	central	central	ADJ
ejde-637	506	24	universities	university	NOUN
ejde-637	506	25	,	,	PUNCT
ejde-637	506	26	hust(2015qn128	hust(2015qn128	NOUN
ejde-637	506	27	)	)	PUNCT
ejde-637	506	28	.	.	PUNCT
ejde-637	507	1	references	reference	NOUN
ejde-637	507	2	[	[	X
ejde-637	507	3	1	1	NUM
ejde-637	507	4	]	]	PUNCT
ejde-637	507	5	andronov	andronov	PROPN
ejde-637	507	6	,	,	PUNCT
ejde-637	507	7	a.	a.	NOUN
ejde-637	507	8	a.	a.	NOUN
ejde-637	507	9	;	;	PUNCT
ejde-637	507	10	vitt	vitt	PROPN
ejde-637	507	11	,	,	PUNCT
ejde-637	507	12	a.	a.	NOUN
ejde-637	507	13	;	;	PUNCT
ejde-637	507	14	khaikin	khaikin	PROPN
ejde-637	507	15	,	,	PUNCT
ejde-637	507	16	s.	s.	PROPN
ejde-637	507	17	;	;	PUNCT
ejde-637	507	18	theory	theory	NOUN
ejde-637	507	19	of	of	ADP
ejde-637	507	20	oscillators	oscillator	NOUN
ejde-637	507	21	,	,	PUNCT
ejde-637	507	22	pergamon	pergamon	PROPN
ejde-637	507	23	press	press	PROPN
ejde-637	507	24	,	,	PUNCT
ejde-637	507	25	oxford	oxford	PROPN
ejde-637	507	26	-	-	PUNCT
ejde-637	507	27	new	new	PROPN
ejde-637	507	28	york	york	PROPN
ejde-637	507	29	-	-	PUNCT
ejde-637	507	30	toronto	toronto	PROPN
ejde-637	507	31	,	,	PUNCT
ejde-637	507	32	ont	ont	PROPN
ejde-637	507	33	.	.	PROPN
ejde-637	507	34	,	,	PUNCT
ejde-637	507	35	1966	1966	NUM
ejde-637	507	36	.	.	PUNCT
ejde-637	508	1	ejde-2024/57	ejde-2024/57	NOUN
ejde-637	508	2	planar	planar	VERB
ejde-637	508	3	sector	sector	NOUN
ejde-637	508	4	-	-	PUNCT
ejde-637	508	5	wise	wise	ADJ
ejde-637	508	6	linear	linear	PROPN
ejde-637	508	7	systems	system	NOUN
ejde-637	508	8	21	21	NUM
ejde-637	508	9	figure	figure	NOUN
ejde-637	508	10	9	9	NUM
ejde-637	508	11	.	.	PUNCT
ejde-637	508	12	eexpansion	eexpansion	NOUN
ejde-637	508	13	of	of	ADP
ejde-637	508	14	the	the	DET
ejde-637	508	15	attractive	attractive	ADJ
ejde-637	508	16	limit	limit	NOUN
ejde-637	508	17	cycle	cycle	NOUN
ejde-637	508	18	in	in	ADP
ejde-637	508	19	figure	figure	NOUN
ejde-637	508	20	8	8	NUM
ejde-637	508	21	[	[	X
ejde-637	508	22	2	2	NUM
ejde-637	508	23	]	]	PUNCT
ejde-637	508	24	barnet	barnet	NOUN
ejde-637	508	25	,	,	PUNCT
ejde-637	508	26	s.	s.	PROPN
ejde-637	508	27	;	;	PUNCT
ejde-637	508	28	cameron	cameron	PROPN
ejde-637	508	29	,	,	PUNCT
ejde-637	508	30	r.	r.	PROPN
ejde-637	508	31	g.	g.	PROPN
ejde-637	508	32	;	;	PUNCT
ejde-637	508	33	introduction	introduction	NOUN
ejde-637	508	34	to	to	ADP
ejde-637	508	35	mathematical	mathematical	ADJ
ejde-637	508	36	control	control	NOUN
ejde-637	508	37	theory	theory	NOUN
ejde-637	508	38	,	,	PUNCT
ejde-637	508	39	oxford	oxford	PROPN
ejde-637	508	40	university	university	PROPN
ejde-637	508	41	press	press	NOUN
ejde-637	508	42	,	,	PUNCT
ejde-637	508	43	new	new	PROPN
ejde-637	508	44	york	york	PROPN
ejde-637	508	45	,	,	PUNCT
ejde-637	508	46	1985	1985	NUM
ejde-637	508	47	.	.	PUNCT
ejde-637	509	1	[	[	X
ejde-637	509	2	3	3	NUM
ejde-637	509	3	]	]	X
ejde-637	509	4	bazykin	bazykin	NOUN
ejde-637	509	5	,	,	PUNCT
ejde-637	509	6	a.	a.	PROPN
ejde-637	509	7	d.	d.	PROPN
ejde-637	509	8	;	;	PUNCT
ejde-637	509	9	nonlinear	nonlinear	ADJ
ejde-637	509	10	dynamics	dynamic	NOUN
ejde-637	509	11	of	of	ADP
ejde-637	509	12	interacting	interact	VERB
ejde-637	509	13	populations	population	NOUN
ejde-637	509	14	,	,	PUNCT
ejde-637	509	15	world	world	NOUN
ejde-637	509	16	scientific	scientific	ADJ
ejde-637	509	17	,	,	PUNCT
ejde-637	509	18	riveredge	riveredge	NOUN
ejde-637	509	19	,	,	PUNCT
ejde-637	509	20	1998	1998	NUM
ejde-637	509	21	.	.	PUNCT
ejde-637	510	1	[	[	X
ejde-637	510	2	4	4	NUM
ejde-637	510	3	]	]	X
ejde-637	510	4	di	di	X
ejde-637	510	5	bernardo	bernardo	PROPN
ejde-637	510	6	,	,	PUNCT
ejde-637	510	7	m.	m.	NOUN
ejde-637	510	8	;	;	PUNCT
ejde-637	510	9	budd	budd	PROPN
ejde-637	510	10	,	,	PUNCT
ejde-637	510	11	c.	c.	PROPN
ejde-637	510	12	j.	j.	PROPN
ejde-637	510	13	;	;	PUNCT
ejde-637	510	14	champneys	champney	NOUN
ejde-637	510	15	,	,	PUNCT
ejde-637	510	16	a.	a.	PROPN
ejde-637	510	17	r.	r.	PROPN
ejde-637	510	18	;	;	PUNCT
ejde-637	510	19	kowalczyk	kowalczyk	VERB
ejde-637	510	20	,	,	PUNCT
ejde-637	510	21	p.	p.	NOUN
ejde-637	510	22	;	;	PUNCT
ejde-637	510	23	piecewise	piecewise	NOUN
ejde-637	510	24	-	-	PUNCT
ejde-637	510	25	smooth	smooth	ADJ
ejde-637	510	26	dynamical	dynamical	ADJ
ejde-637	510	27	systems	system	NOUN
ejde-637	510	28	theory	theory	NOUN
ejde-637	510	29	and	and	CCONJ
ejde-637	510	30	applications	application	NOUN
ejde-637	510	31	,	,	PUNCT
ejde-637	510	32	springer	springer	NOUN
ejde-637	510	33	-	-	PUNCT
ejde-637	510	34	verlag	verlag	PROPN
ejde-637	510	35	,	,	PUNCT
ejde-637	510	36	london	london	PROPN
ejde-637	510	37	,	,	PUNCT
ejde-637	510	38	2008	2008	NUM
ejde-637	510	39	.	.	PUNCT
ejde-637	511	1	[	[	X
ejde-637	511	2	5	5	NUM
ejde-637	511	3	]	]	PUNCT
ejde-637	511	4	braga	braga	NOUN
ejde-637	511	5	,	,	PUNCT
ejde-637	511	6	d.	d.	PROPN
ejde-637	511	7	d.	d.	PROPN
ejde-637	511	8	c.	c.	PROPN
ejde-637	511	9	;	;	PUNCT
ejde-637	511	10	mello	mello	PROPN
ejde-637	511	11	,	,	PUNCT
ejde-637	511	12	l.	l.	PROPN
ejde-637	511	13	f.	f.	PROPN
ejde-637	511	14	;	;	PUNCT
ejde-637	511	15	limit	limit	VERB
ejde-637	511	16	cycles	cycle	NOUN
ejde-637	511	17	in	in	ADP
ejde-637	511	18	a	a	DET
ejde-637	511	19	family	family	NOUN
ejde-637	511	20	of	of	ADP
ejde-637	511	21	discontinuou	discontinuou	NOUN
ejde-637	511	22	piecewise	piecewise	PROPN
ejde-637	511	23	linear	linear	PROPN
ejde-637	511	24	differential	differential	NOUN
ejde-637	511	25	systems	system	NOUN
ejde-637	511	26	with	with	ADP
ejde-637	511	27	two	two	NUM
ejde-637	511	28	zones	zone	NOUN
ejde-637	511	29	in	in	ADP
ejde-637	511	30	the	the	DET
ejde-637	511	31	plane	plane	NOUN
ejde-637	511	32	.	.	PUNCT
ejde-637	512	1	nonlinear	nonlinear	PROPN
ejde-637	512	2	dyn	dyn	PROPN
ejde-637	512	3	,	,	PUNCT
ejde-637	512	4	73	73	NUM
ejde-637	512	5	(	(	PUNCT
ejde-637	512	6	2013	2013	NUM
ejde-637	512	7	):	):	PUNCT
ejde-637	512	8	1283–1288	1283–1288	NUM
ejde-637	512	9	.	.	PUNCT
ejde-637	513	1	[	[	X
ejde-637	513	2	6	6	NUM
ejde-637	513	3	]	]	PUNCT
ejde-637	513	4	brogliato	brogliato	NOUN
ejde-637	513	5	,	,	PUNCT
ejde-637	513	6	b.	b.	PROPN
ejde-637	513	7	;	;	PUNCT
ejde-637	513	8	nonsmooth	nonsmooth	NOUN
ejde-637	513	9	mechanics	mechanic	NOUN
ejde-637	513	10	,	,	PUNCT
ejde-637	513	11	springer	springer	NOUN
ejde-637	513	12	,	,	PUNCT
ejde-637	513	13	new	new	PROPN
ejde-637	513	14	york	york	PROPN
ejde-637	513	15	,	,	PUNCT
ejde-637	513	16	1999	1999	NUM
ejde-637	513	17	.	.	PUNCT
ejde-637	514	1	[	[	X
ejde-637	514	2	7	7	X
ejde-637	514	3	]	]	X
ejde-637	514	4	cardin	cardin	PROPN
ejde-637	514	5	,	,	PUNCT
ejde-637	514	6	p.	p.	PROPN
ejde-637	514	7	t.	t.	PROPN
ejde-637	514	8	;	;	PUNCT
ejde-637	514	9	torregrosa	torregrosa	PROPN
ejde-637	514	10	,	,	PUNCT
ejde-637	514	11	j.	j.	PROPN
ejde-637	514	12	;	;	PUNCT
ejde-637	514	13	limit	limit	VERB
ejde-637	514	14	cycles	cycle	NOUN
ejde-637	514	15	in	in	ADP
ejde-637	514	16	planar	planar	ADJ
ejde-637	514	17	piecewise	piecewise	NOUN
ejde-637	514	18	linear	linear	PROPN
ejde-637	514	19	differential	differential	NOUN
ejde-637	514	20	systems	system	NOUN
ejde-637	514	21	with	with	ADP
ejde-637	514	22	nonregular	nonregular	ADJ
ejde-637	514	23	separation	separation	NOUN
ejde-637	514	24	line	line	NOUN
ejde-637	514	25	.	.	PUNCT
ejde-637	515	1	phys	phy	NOUN
ejde-637	515	2	.	.	PUNCT
ejde-637	516	1	d	d	X
ejde-637	516	2	,	,	PUNCT
ejde-637	516	3	337	337	NUM
ejde-637	516	4	(	(	PUNCT
ejde-637	516	5	2016	2016	NUM
ejde-637	516	6	):	):	PUNCT
ejde-637	516	7	67–82	67–82	NUM
ejde-637	516	8	.	.	PUNCT
ejde-637	517	1	[	[	X
ejde-637	517	2	8	8	NUM
ejde-637	517	3	]	]	X
ejde-637	517	4	castillo	castillo	PROPN
ejde-637	517	5	,	,	PUNCT
ejde-637	517	6	j.	j.	PROPN
ejde-637	517	7	;	;	PUNCT
ejde-637	517	8	llibre	llibre	PROPN
ejde-637	517	9	,	,	PUNCT
ejde-637	517	10	j.	j.	PROPN
ejde-637	517	11	;	;	PUNCT
ejde-637	517	12	verduzco	verduzco	PROPN
ejde-637	517	13	,	,	PUNCT
ejde-637	517	14	f.	f.	PROPN
ejde-637	517	15	;	;	PUNCT
ejde-637	517	16	the	the	DET
ejde-637	517	17	pseudo	pseudo	NOUN
ejde-637	517	18	-	-	ADJ
ejde-637	517	19	hopf	hopf	ADJ
ejde-637	517	20	bifurcation	bifurcation	NOUN
ejde-637	517	21	for	for	ADP
ejde-637	517	22	planar	planar	ADJ
ejde-637	517	23	discontinuous	discontinuous	ADJ
ejde-637	517	24	piecewise	piecewise	NOUN
ejde-637	517	25	linear	linear	PROPN
ejde-637	517	26	differential	differential	NOUN
ejde-637	517	27	systems	system	NOUN
ejde-637	517	28	.	.	PUNCT
ejde-637	518	1	nonlinear	nonlinear	PROPN
ejde-637	518	2	dyn	dyn	PROPN
ejde-637	518	3	,	,	PUNCT
ejde-637	518	4	90	90	NUM
ejde-637	518	5	(	(	PUNCT
ejde-637	518	6	2017	2017	NUM
ejde-637	518	7	):	):	PUNCT
ejde-637	518	8	1829–1840	1829–1840	NUM
ejde-637	518	9	.	.	PUNCT
ejde-637	519	1	[	[	X
ejde-637	519	2	9	9	NUM
ejde-637	519	3	]	]	PUNCT
ejde-637	519	4	coombes	coombe	NOUN
ejde-637	519	5	,	,	PUNCT
ejde-637	519	6	s.	s.	PROPN
ejde-637	519	7	;	;	PUNCT
ejde-637	519	8	thul	thul	PROPN
ejde-637	519	9	,	,	PUNCT
ejde-637	519	10	r.	r.	PROPN
ejde-637	519	11	;	;	PUNCT
ejde-637	519	12	wedgwood	wedgwood	PROPN
ejde-637	519	13	,	,	PUNCT
ejde-637	519	14	k.	k.	PROPN
ejde-637	519	15	c.	c.	PROPN
ejde-637	519	16	a.	a.	PROPN
ejde-637	519	17	;	;	PUNCT
ejde-637	519	18	nonsmooth	nonsmooth	NOUN
ejde-637	519	19	dynamics	dynamic	NOUN
ejde-637	519	20	in	in	ADP
ejde-637	519	21	spiking	spike	VERB
ejde-637	519	22	neuron	neuron	NOUN
ejde-637	519	23	models	model	NOUN
ejde-637	519	24	.	.	PUNCT
ejde-637	520	1	phys	phy	NOUN
ejde-637	520	2	.	.	PUNCT
ejde-637	521	1	d	d	X
ejde-637	521	2	,	,	PUNCT
ejde-637	521	3	241	241	NUM
ejde-637	521	4	(	(	PUNCT
ejde-637	521	5	2012	2012	NUM
ejde-637	521	6	):	):	PUNCT
ejde-637	521	7	2042–2057	2042–2057	NOUN
ejde-637	521	8	.	.	PUNCT
ejde-637	522	1	[	[	X
ejde-637	522	2	10	10	NUM
ejde-637	522	3	]	]	X
ejde-637	522	4	dercole	dercole	NOUN
ejde-637	522	5	,	,	PUNCT
ejde-637	522	6	f.	f.	PROPN
ejde-637	522	7	;	;	PUNCT
ejde-637	522	8	gragnani	gragnani	PROPN
ejde-637	522	9	,	,	PUNCT
ejde-637	522	10	s.	s.	PROPN
ejde-637	522	11	;	;	PUNCT
ejde-637	522	12	rinaldi	rinaldi	PROPN
ejde-637	522	13	,	,	PUNCT
ejde-637	522	14	s.	s.	PROPN
ejde-637	522	15	;	;	PUNCT
ejde-637	522	16	bifurcation	bifurcation	NOUN
ejde-637	522	17	analysis	analysis	NOUN
ejde-637	522	18	of	of	ADP
ejde-637	522	19	piecewise	piecewise	NOUN
ejde-637	522	20	smooth	smooth	ADJ
ejde-637	522	21	ecological	ecological	ADJ
ejde-637	522	22	models	model	NOUN
ejde-637	522	23	.	.	PUNCT
ejde-637	523	1	theor	theor	PROPN
ejde-637	523	2	popul	popul	PROPN
ejde-637	523	3	biol	biol	PROPN
ejde-637	523	4	,	,	PUNCT
ejde-637	523	5	72	72	NUM
ejde-637	523	6	(	(	PUNCT
ejde-637	523	7	2007	2007	NUM
ejde-637	523	8	):	):	PUNCT
ejde-637	523	9	197–213	197–213	NUM
ejde-637	523	10	.	.	PUNCT
ejde-637	524	1	[	[	X
ejde-637	524	2	11	11	NUM
ejde-637	524	3	]	]	SYM
ejde-637	524	4	du	du	X
ejde-637	524	5	,	,	PUNCT
ejde-637	524	6	z.	z.	PROPN
ejde-637	524	7	d.	d.	PROPN
ejde-637	524	8	;	;	PUNCT
ejde-637	524	9	li	li	PROPN
ejde-637	524	10	,	,	PUNCT
ejde-637	524	11	y.	y.	PROPN
ejde-637	524	12	r.	r.	PROPN
ejde-637	524	13	;	;	PUNCT
ejde-637	524	14	zhang	zhang	PROPN
ejde-637	524	15	,	,	PUNCT
ejde-637	524	16	w.	w.	PROPN
ejde-637	524	17	n.	n.	PROPN
ejde-637	524	18	;	;	PUNCT
ejde-637	524	19	bifurcation	bifurcation	NOUN
ejde-637	524	20	of	of	ADP
ejde-637	524	21	periodic	periodic	ADJ
ejde-637	524	22	orbits	orbit	NOUN
ejde-637	524	23	in	in	ADP
ejde-637	524	24	a	a	DET
ejde-637	524	25	class	class	NOUN
ejde-637	524	26	of	of	ADP
ejde-637	524	27	planar	planar	ADJ
ejde-637	524	28	filippov	filippov	ADJ
ejde-637	524	29	systems	system	NOUN
ejde-637	524	30	.	.	PUNCT
ejde-637	525	1	nonlinear	nonlinear	ADJ
ejde-637	525	2	anal	anal	PROPN
ejde-637	525	3	-	-	PUNCT
ejde-637	525	4	theor	theor	PROPN
ejde-637	525	5	,	,	PUNCT
ejde-637	525	6	69	69	NUM
ejde-637	525	7	(	(	PUNCT
ejde-637	525	8	2008	2008	NUM
ejde-637	525	9	):	):	PUNCT
ejde-637	525	10	3610	3610	NUM
ejde-637	525	11	-	-	SYM
ejde-637	525	12	3628	3628	NUM
ejde-637	525	13	.	.	PUNCT
ejde-637	526	1	[	[	X
ejde-637	526	2	12	12	NUM
ejde-637	526	3	]	]	X
ejde-637	526	4	euzébio	euzébio	PROPN
ejde-637	526	5	,	,	PUNCT
ejde-637	526	6	r.	r.	PROPN
ejde-637	526	7	d.	d.	PROPN
ejde-637	526	8	;	;	PUNCT
ejde-637	526	9	llibre	llibre	PROPN
ejde-637	526	10	,	,	PUNCT
ejde-637	526	11	j.	j.	PROPN
ejde-637	526	12	;	;	PUNCT
ejde-637	526	13	on	on	ADP
ejde-637	526	14	the	the	DET
ejde-637	526	15	number	number	NOUN
ejde-637	526	16	of	of	ADP
ejde-637	526	17	limit	limit	NOUN
ejde-637	526	18	cycles	cycle	NOUN
ejde-637	526	19	in	in	ADP
ejde-637	526	20	discontinuous	discontinuous	ADJ
ejde-637	526	21	piecewise	piecewise	NOUN
ejde-637	526	22	linear	linear	PROPN
ejde-637	526	23	differential	differential	NOUN
ejde-637	526	24	systems	system	NOUN
ejde-637	526	25	with	with	ADP
ejde-637	526	26	two	two	NUM
ejde-637	526	27	pieces	piece	NOUN
ejde-637	526	28	separated	separate	VERB
ejde-637	526	29	by	by	ADP
ejde-637	526	30	a	a	DET
ejde-637	526	31	straight	straight	ADJ
ejde-637	526	32	line	line	NOUN
ejde-637	526	33	.	.	PUNCT
ejde-637	527	1	j.	j.	PROPN
ejde-637	527	2	math	math	PROPN
ejde-637	527	3	.	.	PUNCT
ejde-637	528	1	anal	anal	PROPN
ejde-637	528	2	.	.	PUNCT
ejde-637	528	3	appl	appl	PROPN
ejde-637	528	4	,	,	PUNCT
ejde-637	528	5	424	424	NUM
ejde-637	528	6	(	(	PUNCT
ejde-637	528	7	2015	2015	NUM
ejde-637	528	8	):	):	PUNCT
ejde-637	528	9	475–486	475–486	NUM
ejde-637	528	10	.	.	PUNCT
ejde-637	529	1	[	[	X
ejde-637	529	2	13	13	NUM
ejde-637	529	3	]	]	X
ejde-637	529	4	filippov	filippov	NOUN
ejde-637	529	5	,	,	PUNCT
ejde-637	529	6	a.	a.	PROPN
ejde-637	529	7	f.	f.	PROPN
ejde-637	529	8	;	;	PUNCT
ejde-637	529	9	differential	differential	ADJ
ejde-637	529	10	equations	equation	NOUN
ejde-637	529	11	with	with	ADP
ejde-637	529	12	discontinuous	discontinuous	ADJ
ejde-637	529	13	righthand	righthand	NOUN
ejde-637	529	14	sides	side	NOUN
ejde-637	529	15	,	,	PUNCT
ejde-637	529	16	kluwer	kluwer	NOUN
ejde-637	529	17	,	,	PUNCT
ejde-637	529	18	dordrecht	dordrecht	PROPN
ejde-637	529	19	,	,	PUNCT
ejde-637	529	20	1988	1988	NUM
ejde-637	529	21	.	.	PUNCT
ejde-637	530	1	[	[	X
ejde-637	530	2	14	14	NUM
ejde-637	530	3	]	]	SYM
ejde-637	530	4	freire	freire	PROPN
ejde-637	530	5	,	,	PUNCT
ejde-637	530	6	e.	e.	PROPN
ejde-637	530	7	;	;	PUNCT
ejde-637	530	8	ponce	ponce	PROPN
ejde-637	530	9	,	,	PUNCT
ejde-637	530	10	e.	e.	PROPN
ejde-637	530	11	;	;	PUNCT
ejde-637	530	12	rodrigo	rodrigo	PROPN
ejde-637	530	13	,	,	PUNCT
ejde-637	530	14	f.	f.	PROPN
ejde-637	530	15	;	;	PUNCT
ejde-637	530	16	torres	torre	NOUN
ejde-637	530	17	,	,	PUNCT
ejde-637	530	18	f.	f.	PROPN
ejde-637	530	19	;	;	PUNCT
ejde-637	530	20	bifurcation	bifurcation	NOUN
ejde-637	530	21	sets	set	NOUN
ejde-637	530	22	of	of	ADP
ejde-637	530	23	continuous	continuous	ADJ
ejde-637	530	24	piecewise	piecewise	NOUN
ejde-637	530	25	linear	linear	NOUN
ejde-637	530	26	systems	system	NOUN
ejde-637	530	27	with	with	ADP
ejde-637	530	28	two	two	NUM
ejde-637	530	29	zone	zone	NOUN
ejde-637	530	30	.	.	PUNCT
ejde-637	531	1	internat	internat	PROPN
ejde-637	531	2	.	.	PUNCT
ejde-637	532	1	j.	j.	PROPN
ejde-637	532	2	bifur	bifur	PROPN
ejde-637	532	3	.	.	PUNCT
ejde-637	533	1	chaos	chaos	NOUN
ejde-637	533	2	,	,	PUNCT
ejde-637	533	3	8	8	NUM
ejde-637	533	4	(	(	PUNCT
ejde-637	533	5	1998	1998	NUM
ejde-637	533	6	):	):	PUNCT
ejde-637	533	7	2073–2097	2073–2097	NUM
ejde-637	533	8	.	.	PUNCT
ejde-637	534	1	[	[	X
ejde-637	534	2	15	15	NUM
ejde-637	534	3	]	]	SYM
ejde-637	534	4	freire	freire	NOUN
ejde-637	534	5	,	,	PUNCT
ejde-637	534	6	e.	e.	PROPN
ejde-637	534	7	;	;	PUNCT
ejde-637	534	8	ponce	ponce	PROPN
ejde-637	534	9	,	,	PUNCT
ejde-637	534	10	e.	e.	PROPN
ejde-637	534	11	;	;	PUNCT
ejde-637	534	12	torres	torre	NOUN
ejde-637	534	13	,	,	PUNCT
ejde-637	534	14	f.	f.	PROPN
ejde-637	534	15	;	;	PUNCT
ejde-637	534	16	canonical	canonical	ADJ
ejde-637	534	17	discontinuous	discontinuous	ADJ
ejde-637	534	18	planar	planar	ADJ
ejde-637	534	19	piecewise	piecewise	NOUN
ejde-637	534	20	linear	linear	NOUN
ejde-637	534	21	systems	system	NOUN
ejde-637	534	22	.	.	PUNCT
ejde-637	535	1	siam	siam	PROPN
ejde-637	535	2	j.	j.	PROPN
ejde-637	535	3	appl	appl	PROPN
ejde-637	535	4	.	.	PUNCT
ejde-637	536	1	dyn	dyn	PROPN
ejde-637	536	2	.	.	PUNCT
ejde-637	537	1	syst	syst	PROPN
ejde-637	537	2	,	,	PUNCT
ejde-637	537	3	11	11	NUM
ejde-637	537	4	(	(	PUNCT
ejde-637	537	5	2012	2012	NUM
ejde-637	537	6	):	):	PUNCT
ejde-637	537	7	181–211	181–211	NUM
ejde-637	537	8	.	.	PUNCT
ejde-637	538	1	[	[	X
ejde-637	538	2	16	16	NUM
ejde-637	538	3	]	]	SYM
ejde-637	538	4	freire	freire	PROPN
ejde-637	538	5	,	,	PUNCT
ejde-637	538	6	e.	e.	PROPN
ejde-637	538	7	;	;	PUNCT
ejde-637	538	8	ponce	ponce	PROPN
ejde-637	538	9	,	,	PUNCT
ejde-637	538	10	e.	e.	PROPN
ejde-637	538	11	;	;	PUNCT
ejde-637	538	12	torres	torre	NOUN
ejde-637	538	13	,	,	PUNCT
ejde-637	538	14	f.	f.	PROPN
ejde-637	538	15	;	;	PUNCT
ejde-637	538	16	the	the	DET
ejde-637	538	17	discontinuous	discontinuous	ADJ
ejde-637	538	18	matching	matching	NOUN
ejde-637	538	19	of	of	ADP
ejde-637	538	20	two	two	NUM
ejde-637	538	21	planar	planar	ADJ
ejde-637	538	22	linear	linear	ADJ
ejde-637	538	23	foci	focus	NOUN
ejde-637	538	24	can	can	AUX
ejde-637	538	25	have	have	VERB
ejde-637	538	26	three	three	NUM
ejde-637	538	27	nested	nested	ADJ
ejde-637	538	28	crossing	crossing	NOUN
ejde-637	538	29	limit	limit	NOUN
ejde-637	538	30	cycles	cycle	NOUN
ejde-637	538	31	.	.	PUNCT
ejde-637	539	1	publ	publ	NOUN
ejde-637	539	2	.	.	PUNCT
ejde-637	540	1	mat	mat	NOUN
ejde-637	540	2	,	,	PUNCT
ejde-637	540	3	extra	extra	ADJ
ejde-637	540	4	(	(	PUNCT
ejde-637	540	5	2014a	2014a	NUM
ejde-637	540	6	)	)	PUNCT
ejde-637	540	7	,	,	PUNCT
ejde-637	540	8	221–253	221–253	NUM
ejde-637	540	9	.	.	PUNCT
ejde-637	541	1	[	[	X
ejde-637	541	2	17	17	NUM
ejde-637	541	3	]	]	SYM
ejde-637	541	4	freire	freire	NOUN
ejde-637	541	5	,	,	PUNCT
ejde-637	541	6	e.	e.	PROPN
ejde-637	541	7	;	;	PUNCT
ejde-637	541	8	ponce	ponce	PROPN
ejde-637	541	9	,	,	PUNCT
ejde-637	541	10	e.	e.	PROPN
ejde-637	541	11	;	;	PUNCT
ejde-637	541	12	torres	torre	NOUN
ejde-637	541	13	,	,	PUNCT
ejde-637	541	14	f.	f.	PROPN
ejde-637	541	15	;	;	PUNCT
ejde-637	541	16	a	a	DET
ejde-637	541	17	general	general	ADJ
ejde-637	541	18	mechanism	mechanism	NOUN
ejde-637	541	19	to	to	PART
ejde-637	541	20	generate	generate	VERB
ejde-637	541	21	three	three	NUM
ejde-637	541	22	limit	limit	NOUN
ejde-637	541	23	cycles	cycle	NOUN
ejde-637	541	24	in	in	ADP
ejde-637	541	25	planar	planar	ADJ
ejde-637	541	26	filippov	filippov	ADJ
ejde-637	541	27	systems	system	NOUN
ejde-637	541	28	with	with	ADP
ejde-637	541	29	two	two	NUM
ejde-637	541	30	zones	zone	NOUN
ejde-637	541	31	.	.	PUNCT
ejde-637	542	1	nonlinear	nonlinear	ADJ
ejde-637	542	2	dyn	dyn	PROPN
ejde-637	542	3	,	,	PUNCT
ejde-637	542	4	78	78	NUM
ejde-637	542	5	(	(	PUNCT
ejde-637	542	6	2014b	2014b	NUM
ejde-637	542	7	):	):	PUNCT
ejde-637	542	8	251–263	251–263	NUM
ejde-637	542	9	.	.	PUNCT
ejde-637	543	1	[	[	X
ejde-637	543	2	18	18	NUM
ejde-637	543	3	]	]	PUNCT
ejde-637	543	4	guardia	guardia	PROPN
ejde-637	543	5	,	,	PUNCT
ejde-637	543	6	m.	m.	NOUN
ejde-637	543	7	;	;	PUNCT
ejde-637	543	8	seara	seara	X
ejde-637	543	9	,	,	PUNCT
ejde-637	543	10	t.	t.	PROPN
ejde-637	543	11	;	;	PUNCT
ejde-637	543	12	teixeira	teixeira	PROPN
ejde-637	543	13	,	,	PUNCT
ejde-637	543	14	m.a	m.a	PROPN
ejde-637	543	15	.	.	PROPN
ejde-637	543	16	;	;	PUNCT
ejde-637	543	17	generic	generic	ADJ
ejde-637	543	18	bifurcations	bifurcation	NOUN
ejde-637	543	19	of	of	ADP
ejde-637	543	20	low	low	ADJ
ejde-637	543	21	codimension	codimension	NOUN
ejde-637	543	22	of	of	ADP
ejde-637	543	23	planar	planar	ADJ
ejde-637	543	24	filippov	filippov	ADJ
ejde-637	543	25	systems	system	NOUN
ejde-637	543	26	.	.	PUNCT
ejde-637	544	1	j.	j.	PROPN
ejde-637	544	2	diff	diff	PROPN
ejde-637	544	3	.	.	PUNCT
ejde-637	545	1	eqs	eqs	PROPN
ejde-637	545	2	.	.	PROPN
ejde-637	545	3	,	,	PUNCT
ejde-637	545	4	250	250	NUM
ejde-637	545	5	(	(	PUNCT
ejde-637	545	6	2011	2011	NUM
ejde-637	545	7	):	):	PUNCT
ejde-637	545	8	1967	1967	NUM
ejde-637	545	9	-	-	SYM
ejde-637	545	10	2023	2023	NUM
ejde-637	545	11	.	.	PUNCT
ejde-637	546	1	[	[	X
ejde-637	546	2	19	19	NUM
ejde-637	546	3	]	]	SYM
ejde-637	546	4	gu	gu	NOUN
ejde-637	546	5	,	,	PUNCT
ejde-637	546	6	e.	e.	PROPN
ejde-637	546	7	;	;	PUNCT
ejde-637	546	8	bifurcations	bifurcation	NOUN
ejde-637	546	9	and	and	CCONJ
ejde-637	546	10	chaos	chaos	NOUN
ejde-637	546	11	for	for	ADP
ejde-637	546	12	2d	2d	NUM
ejde-637	546	13	discontinuous	discontinuous	ADJ
ejde-637	546	14	dynamical	dynamical	ADJ
ejde-637	546	15	model	model	NOUN
ejde-637	546	16	of	of	ADP
ejde-637	546	17	financial	financial	ADJ
ejde-637	546	18	markets	market	NOUN
ejde-637	546	19	.	.	PUNCT
ejde-637	547	1	internat	internat	PROPN
ejde-637	547	2	.	.	PUNCT
ejde-637	548	1	j.	j.	PROPN
ejde-637	548	2	bifur	bifur	PROPN
ejde-637	548	3	.	.	PUNCT
ejde-637	549	1	chaos	chaos	NOUN
ejde-637	549	2	,	,	PUNCT
ejde-637	549	3	27	27	NUM
ejde-637	549	4	(	(	PUNCT
ejde-637	549	5	2017	2017	NUM
ejde-637	549	6	):	):	PUNCT
ejde-637	549	7	1750185	1750185	NUM
ejde-637	549	8	-	-	SYM
ejde-637	549	9	1	1	NUM
ejde-637	549	10	-	-	SYM
ejde-637	549	11	20	20	NUM
ejde-637	549	12	.	.	PUNCT
ejde-637	550	1	22	22	NUM
ejde-637	550	2	q.-q	q.-q	PROPN
ejde-637	550	3	.	.	PUNCT
ejde-637	551	1	han	han	PROPN
ejde-637	551	2	,	,	PUNCT
ejde-637	551	3	s.-m	s.-m	PROPN
ejde-637	551	4	.	.	PUNCT
ejde-637	552	1	huan	huan	PROPN
ejde-637	552	2	ejde-2024/57	ejde-2024/57	PROPN
ejde-637	553	1	[	[	X
ejde-637	553	2	20	20	NUM
ejde-637	553	3	]	]	X
ejde-637	553	4	guo	guo	PROPN
ejde-637	553	5	,	,	PUNCT
ejde-637	553	6	x.	x.	PROPN
ejde-637	553	7	s.	s.	PROPN
ejde-637	553	8	;	;	PUNCT
ejde-637	553	9	pi	pi	PROPN
ejde-637	553	10	,	,	PUNCT
ejde-637	553	11	d.	d.	PROPN
ejde-637	553	12	h.	h.	PROPN
ejde-637	553	13	;	;	PUNCT
ejde-637	553	14	gao	gao	PROPN
ejde-637	553	15	,	,	PUNCT
ejde-637	553	16	z.	z.	PROPN
ejde-637	553	17	s.	s.	PROPN
ejde-637	553	18	;	;	PUNCT
ejde-637	553	19	bifurcation	bifurcation	NOUN
ejde-637	553	20	analysis	analysis	NOUN
ejde-637	553	21	of	of	ADP
ejde-637	553	22	planar	planar	ADJ
ejde-637	553	23	piecewise	piecewise	NOUN
ejde-637	553	24	linear	linear	NOUN
ejde-637	553	25	system	system	NOUN
ejde-637	553	26	with	with	ADP
ejde-637	553	27	different	different	ADJ
ejde-637	553	28	dynamics	dynamic	NOUN
ejde-637	553	29	.	.	PUNCT
ejde-637	554	1	internat	internat	PROPN
ejde-637	554	2	.	.	PUNCT
ejde-637	555	1	j.	j.	PROPN
ejde-637	555	2	bifur	bifur	PROPN
ejde-637	555	3	.	.	PUNCT
ejde-637	556	1	chaos	chaos	NOUN
ejde-637	556	2	,	,	PUNCT
ejde-637	556	3	26	26	NUM
ejde-637	556	4	(	(	PUNCT
ejde-637	556	5	2016	2016	NUM
ejde-637	556	6	):	):	PUNCT
ejde-637	556	7	1650185	1650185	NUM
ejde-637	556	8	-	-	SYM
ejde-637	556	9	1	1	NUM
ejde-637	556	10	-	-	SYM
ejde-637	556	11	19	19	NUM
ejde-637	556	12	.	.	PUNCT
ejde-637	557	1	[	[	X
ejde-637	557	2	21	21	NUM
ejde-637	557	3	]	]	X
ejde-637	557	4	giannakopoulos	giannakopoulos	PROPN
ejde-637	557	5	,	,	PUNCT
ejde-637	557	6	f.	f.	PROPN
ejde-637	557	7	;	;	PUNCT
ejde-637	557	8	pliete	pliete	PROPN
ejde-637	557	9	,	,	PUNCT
ejde-637	557	10	k.	k.	PROPN
ejde-637	557	11	;	;	PUNCT
ejde-637	557	12	planar	planar	ADJ
ejde-637	557	13	systems	system	NOUN
ejde-637	557	14	of	of	ADP
ejde-637	557	15	piecewise	piecewise	NOUN
ejde-637	557	16	linear	linear	PROPN
ejde-637	557	17	differential	differential	NOUN
ejde-637	557	18	equations	equation	NOUN
ejde-637	557	19	with	with	ADP
ejde-637	557	20	a	a	DET
ejde-637	557	21	line	line	NOUN
ejde-637	557	22	of	of	ADP
ejde-637	557	23	discontinuity	discontinuity	NOUN
ejde-637	557	24	.	.	PUNCT
ejde-637	558	1	nonlinearity	nonlinearity	NOUN
ejde-637	558	2	,	,	PUNCT
ejde-637	558	3	14	14	NUM
ejde-637	558	4	(	(	PUNCT
ejde-637	558	5	2001	2001	NUM
ejde-637	558	6	):	):	PUNCT
ejde-637	558	7	1611	1611	NUM
ejde-637	558	8	.	.	PUNCT
ejde-637	559	1	[	[	X
ejde-637	559	2	22	22	NUM
ejde-637	559	3	]	]	X
ejde-637	559	4	giannakopoulos	giannakopoulos	PROPN
ejde-637	559	5	,	,	PUNCT
ejde-637	559	6	f.	f.	PROPN
ejde-637	559	7	;	;	PUNCT
ejde-637	559	8	pliete	pliete	PROPN
ejde-637	559	9	,	,	PUNCT
ejde-637	559	10	k.	k.	PROPN
ejde-637	559	11	;	;	PUNCT
ejde-637	559	12	closed	close	VERB
ejde-637	559	13	trajectories	trajectory	NOUN
ejde-637	559	14	in	in	ADP
ejde-637	559	15	planar	planar	ADJ
ejde-637	559	16	relay	relay	NOUN
ejde-637	559	17	feedback	feedback	NOUN
ejde-637	559	18	systems	system	NOUN
ejde-637	559	19	.	.	PUNCT
ejde-637	560	1	dynam	dynam	PROPN
ejde-637	560	2	syst	syst	PROPN
ejde-637	560	3	,	,	PUNCT
ejde-637	560	4	17	17	NUM
ejde-637	560	5	(	(	PUNCT
ejde-637	560	6	2002	2002	NUM
ejde-637	560	7	):	):	PUNCT
ejde-637	560	8	343	343	NUM
ejde-637	560	9	-	-	SYM
ejde-637	560	10	358	358	NUM
ejde-637	560	11	.	.	PUNCT
ejde-637	561	1	[	[	X
ejde-637	561	2	23	23	NUM
ejde-637	561	3	]	]	X
ejde-637	561	4	han	han	PROPN
ejde-637	561	5	,	,	PUNCT
ejde-637	561	6	m.	m.	NOUN
ejde-637	561	7	a.	a.	PROPN
ejde-637	561	8	;	;	PUNCT
ejde-637	561	9	zhang	zhang	PROPN
ejde-637	561	10	,	,	PUNCT
ejde-637	561	11	w.	w.	PROPN
ejde-637	561	12	n.	n.	PROPN
ejde-637	561	13	;	;	PUNCT
ejde-637	561	14	on	on	ADP
ejde-637	561	15	hopf	hopf	ADJ
ejde-637	561	16	bifurcation	bifurcation	NOUN
ejde-637	561	17	in	in	ADP
ejde-637	561	18	non	non	ADJ
ejde-637	561	19	-	-	ADJ
ejde-637	561	20	smooth	smooth	ADJ
ejde-637	561	21	planar	planar	ADJ
ejde-637	561	22	systems	system	NOUN
ejde-637	561	23	.	.	PUNCT
ejde-637	562	1	j.	j.	PROPN
ejde-637	562	2	diff	diff	PROPN
ejde-637	562	3	.	.	PUNCT
ejde-637	563	1	eqs	eqs	PROPN
ejde-637	563	2	.	.	PROPN
ejde-637	563	3	,	,	PUNCT
ejde-637	563	4	248	248	NUM
ejde-637	563	5	(	(	PUNCT
ejde-637	563	6	2010	2010	NUM
ejde-637	563	7	):	):	PUNCT
ejde-637	563	8	2399	2399	NUM
ejde-637	563	9	-	-	SYM
ejde-637	563	10	2416	2416	NUM
ejde-637	563	11	.	.	PUNCT
ejde-637	564	1	[	[	X
ejde-637	564	2	24	24	NUM
ejde-637	564	3	]	]	X
ejde-637	564	4	huan	huan	PROPN
ejde-637	564	5	,	,	PUNCT
ejde-637	564	6	s.	s.	PROPN
ejde-637	564	7	m.	m.	PROPN
ejde-637	564	8	;	;	PUNCT
ejde-637	564	9	yang	yang	PROPN
ejde-637	564	10	,	,	PUNCT
ejde-637	564	11	x.	x.	PROPN
ejde-637	564	12	s.	s.	PROPN
ejde-637	564	13	;	;	PUNCT
ejde-637	564	14	generalized	generalize	VERB
ejde-637	564	15	hopf	hopf	ADJ
ejde-637	564	16	bifurcation	bifurcation	NOUN
ejde-637	564	17	emerged	emerge	VERB
ejde-637	564	18	from	from	ADP
ejde-637	564	19	a	a	DET
ejde-637	564	20	corner	corner	NOUN
ejde-637	564	21	in	in	ADP
ejde-637	564	22	general	general	ADJ
ejde-637	564	23	planar	planar	ADJ
ejde-637	564	24	piecewise	piecewise	NOUN
ejde-637	564	25	smooth	smooth	ADJ
ejde-637	564	26	systems	system	NOUN
ejde-637	564	27	.	.	PUNCT
ejde-637	565	1	nonlin	nonlin	PROPN
ejde-637	565	2	.	.	PUNCT
ejde-637	566	1	anal	anal	PROPN
ejde-637	566	2	,	,	PUNCT
ejde-637	566	3	75	75	NUM
ejde-637	566	4	(	(	PUNCT
ejde-637	566	5	2012a	2012a	NUM
ejde-637	566	6	):	):	PUNCT
ejde-637	566	7	6260–6274	6260–6274	NOUN
ejde-637	566	8	.	.	PUNCT
ejde-637	567	1	[	[	X
ejde-637	567	2	25	25	NUM
ejde-637	567	3	]	]	X
ejde-637	567	4	huan	huan	PROPN
ejde-637	567	5	,	,	PUNCT
ejde-637	567	6	s.	s.	PROPN
ejde-637	567	7	m.	m.	PROPN
ejde-637	567	8	;	;	PUNCT
ejde-637	567	9	yang	yang	PROPN
ejde-637	567	10	,	,	PUNCT
ejde-637	567	11	x.	x.	PROPN
ejde-637	567	12	s.	s.	PROPN
ejde-637	567	13	;	;	PUNCT
ejde-637	567	14	on	on	ADP
ejde-637	567	15	the	the	DET
ejde-637	567	16	number	number	NOUN
ejde-637	567	17	of	of	ADP
ejde-637	567	18	limit	limit	NOUN
ejde-637	567	19	cycles	cycle	NOUN
ejde-637	567	20	in	in	ADP
ejde-637	567	21	general	general	ADJ
ejde-637	567	22	planar	planar	ADJ
ejde-637	567	23	piecewise	piecewise	NOUN
ejde-637	567	24	systems	system	NOUN
ejde-637	567	25	.	.	PUNCT
ejde-637	568	1	discrete	discrete	ADJ
ejde-637	568	2	contin	contin	NOUN
ejde-637	568	3	.	.	PUNCT
ejde-637	569	1	dyn	dyn	NOUN
ejde-637	569	2	.	.	PUNCT
ejde-637	570	1	syst	syst	PROPN
ejde-637	570	2	,	,	PUNCT
ejde-637	570	3	32	32	NUM
ejde-637	570	4	(	(	PUNCT
ejde-637	570	5	2012b	2012b	NOUN
ejde-637	570	6	):	):	PUNCT
ejde-637	570	7	2147–2164	2147–2164	NOUN
ejde-637	570	8	.	.	PUNCT
ejde-637	571	1	[	[	X
ejde-637	571	2	26	26	NUM
ejde-637	571	3	]	]	X
ejde-637	571	4	huan	huan	PROPN
ejde-637	571	5	,	,	PUNCT
ejde-637	571	6	s.	s.	PROPN
ejde-637	571	7	m.	m.	PROPN
ejde-637	571	8	;	;	PUNCT
ejde-637	571	9	yang	yang	PROPN
ejde-637	571	10	,	,	PUNCT
ejde-637	571	11	x.	x.	PROPN
ejde-637	571	12	s.	s.	PROPN
ejde-637	571	13	;	;	PUNCT
ejde-637	571	14	existence	existence	NOUN
ejde-637	571	15	of	of	ADP
ejde-637	571	16	limit	limit	NOUN
ejde-637	571	17	cycles	cycle	NOUN
ejde-637	571	18	in	in	ADP
ejde-637	571	19	general	general	ADJ
ejde-637	571	20	planar	planar	ADJ
ejde-637	571	21	piecewise	piecewise	NOUN
ejde-637	571	22	linear	linear	NOUN
ejde-637	571	23	systems	system	NOUN
ejde-637	571	24	of	of	ADP
ejde-637	571	25	saddle	saddle	NOUN
ejde-637	571	26	-	-	PUNCT
ejde-637	571	27	saddle	saddle	NOUN
ejde-637	571	28	dynamics	dynamic	NOUN
ejde-637	571	29	.	.	PUNCT
ejde-637	572	1	nonlinear	nonlinear	ADJ
ejde-637	572	2	anal	anal	NOUN
ejde-637	572	3	,	,	PUNCT
ejde-637	572	4	92	92	NUM
ejde-637	572	5	(	(	PUNCT
ejde-637	572	6	2013	2013	NUM
ejde-637	572	7	):	):	PUNCT
ejde-637	572	8	82–95	82–95	NUM
ejde-637	572	9	.	.	PUNCT
ejde-637	573	1	[	[	X
ejde-637	573	2	27	27	NUM
ejde-637	573	3	]	]	X
ejde-637	573	4	huan	huan	PROPN
ejde-637	573	5	,	,	PUNCT
ejde-637	573	6	s.	s.	PROPN
ejde-637	573	7	m.	m.	PROPN
ejde-637	573	8	;	;	PUNCT
ejde-637	573	9	yang	yang	PROPN
ejde-637	573	10	,	,	PUNCT
ejde-637	573	11	x.	x.	PROPN
ejde-637	573	12	s.	s.	PROPN
ejde-637	573	13	;	;	PUNCT
ejde-637	573	14	on	on	ADP
ejde-637	573	15	the	the	DET
ejde-637	573	16	number	number	NOUN
ejde-637	573	17	of	of	ADP
ejde-637	573	18	limit	limit	NOUN
ejde-637	573	19	cycles	cycle	NOUN
ejde-637	573	20	in	in	ADP
ejde-637	573	21	general	general	ADJ
ejde-637	573	22	planar	planar	ADJ
ejde-637	573	23	piecewise	piecewise	NOUN
ejde-637	573	24	linear	linear	NOUN
ejde-637	573	25	systems	system	NOUN
ejde-637	573	26	of	of	ADP
ejde-637	573	27	node	node	NOUN
ejde-637	573	28	-	-	PUNCT
ejde-637	573	29	node	node	ADJ
ejde-637	573	30	types	type	NOUN
ejde-637	573	31	.	.	PUNCT
ejde-637	574	1	j.	j.	PROPN
ejde-637	574	2	math	math	PROPN
ejde-637	574	3	.	.	PUNCT
ejde-637	575	1	anal	anal	PROPN
ejde-637	575	2	.	.	PUNCT
ejde-637	575	3	appl	appl	PROPN
ejde-637	575	4	,	,	PUNCT
ejde-637	575	5	411	411	NUM
ejde-637	575	6	(	(	PUNCT
ejde-637	575	7	2014a	2014a	NUM
ejde-637	575	8	):	):	PUNCT
ejde-637	575	9	340–353	340–353	NUM
ejde-637	575	10	.	.	PUNCT
ejde-637	576	1	[	[	X
ejde-637	576	2	28	28	NUM
ejde-637	576	3	]	]	X
ejde-637	576	4	huan	huan	PROPN
ejde-637	576	5	,	,	PUNCT
ejde-637	576	6	s.	s.	PROPN
ejde-637	576	7	m.	m.	PROPN
ejde-637	576	8	;	;	PUNCT
ejde-637	576	9	yang	yang	PROPN
ejde-637	576	10	,	,	PUNCT
ejde-637	576	11	x.	x.	PROPN
ejde-637	576	12	s.	s.	PROPN
ejde-637	576	13	;	;	PUNCT
ejde-637	576	14	limit	limit	VERB
ejde-637	576	15	cycles	cycle	NOUN
ejde-637	576	16	in	in	ADP
ejde-637	576	17	a	a	DET
ejde-637	576	18	family	family	NOUN
ejde-637	576	19	of	of	ADP
ejde-637	576	20	planar	planar	ADJ
ejde-637	576	21	piecewise	piecewise	NOUN
ejde-637	576	22	linear	linear	PROPN
ejde-637	576	23	differential	differential	NOUN
ejde-637	576	24	systems	system	NOUN
ejde-637	576	25	with	with	ADP
ejde-637	576	26	a	a	DET
ejde-637	576	27	nonregular	nonregular	ADJ
ejde-637	576	28	separation	separation	NOUN
ejde-637	576	29	line	line	NOUN
ejde-637	576	30	.	.	PUNCT
ejde-637	577	1	internat	internat	PROPN
ejde-637	577	2	.	.	PUNCT
ejde-637	578	1	j.	j.	PROPN
ejde-637	578	2	bifur	bifur	PROPN
ejde-637	578	3	.	.	PUNCT
ejde-637	579	1	chaos	chaos	PROPN
ejde-637	579	2	.	.	PUNCT
ejde-637	579	3	,	,	PUNCT
ejde-637	579	4	29	29	NUM
ejde-637	579	5	(	(	PUNCT
ejde-637	579	6	2019	2019	NUM
ejde-637	579	7	):	):	PUNCT
ejde-637	579	8	1950109	1950109	NUM
ejde-637	579	9	-	-	SYM
ejde-637	579	10	1	1	NUM
ejde-637	579	11	–	–	PUNCT
ejde-637	579	12	22	22	NUM
ejde-637	579	13	.	.	PUNCT
ejde-637	580	1	[	[	X
ejde-637	580	2	29	29	NUM
ejde-637	580	3	]	]	X
ejde-637	580	4	huan	huan	PROPN
ejde-637	580	5	,	,	PUNCT
ejde-637	580	6	s.	s.	PROPN
ejde-637	580	7	m.	m.	PROPN
ejde-637	580	8	;	;	PUNCT
ejde-637	580	9	wu	wu	PROPN
ejde-637	580	10	,	,	PUNCT
ejde-637	580	11	t.	t.	PROPN
ejde-637	580	12	t.	t.	PROPN
ejde-637	580	13	;	;	PUNCT
ejde-637	580	14	wang	wang	PROPN
ejde-637	580	15	,	,	PUNCT
ejde-637	580	16	l.	l.	PROPN
ejde-637	580	17	;	;	PUNCT
ejde-637	580	18	poincaré	poincaré	ADJ
ejde-637	580	19	bifurcations	bifurcation	NOUN
ejde-637	580	20	induced	induce	VERB
ejde-637	580	21	by	by	ADP
ejde-637	580	22	a	a	DET
ejde-637	580	23	non	non	ADJ
ejde-637	580	24	-	-	ADJ
ejde-637	580	25	regular	regular	ADJ
ejde-637	580	26	point	point	NOUN
ejde-637	580	27	on	on	ADP
ejde-637	580	28	the	the	DET
ejde-637	580	29	discontinuity	discontinuity	NOUN
ejde-637	580	30	boundary	boundary	NOUN
ejde-637	580	31	in	in	ADP
ejde-637	580	32	a	a	DET
ejde-637	580	33	family	family	NOUN
ejde-637	580	34	of	of	ADP
ejde-637	580	35	planar	planar	ADJ
ejde-637	580	36	piecewise	piecewise	NOUN
ejde-637	580	37	linear	linear	PROPN
ejde-637	580	38	differential	differential	NOUN
ejde-637	580	39	systems	system	NOUN
ejde-637	580	40	.	.	PUNCT
ejde-637	581	1	internat	internat	PROPN
ejde-637	581	2	.	.	PUNCT
ejde-637	582	1	j.	j.	PROPN
ejde-637	582	2	bifur	bifur	PROPN
ejde-637	582	3	.	.	PUNCT
ejde-637	583	1	chaos	chaos	PROPN
ejde-637	583	2	.	.	PUNCT
ejde-637	583	3	,	,	PUNCT
ejde-637	583	4	31	31	NUM
ejde-637	583	5	(	(	PUNCT
ejde-637	583	6	2021a	2021a	NUM
ejde-637	583	7	):	):	PUNCT
ejde-637	583	8	2150076	2150076	NUM
ejde-637	583	9	-	-	PUNCT
ejde-637	583	10	1–19	1–19	NOUN
ejde-637	583	11	.	.	PUNCT
ejde-637	584	1	[	[	X
ejde-637	584	2	30	30	NUM
ejde-637	584	3	]	]	X
ejde-637	584	4	huan	huan	PROPN
ejde-637	584	5	,	,	PUNCT
ejde-637	584	6	s.	s.	PROPN
ejde-637	584	7	m.	m.	PROPN
ejde-637	584	8	;	;	PUNCT
ejde-637	584	9	on	on	ADP
ejde-637	584	10	the	the	DET
ejde-637	584	11	number	number	NOUN
ejde-637	584	12	of	of	ADP
ejde-637	584	13	limit	limit	NOUN
ejde-637	584	14	cycles	cycle	NOUN
ejde-637	584	15	in	in	ADP
ejde-637	584	16	general	general	ADJ
ejde-637	584	17	planar	planar	ADJ
ejde-637	584	18	piecewise	piecewise	NOUN
ejde-637	584	19	linear	linear	PROPN
ejde-637	584	20	differential	differential	NOUN
ejde-637	584	21	systems	system	NOUN
ejde-637	584	22	with	with	ADP
ejde-637	584	23	two	two	NUM
ejde-637	584	24	zones	zone	NOUN
ejde-637	584	25	having	have	VERB
ejde-637	584	26	two	two	NUM
ejde-637	584	27	real	real	ADJ
ejde-637	584	28	equilibria	equilibrium	NOUN
ejde-637	584	29	.	.	PUNCT
ejde-637	585	1	qual	qual	X
ejde-637	585	2	.	.	PUNCT
ejde-637	585	3	theory	theory	NOUN
ejde-637	585	4	dyn	dyn	PROPN
ejde-637	585	5	.	.	PUNCT
ejde-637	586	1	syst	syst	PROPN
ejde-637	586	2	.	.	PROPN
ejde-637	586	3	,	,	PUNCT
ejde-637	586	4	20	20	NUM
ejde-637	586	5	(	(	PUNCT
ejde-637	586	6	2021b	2021b	NUM
ejde-637	586	7	):	):	PUNCT
ejde-637	586	8	1–31	1–31	PROPN
ejde-637	586	9	.	.	PUNCT
ejde-637	587	1	[	[	X
ejde-637	587	2	31	31	NUM
ejde-637	587	3	]	]	SYM
ejde-637	587	4	han	han	PROPN
ejde-637	587	5	,	,	PUNCT
ejde-637	587	6	q.	q.	PROPN
ejde-637	587	7	q	q	PROPN
ejde-637	587	8	,	,	PUNCT
ejde-637	587	9	;	;	PUNCT
ejde-637	587	10	huan	huan	PROPN
ejde-637	587	11	,	,	PUNCT
ejde-637	587	12	s.	s.	PROPN
ejde-637	587	13	m.	m.	PROPN
ejde-637	587	14	;	;	PUNCT
ejde-637	587	15	dynamics	dynamic	NOUN
ejde-637	587	16	in	in	ADP
ejde-637	587	17	sliding	slide	VERB
ejde-637	587	18	set	set	NOUN
ejde-637	587	19	of	of	ADP
ejde-637	587	20	planar	planar	ADJ
ejde-637	587	21	sector	sector	NOUN
ejde-637	587	22	-	-	PUNCT
ejde-637	587	23	wise	wise	ADJ
ejde-637	587	24	linear	linear	NOUN
ejde-637	587	25	systems	system	NOUN
ejde-637	587	26	.	.	PUNCT
ejde-637	588	1	physica	physica	PROPN
ejde-637	588	2	scripta	scripta	PROPN
ejde-637	588	3	,	,	PUNCT
ejde-637	588	4	98(9	98(9	NOUN
ejde-637	588	5	)	)	PUNCT
ejde-637	588	6	(	(	PUNCT
ejde-637	588	7	2023	2023	NUM
ejde-637	588	8	):	):	PUNCT
ejde-637	588	9	095247	095247	NUM
ejde-637	588	10	.	.	PUNCT
ejde-637	589	1	[	[	X
ejde-637	589	2	32	32	NUM
ejde-637	589	3	]	]	X
ejde-637	589	4	henry	henry	PROPN
ejde-637	589	5	,	,	PUNCT
ejde-637	589	6	c.	c.	PROPN
ejde-637	589	7	;	;	PUNCT
ejde-637	589	8	differential	differential	ADJ
ejde-637	589	9	equations	equation	NOUN
ejde-637	589	10	with	with	ADP
ejde-637	589	11	discontinuous	discontinuous	ADJ
ejde-637	589	12	righthand	righthand	NOUN
ejde-637	589	13	side	side	NOUN
ejde-637	589	14	for	for	ADP
ejde-637	589	15	planning	planning	NOUN
ejde-637	589	16	procedure	procedure	NOUN
ejde-637	589	17	.	.	PUNCT
ejde-637	590	1	j.	j.	PROPN
ejde-637	590	2	econ	econ	PROPN
ejde-637	590	3	.	.	PUNCT
ejde-637	591	1	theory	theory	NOUN
ejde-637	591	2	,	,	PUNCT
ejde-637	591	3	4	4	NUM
ejde-637	591	4	(	(	PUNCT
ejde-637	591	5	1972	1972	NUM
ejde-637	591	6	):	):	PUNCT
ejde-637	591	7	541–551	541–551	NUM
ejde-637	591	8	.	.	PUNCT
ejde-637	592	1	[	[	X
ejde-637	592	2	33	33	NUM
ejde-637	592	3	]	]	X
ejde-637	592	4	jeffrey	jeffrey	PROPN
ejde-637	592	5	,	,	PUNCT
ejde-637	592	6	m.	m.	PROPN
ejde-637	592	7	r.	r.	PROPN
ejde-637	592	8	;	;	PUNCT
ejde-637	592	9	modeling	model	VERB
ejde-637	592	10	with	with	ADP
ejde-637	592	11	nonsmooth	nonsmooth	ADJ
ejde-637	592	12	dynamics	dynamic	NOUN
ejde-637	592	13	,	,	PUNCT
ejde-637	592	14	springer	springer	NOUN
ejde-637	592	15	,	,	PUNCT
ejde-637	592	16	cham	cham	NOUN
ejde-637	592	17	,	,	PUNCT
ejde-637	592	18	2020	2020	NUM
ejde-637	592	19	.	.	PUNCT
ejde-637	593	1	[	[	X
ejde-637	593	2	34	34	NUM
ejde-637	593	3	]	]	X
ejde-637	593	4	krivan	krivan	NOUN
ejde-637	593	5	,	,	PUNCT
ejde-637	593	6	v.	v.	CCONJ
ejde-637	593	7	;	;	PUNCT
ejde-637	593	8	on	on	ADP
ejde-637	593	9	the	the	DET
ejde-637	593	10	gause	gause	PROPN
ejde-637	593	11	predator	predator	NOUN
ejde-637	593	12	-	-	PUNCT
ejde-637	593	13	prey	prey	NOUN
ejde-637	593	14	model	model	NOUN
ejde-637	593	15	with	with	ADP
ejde-637	593	16	a	a	DET
ejde-637	593	17	refuge	refuge	NOUN
ejde-637	593	18	:	:	PUNCT
ejde-637	593	19	a	a	DET
ejde-637	593	20	fresh	fresh	ADJ
ejde-637	593	21	look	look	NOUN
ejde-637	593	22	at	at	ADP
ejde-637	593	23	the	the	DET
ejde-637	593	24	history	history	NOUN
ejde-637	593	25	.	.	PUNCT
ejde-637	594	1	j.	j.	PROPN
ejde-637	594	2	theor	theor	PROPN
ejde-637	594	3	.	.	PUNCT
ejde-637	595	1	biol	biol	PROPN
ejde-637	595	2	,	,	PUNCT
ejde-637	595	3	274	274	NUM
ejde-637	595	4	(	(	PUNCT
ejde-637	595	5	2011	2011	NUM
ejde-637	595	6	):	):	PUNCT
ejde-637	595	7	67–73	67–73	NUM
ejde-637	595	8	.	.	PUNCT
ejde-637	596	1	[	[	X
ejde-637	596	2	35	35	NUM
ejde-637	596	3	]	]	X
ejde-637	596	4	kunze	kunze	PROPN
ejde-637	596	5	,	,	PUNCT
ejde-637	596	6	m.	m.	NOUN
ejde-637	596	7	;	;	PUNCT
ejde-637	596	8	non	non	ADJ
ejde-637	596	9	-	-	ADJ
ejde-637	596	10	smooth	smooth	ADJ
ejde-637	596	11	dynamical	dynamical	ADJ
ejde-637	596	12	systems	system	NOUN
ejde-637	596	13	,	,	PUNCT
ejde-637	596	14	lecture	lecture	NOUN
ejde-637	596	15	notes	note	NOUN
ejde-637	596	16	in	in	ADP
ejde-637	596	17	mathmatics	mathmatics	NOUN
ejde-637	596	18	,	,	PUNCT
ejde-637	596	19	vol	vol	NOUN
ejde-637	596	20	.	.	NOUN
ejde-637	596	21	1744	1744	NUM
ejde-637	596	22	,	,	PUNCT
ejde-637	596	23	springer	springer	NOUN
ejde-637	596	24	-	-	PUNCT
ejde-637	596	25	verlag	verlag	PROPN
ejde-637	596	26	,	,	PUNCT
ejde-637	596	27	berlin	berlin	PROPN
ejde-637	596	28	,	,	PUNCT
ejde-637	596	29	2000	2000	NUM
ejde-637	596	30	.	.	PUNCT
ejde-637	597	1	[	[	X
ejde-637	597	2	36	36	NUM
ejde-637	597	3	]	]	X
ejde-637	597	4	kuznetsov	kuznetsov	NOUN
ejde-637	597	5	,	,	PUNCT
ejde-637	597	6	y.	y.	PROPN
ejde-637	597	7	a.	a.	PROPN
ejde-637	597	8	;	;	PUNCT
ejde-637	597	9	rinaldi	rinaldi	PROPN
ejde-637	597	10	,	,	PUNCT
ejde-637	597	11	s.	s.	PROPN
ejde-637	597	12	;	;	PUNCT
ejde-637	597	13	gragnani	gragnani	PROPN
ejde-637	597	14	,	,	PUNCT
ejde-637	597	15	a.	a.	NOUN
ejde-637	597	16	;	;	PUNCT
ejde-637	597	17	one	one	NUM
ejde-637	597	18	-	-	PUNCT
ejde-637	597	19	parameter	parameter	NOUN
ejde-637	597	20	bifurcations	bifurcation	NOUN
ejde-637	597	21	in	in	ADP
ejde-637	597	22	planar	planar	ADJ
ejde-637	597	23	filippov	filippov	ADJ
ejde-637	597	24	systems	system	NOUN
ejde-637	597	25	.	.	PUNCT
ejde-637	598	1	internat	internat	PROPN
ejde-637	598	2	.	.	PUNCT
ejde-637	599	1	j.	j.	PROPN
ejde-637	599	2	bifur	bifur	PROPN
ejde-637	599	3	.	.	PUNCT
ejde-637	600	1	chaos	chaos	NOUN
ejde-637	600	2	,	,	PUNCT
ejde-637	600	3	13	13	NUM
ejde-637	600	4	(	(	PUNCT
ejde-637	600	5	2003	2003	NUM
ejde-637	600	6	):	):	PUNCT
ejde-637	600	7	2157	2157	NUM
ejde-637	600	8	-	-	SYM
ejde-637	600	9	2188	2188	NUM
ejde-637	600	10	.	.	PUNCT
ejde-637	601	1	[	[	X
ejde-637	601	2	37	37	NUM
ejde-637	601	3	]	]	X
ejde-637	601	4	lefschetz	lefschetz	PROPN
ejde-637	601	5	,	,	PUNCT
ejde-637	601	6	s.	s.	PROPN
ejde-637	601	7	;	;	PUNCT
ejde-637	601	8	stability	stability	NOUN
ejde-637	601	9	of	of	ADP
ejde-637	601	10	nonlinear	nonlinear	PROPN
ejde-637	601	11	control	control	PROPN
ejde-637	601	12	systems	system	NOUN
ejde-637	601	13	,	,	PUNCT
ejde-637	601	14	academic	academic	ADJ
ejde-637	601	15	,	,	PUNCT
ejde-637	601	16	new	new	PROPN
ejde-637	601	17	york	york	PROPN
ejde-637	601	18	,	,	PUNCT
ejde-637	601	19	1965	1965	NUM
ejde-637	601	20	.	.	PUNCT
ejde-637	602	1	[	[	X
ejde-637	602	2	38	38	NUM
ejde-637	602	3	]	]	PUNCT
ejde-637	602	4	llibre	llibre	NOUN
ejde-637	602	5	,	,	PUNCT
ejde-637	602	6	j.	j.	PROPN
ejde-637	602	7	;	;	PUNCT
ejde-637	602	8	ponce	ponce	PROPN
ejde-637	602	9	,	,	PUNCT
ejde-637	602	10	e.	e.	PROPN
ejde-637	602	11	;	;	PUNCT
ejde-637	602	12	three	three	NUM
ejde-637	602	13	nested	nest	VERB
ejde-637	602	14	limit	limit	NOUN
ejde-637	602	15	cycles	cycle	NOUN
ejde-637	602	16	in	in	ADP
ejde-637	602	17	discontinous	discontinous	ADJ
ejde-637	602	18	piecewise	piecewise	NOUN
ejde-637	602	19	linear	linear	PROPN
ejde-637	602	20	differential	differential	NOUN
ejde-637	602	21	systems	system	NOUN
ejde-637	602	22	.	.	PUNCT
ejde-637	603	1	dyn	dyn	NOUN
ejde-637	603	2	.	.	PUNCT
ejde-637	604	1	continuous	continuous	ADJ
ejde-637	604	2	discrete	discrete	ADJ
ejde-637	604	3	impuls	impul	NOUN
ejde-637	604	4	.	.	PUNCT
ejde-637	605	1	syst	syst	NOUN
ejde-637	605	2	.	.	PUNCT
ejde-637	606	1	b	b	X
ejde-637	606	2	,	,	PUNCT
ejde-637	606	3	19	19	NUM
ejde-637	606	4	(	(	PUNCT
ejde-637	606	5	2012	2012	NUM
ejde-637	606	6	):	):	PUNCT
ejde-637	607	1	325–335	325–335	NUM
ejde-637	607	2	.	.	PUNCT
ejde-637	608	1	[	[	X
ejde-637	608	2	39	39	NUM
ejde-637	608	3	]	]	PUNCT
ejde-637	608	4	llibre	llibre	NOUN
ejde-637	608	5	,	,	PUNCT
ejde-637	608	6	j.	j.	PROPN
ejde-637	608	7	;	;	PUNCT
ejde-637	608	8	teixeira	teixeira	PROPN
ejde-637	608	9	,	,	PUNCT
ejde-637	608	10	m.	m.	NOUN
ejde-637	608	11	a.	a.	PROPN
ejde-637	608	12	;	;	PUNCT
ejde-637	608	13	torregrosa	torregrosa	PROPN
ejde-637	608	14	,	,	PUNCT
ejde-637	608	15	j.	j.	PROPN
ejde-637	608	16	;	;	PUNCT
ejde-637	608	17	lower	low	ADJ
ejde-637	608	18	bounds	bound	NOUN
ejde-637	608	19	for	for	ADP
ejde-637	608	20	the	the	DET
ejde-637	608	21	maximum	maximum	ADJ
ejde-637	608	22	number	number	NOUN
ejde-637	608	23	of	of	ADP
ejde-637	608	24	limit	limit	NOUN
ejde-637	608	25	cycles	cycle	NOUN
ejde-637	608	26	of	of	ADP
ejde-637	608	27	discontinuous	discontinuous	ADJ
ejde-637	608	28	piecewise	piecewise	NOUN
ejde-637	608	29	linear	linear	PROPN
ejde-637	608	30	differential	differential	NOUN
ejde-637	608	31	systems	system	NOUN
ejde-637	608	32	with	with	ADP
ejde-637	608	33	a	a	DET
ejde-637	608	34	straight	straight	ADJ
ejde-637	608	35	line	line	NOUN
ejde-637	608	36	of	of	ADP
ejde-637	608	37	separation	separation	NOUN
ejde-637	608	38	.	.	PUNCT
ejde-637	609	1	internat	internat	PROPN
ejde-637	609	2	.	.	PUNCT
ejde-637	610	1	j.	j.	PROPN
ejde-637	610	2	bifur	bifur	PROPN
ejde-637	610	3	.	.	PUNCT
ejde-637	611	1	chaos	chaos	NOUN
ejde-637	611	2	,	,	PUNCT
ejde-637	611	3	23	23	NUM
ejde-637	611	4	(	(	PUNCT
ejde-637	611	5	2013	2013	NUM
ejde-637	611	6	):	):	PUNCT
ejde-637	611	7	1350066	1350066	NUM
ejde-637	611	8	-	-	PUNCT
ejde-637	611	9	1–10	1–10	NOUN
ejde-637	611	10	.	.	PUNCT
ejde-637	612	1	[	[	X
ejde-637	612	2	40	40	NUM
ejde-637	612	3	]	]	PUNCT
ejde-637	612	4	llibre	llibre	NOUN
ejde-637	612	5	,	,	PUNCT
ejde-637	612	6	j.	j.	PROPN
ejde-637	612	7	;	;	PUNCT
ejde-637	612	8	novaes	novaes	PROPN
ejde-637	612	9	,	,	PUNCT
ejde-637	612	10	d.	d.	PROPN
ejde-637	612	11	d.	d.	PROPN
ejde-637	612	12	;	;	PUNCT
ejde-637	612	13	teixeira	teixeira	PROPN
ejde-637	612	14	,	,	PUNCT
ejde-637	612	15	m.	m.	NOUN
ejde-637	612	16	a.	a.	PROPN
ejde-637	612	17	;	;	PUNCT
ejde-637	612	18	limit	limit	VERB
ejde-637	612	19	cycles	cycle	NOUN
ejde-637	612	20	bifurcating	bifurcate	VERB
ejde-637	612	21	from	from	ADP
ejde-637	612	22	the	the	DET
ejde-637	612	23	periodic	periodic	ADJ
ejde-637	612	24	orbits	orbit	NOUN
ejde-637	612	25	of	of	ADP
ejde-637	612	26	a	a	DET
ejde-637	612	27	discontinuous	discontinuous	ADJ
ejde-637	612	28	piecewise	piecewise	NOUN
ejde-637	612	29	linear	linear	PROPN
ejde-637	612	30	differentiable	differentiable	ADJ
ejde-637	612	31	center	center	NOUN
ejde-637	612	32	with	with	ADP
ejde-637	612	33	two	two	NUM
ejde-637	612	34	zones	zone	NOUN
ejde-637	612	35	.	.	PUNCT
ejde-637	613	1	internat	internat	PROPN
ejde-637	613	2	.	.	PUNCT
ejde-637	614	1	j.	j.	PROPN
ejde-637	614	2	bifur	bifur	PROPN
ejde-637	614	3	.	.	PUNCT
ejde-637	615	1	chaos	chaos	NOUN
ejde-637	615	2	,	,	PUNCT
ejde-637	615	3	25	25	NUM
ejde-637	615	4	:	:	SYM
ejde-637	615	5	1550144	1550144	NUM
ejde-637	615	6	-	-	PUNCT
ejde-637	615	7	1–11	1–11	PROPN
ejde-637	615	8	,	,	PUNCT
ejde-637	615	9	2015a	2015a	NUM
ejde-637	615	10	.	.	PUNCT
ejde-637	616	1	[	[	X
ejde-637	616	2	41	41	NUM
ejde-637	616	3	]	]	PUNCT
ejde-637	616	4	llibre	llibre	NOUN
ejde-637	616	5	,	,	PUNCT
ejde-637	616	6	j.	j.	PROPN
ejde-637	616	7	,	,	PUNCT
ejde-637	616	8	novaes	novaes	PROPN
ejde-637	616	9	,	,	PUNCT
ejde-637	616	10	d.	d.	PROPN
ejde-637	616	11	d.	d.	PROPN
ejde-637	616	12	&	&	CCONJ
ejde-637	616	13	teixeira	teixeira	PROPN
ejde-637	616	14	,	,	PUNCT
ejde-637	616	15	m.	m.	NOUN
ejde-637	616	16	a.	a.	NOUN
ejde-637	616	17	maximum	maximum	ADJ
ejde-637	616	18	number	number	NOUN
ejde-637	616	19	of	of	ADP
ejde-637	616	20	limit	limit	NOUN
ejde-637	616	21	cycles	cycle	NOUN
ejde-637	616	22	for	for	ADP
ejde-637	616	23	certain	certain	ADJ
ejde-637	616	24	piecewise	piecewise	NOUN
ejde-637	616	25	linear	linear	ADJ
ejde-637	616	26	dynamical	dynamical	ADJ
ejde-637	616	27	systems	system	NOUN
ejde-637	616	28	.	.	PUNCT
ejde-637	617	1	nonlinear	nonlinear	PROPN
ejde-637	617	2	dyn	dyn	PROPN
ejde-637	617	3	,	,	PUNCT
ejde-637	617	4	82	82	NUM
ejde-637	617	5	(	(	PUNCT
ejde-637	617	6	2015b	2015b	NUM
ejde-637	617	7	):	):	PUNCT
ejde-637	617	8	1159–1175	1159–1175	NUM
ejde-637	617	9	.	.	PUNCT
ejde-637	618	1	[	[	X
ejde-637	618	2	42	42	NUM
ejde-637	618	3	]	]	PUNCT
ejde-637	618	4	llibre	llibre	PROPN
ejde-637	618	5	,	,	PUNCT
ejde-637	618	6	j.	j.	PROPN
ejde-637	618	7	;	;	PUNCT
ejde-637	618	8	teixeira	teixeira	PROPN
ejde-637	618	9	,	,	PUNCT
ejde-637	618	10	m.	m.	NOUN
ejde-637	618	11	a.	a.	PROPN
ejde-637	618	12	;	;	PUNCT
ejde-637	618	13	piecewise	piecewise	NOUN
ejde-637	618	14	linear	linear	PROPN
ejde-637	618	15	differential	differential	NOUN
ejde-637	618	16	systems	system	NOUN
ejde-637	618	17	without	without	ADP
ejde-637	618	18	equilibria	equilibrium	NOUN
ejde-637	618	19	produce	produce	VERB
ejde-637	618	20	limit	limit	NOUN
ejde-637	618	21	cycles	cycle	NOUN
ejde-637	618	22	?	?	PUNCT
ejde-637	619	1	nonlinear	nonlinear	ADJ
ejde-637	619	2	dyn	dyn	PROPN
ejde-637	619	3	,	,	PUNCT
ejde-637	619	4	88	88	NUM
ejde-637	619	5	(	(	PUNCT
ejde-637	619	6	2017	2017	NUM
ejde-637	619	7	):	):	PUNCT
ejde-637	619	8	157–164	157–164	NUM
ejde-637	619	9	.	.	PUNCT
ejde-637	620	1	[	[	X
ejde-637	620	2	43	43	NUM
ejde-637	620	3	]	]	PUNCT
ejde-637	620	4	llibre	llibre	PROPN
ejde-637	620	5	,	,	PUNCT
ejde-637	620	6	j.	j.	PROPN
ejde-637	620	7	;	;	PUNCT
ejde-637	620	8	zhang	zhang	PROPN
ejde-637	620	9	,	,	PUNCT
ejde-637	620	10	x.	x.	NOUN
ejde-637	620	11	;	;	PUNCT
ejde-637	620	12	limit	limit	VERB
ejde-637	620	13	cycles	cycle	NOUN
ejde-637	620	14	for	for	ADP
ejde-637	620	15	discontinuous	discontinuous	ADJ
ejde-637	620	16	planar	planar	ADJ
ejde-637	620	17	piecewise	piecewise	NOUN
ejde-637	620	18	linear	linear	PROPN
ejde-637	620	19	differential	differential	NOUN
ejde-637	620	20	systems	system	NOUN
ejde-637	620	21	separated	separate	VERB
ejde-637	620	22	by	by	ADP
ejde-637	620	23	one	one	NUM
ejde-637	620	24	straight	straight	ADJ
ejde-637	620	25	line	line	NOUN
ejde-637	620	26	and	and	CCONJ
ejde-637	620	27	having	have	VERB
ejde-637	620	28	a	a	DET
ejde-637	620	29	center	center	NOUN
ejde-637	620	30	.	.	PUNCT
ejde-637	621	1	j.	j.	PROPN
ejde-637	621	2	math	math	PROPN
ejde-637	621	3	.	.	PUNCT
ejde-637	622	1	anal	anal	PROPN
ejde-637	622	2	.	.	PUNCT
ejde-637	622	3	appl	appl	PROPN
ejde-637	622	4	,	,	PUNCT
ejde-637	622	5	467	467	NUM
ejde-637	622	6	(	(	PUNCT
ejde-637	622	7	2018	2018	NUM
ejde-637	622	8	):	):	PUNCT
ejde-637	622	9	537–549	537–549	NUM
ejde-637	622	10	.	.	PUNCT
ejde-637	623	1	[	[	X
ejde-637	623	2	44	44	NUM
ejde-637	623	3	]	]	PUNCT
ejde-637	623	4	llibre	llibre	PROPN
ejde-637	623	5	,	,	PUNCT
ejde-637	623	6	j.	j.	PROPN
ejde-637	623	7	;	;	PUNCT
ejde-637	623	8	zhang	zhang	PROPN
ejde-637	623	9	,	,	PUNCT
ejde-637	623	10	x.	x.	NOUN
ejde-637	623	11	;	;	PUNCT
ejde-637	623	12	limit	limit	VERB
ejde-637	623	13	cycles	cycle	NOUN
ejde-637	623	14	for	for	ADP
ejde-637	623	15	discontinuous	discontinuous	ADJ
ejde-637	623	16	planar	planar	ADJ
ejde-637	623	17	piecewise	piecewise	NOUN
ejde-637	623	18	linear	linear	PROPN
ejde-637	623	19	differential	differential	NOUN
ejde-637	623	20	systems	system	NOUN
ejde-637	623	21	separated	separate	VERB
ejde-637	623	22	by	by	ADP
ejde-637	623	23	an	an	DET
ejde-637	623	24	algebraic	algebraic	ADJ
ejde-637	623	25	curve	curve	NOUN
ejde-637	623	26	.	.	PUNCT
ejde-637	624	1	internat	internat	PROPN
ejde-637	624	2	.	.	PUNCT
ejde-637	625	1	j.	j.	PROPN
ejde-637	625	2	bifur	bifur	PROPN
ejde-637	625	3	.	.	PUNCT
ejde-637	626	1	chaos	chaos	NOUN
ejde-637	626	2	,	,	PUNCT
ejde-637	626	3	29	29	NUM
ejde-637	626	4	(	(	PUNCT
ejde-637	626	5	2019	2019	NUM
ejde-637	626	6	):	):	PUNCT
ejde-637	626	7	1950017	1950017	NUM
ejde-637	626	8	-	-	SYM
ejde-637	626	9	1–17	1–17	NUM
ejde-637	626	10	.	.	PUNCT
ejde-637	627	1	[	[	X
ejde-637	627	2	45	45	NUM
ejde-637	627	3	]	]	PUNCT
ejde-637	627	4	maggio	maggio	NOUN
ejde-637	627	5	,	,	PUNCT
ejde-637	627	6	g.	g.	PROPN
ejde-637	627	7	m.	m.	PROPN
ejde-637	627	8	;	;	PUNCT
ejde-637	627	9	di	di	NOUN
ejde-637	627	10	bernardo	bernardo	PROPN
ejde-637	627	11	,	,	PUNCT
ejde-637	627	12	m.	m.	NOUN
ejde-637	627	13	;	;	PUNCT
ejde-637	627	14	kennedy	kennedy	PROPN
ejde-637	627	15	,	,	PUNCT
ejde-637	627	16	m.	m.	NOUN
ejde-637	627	17	p.	p.	NOUN
ejde-637	627	18	;	;	PUNCT
ejde-637	627	19	nonsmooth	nonsmooth	NOUN
ejde-637	627	20	bifurcations	bifurcation	NOUN
ejde-637	627	21	in	in	ADP
ejde-637	627	22	a	a	DET
ejde-637	627	23	piecewise	piecewise	NOUN
ejde-637	627	24	linear	linear	NOUN
ejde-637	627	25	model	model	NOUN
ejde-637	627	26	of	of	ADP
ejde-637	627	27	the	the	DET
ejde-637	627	28	colpitts	colpitts	PROPN
ejde-637	627	29	oscillator	oscillator	PROPN
ejde-637	627	30	.	.	PUNCT
ejde-637	628	1	ieee	ieee	PROPN
ejde-637	628	2	trans	trans	PROPN
ejde-637	628	3	.	.	PUNCT
ejde-637	629	1	circuits	circuit	VERB
ejde-637	629	2	systems	system	NOUN
ejde-637	629	3	i	i	PRON
ejde-637	629	4	fund	fund	VERB
ejde-637	629	5	.	.	PUNCT
ejde-637	630	1	theory	theory	NOUN
ejde-637	630	2	appl	appl	PROPN
ejde-637	630	3	.	.	PROPN
ejde-637	631	1	,	,	PUNCT
ejde-637	631	2	47	47	NUM
ejde-637	631	3	(	(	PUNCT
ejde-637	631	4	2000	2000	NUM
ejde-637	631	5	):	):	PUNCT
ejde-637	631	6	1160–1177	1160–1177	NUM
ejde-637	631	7	.	.	PUNCT
ejde-637	632	1	ejde-2024/57	ejde-2024/57	NOUN
ejde-637	632	2	planar	planar	VERB
ejde-637	632	3	sector	sector	NOUN
ejde-637	632	4	-	-	PUNCT
ejde-637	632	5	wise	wise	ADJ
ejde-637	632	6	linear	linear	NOUN
ejde-637	632	7	systems	system	NOUN
ejde-637	632	8	23	23	NUM
ejde-637	633	1	[	[	SYM
ejde-637	633	2	46	46	NUM
ejde-637	633	3	]	]	SYM
ejde-637	633	4	novaes	novaes	PROPN
ejde-637	633	5	,	,	PUNCT
ejde-637	633	6	d.	d.	PROPN
ejde-637	633	7	d.	d.	PROPN
ejde-637	633	8	;	;	PUNCT
ejde-637	633	9	ponce	ponce	PROPN
ejde-637	633	10	,	,	PUNCT
ejde-637	633	11	e.	e.	PROPN
ejde-637	633	12	;	;	PUNCT
ejde-637	633	13	a	a	DET
ejde-637	633	14	simple	simple	ADJ
ejde-637	633	15	solution	solution	NOUN
ejde-637	633	16	to	to	ADP
ejde-637	633	17	the	the	DET
ejde-637	633	18	braga	braga	NOUN
ejde-637	633	19	-	-	PUNCT
ejde-637	633	20	mello	mello	PROPN
ejde-637	633	21	conjecture	conjecture	NOUN
ejde-637	633	22	.	.	PUNCT
ejde-637	634	1	internat	internat	PROPN
ejde-637	634	2	.	.	PUNCT
ejde-637	635	1	j.	j.	PROPN
ejde-637	635	2	bifur	bifur	PROPN
ejde-637	635	3	.	.	PUNCT
ejde-637	636	1	chaos	chaos	NOUN
ejde-637	636	2	,	,	PUNCT
ejde-637	636	3	25	25	NUM
ejde-637	636	4	(	(	PUNCT
ejde-637	636	5	2015	2015	NUM
ejde-637	636	6	):	):	PUNCT
ejde-637	636	7	1550009	1550009	NUM
ejde-637	636	8	-	-	SYM
ejde-637	636	9	1	1	NUM
ejde-637	636	10	-	-	SYM
ejde-637	636	11	7	7	NUM
ejde-637	636	12	.	.	PUNCT
ejde-637	637	1	[	[	X
ejde-637	637	2	47	47	NUM
ejde-637	637	3	]	]	X
ejde-637	637	4	ponce	ponce	NOUN
ejde-637	637	5	,	,	PUNCT
ejde-637	637	6	e.	e.	PROPN
ejde-637	637	7	;	;	PUNCT
ejde-637	637	8	ros	ros	PROPN
ejde-637	637	9	,	,	PUNCT
ejde-637	637	10	j.	j.	PROPN
ejde-637	637	11	;	;	PUNCT
ejde-637	637	12	vela	vela	PROPN
ejde-637	637	13	,	,	PUNCT
ejde-637	637	14	e.	e.	PROPN
ejde-637	637	15	;	;	PUNCT
ejde-637	637	16	the	the	DET
ejde-637	637	17	boundary	boundary	ADJ
ejde-637	637	18	focus	focus	NOUN
ejde-637	637	19	-	-	PUNCT
ejde-637	637	20	saddle	saddle	NOUN
ejde-637	637	21	bifurcation	bifurcation	NOUN
ejde-637	637	22	in	in	ADP
ejde-637	637	23	planar	planar	ADJ
ejde-637	637	24	piecewise	piecewise	NOUN
ejde-637	637	25	linear	linear	NOUN
ejde-637	637	26	systems	system	NOUN
ejde-637	637	27	.	.	PUNCT
ejde-637	638	1	application	application	NOUN
ejde-637	638	2	to	to	ADP
ejde-637	638	3	the	the	DET
ejde-637	638	4	analysis	analysis	NOUN
ejde-637	638	5	of	of	ADP
ejde-637	638	6	memristor	memristor	NOUN
ejde-637	638	7	oscillators	oscillator	NOUN
ejde-637	638	8	.	.	PUNCT
ejde-637	639	1	nonlinear	nonlinear	ADJ
ejde-637	639	2	anal	anal	PROPN
ejde-637	639	3	.	.	PUNCT
ejde-637	640	1	ser	ser	NOUN
ejde-637	640	2	.	.	PUNCT
ejde-637	641	1	b	b	X
ejde-637	641	2	:	:	PUNCT
ejde-637	641	3	real	real	ADJ
ejde-637	641	4	world	world	NOUN
ejde-637	641	5	appl	appl	PROPN
ejde-637	641	6	,	,	PUNCT
ejde-637	641	7	43	43	NUM
ejde-637	641	8	(	(	PUNCT
ejde-637	641	9	2018	2018	NUM
ejde-637	641	10	):	):	PUNCT
ejde-637	641	11	495–514	495–514	NUM
ejde-637	641	12	.	.	PUNCT
ejde-637	642	1	[	[	X
ejde-637	642	2	48	48	NUM
ejde-637	642	3	]	]	SYM
ejde-637	642	4	pi	pi	NOUN
ejde-637	642	5	,	,	PUNCT
ejde-637	642	6	d.	d.	PROPN
ejde-637	642	7	h.	h.	PROPN
ejde-637	642	8	;	;	PUNCT
ejde-637	642	9	yu	yu	PROPN
ejde-637	642	10	,	,	PUNCT
ejde-637	642	11	j.	j.	PROPN
ejde-637	642	12	;	;	PUNCT
ejde-637	642	13	zhang	zhang	PROPN
ejde-637	642	14	,	,	PUNCT
ejde-637	642	15	x.	x.	PROPN
ejde-637	642	16	;	;	PUNCT
ejde-637	642	17	on	on	ADP
ejde-637	642	18	the	the	DET
ejde-637	642	19	sliding	slide	VERB
ejde-637	642	20	bifurcation	bifurcation	NOUN
ejde-637	642	21	of	of	ADP
ejde-637	642	22	a	a	DET
ejde-637	642	23	class	class	NOUN
ejde-637	642	24	of	of	ADP
ejde-637	642	25	planar	planar	ADJ
ejde-637	642	26	filippov	filippov	ADJ
ejde-637	642	27	systems	system	NOUN
ejde-637	642	28	.	.	PUNCT
ejde-637	643	1	internat	internat	PROPN
ejde-637	643	2	.	.	PUNCT
ejde-637	644	1	j.	j.	PROPN
ejde-637	644	2	bifur	bifur	PROPN
ejde-637	644	3	.	.	PUNCT
ejde-637	645	1	chaos	chaos	PROPN
ejde-637	645	2	.	.	PUNCT
ejde-637	645	3	,	,	PUNCT
ejde-637	645	4	23	23	NUM
ejde-637	645	5	(	(	PUNCT
ejde-637	645	6	2013	2013	NUM
ejde-637	645	7	):	):	PUNCT
ejde-637	645	8	1350040	1350040	NUM
ejde-637	645	9	.	.	PUNCT
ejde-637	646	1	[	[	X
ejde-637	646	2	49	49	NUM
ejde-637	646	3	]	]	SYM
ejde-637	646	4	pi	pi	NOUN
ejde-637	646	5	,	,	PUNCT
ejde-637	646	6	d.	d.	PROPN
ejde-637	646	7	h.	h.	PROPN
ejde-637	646	8	;	;	PUNCT
ejde-637	646	9	zhang	zhang	PROPN
ejde-637	646	10	,	,	PUNCT
ejde-637	646	11	x.	x.	PROPN
ejde-637	646	12	;	;	PUNCT
ejde-637	646	13	the	the	DET
ejde-637	646	14	sliding	slide	VERB
ejde-637	646	15	bifurcations	bifurcation	NOUN
ejde-637	646	16	in	in	ADP
ejde-637	646	17	planar	planar	ADJ
ejde-637	646	18	piecewise	piecewise	NOUN
ejde-637	646	19	smooth	smooth	ADJ
ejde-637	646	20	differential	differential	NOUN
ejde-637	646	21	systems	system	NOUN
ejde-637	646	22	.	.	PUNCT
ejde-637	647	1	j.	j.	PROPN
ejde-637	647	2	diff	diff	PROPN
ejde-637	647	3	.	.	PUNCT
ejde-637	648	1	eqs	eqs	PROPN
ejde-637	648	2	.	.	PROPN
ejde-637	648	3	,	,	PUNCT
ejde-637	648	4	25	25	NUM
ejde-637	648	5	(	(	PUNCT
ejde-637	648	6	2013	2013	NUM
ejde-637	648	7	):	):	PUNCT
ejde-637	648	8	1001–1026	1001–1026	NUM
ejde-637	648	9	.	.	PUNCT
ejde-637	649	1	[	[	X
ejde-637	649	2	50	50	NUM
ejde-637	649	3	]	]	SYM
ejde-637	649	4	simpson	simpson	PROPN
ejde-637	649	5	,	,	PUNCT
ejde-637	649	6	d.j.w	d.j.w	PROPN
ejde-637	649	7	.	.	PUNCT
ejde-637	649	8	;	;	PUNCT
ejde-637	649	9	twenty	twenty	NUM
ejde-637	649	10	hopf	hopf	ADV
ejde-637	649	11	-	-	PUNCT
ejde-637	649	12	like	like	ADJ
ejde-637	649	13	bifurcations	bifurcation	NOUN
ejde-637	649	14	in	in	ADP
ejde-637	649	15	piecewise	piecewise	NOUN
ejde-637	649	16	-	-	PUNCT
ejde-637	649	17	smooth	smooth	ADJ
ejde-637	649	18	dynamical	dynamical	ADJ
ejde-637	649	19	systems	system	NOUN
ejde-637	649	20	.	.	PUNCT
ejde-637	650	1	pr	pr	NOUN
ejde-637	650	2	,	,	PUNCT
ejde-637	650	3	970	970	NUM
ejde-637	650	4	(	(	PUNCT
ejde-637	650	5	2022	2022	NUM
ejde-637	650	6	):	):	PUNCT
ejde-637	650	7	1	1	NUM
ejde-637	650	8	-	-	SYM
ejde-637	650	9	80	80	NUM
ejde-637	650	10	.	.	PUNCT
ejde-637	651	1	[	[	X
ejde-637	651	2	51	51	NUM
ejde-637	651	3	]	]	SYM
ejde-637	651	4	stoker	stoker	NOUN
ejde-637	651	5	,	,	PUNCT
ejde-637	651	6	j.	j.	PROPN
ejde-637	651	7	j.	j.	PROPN
ejde-637	651	8	;	;	PUNCT
ejde-637	651	9	nonlinear	nonlinear	ADJ
ejde-637	651	10	vibrations	vibration	NOUN
ejde-637	651	11	in	in	ADP
ejde-637	651	12	mechanical	mechanical	ADJ
ejde-637	651	13	and	and	CCONJ
ejde-637	651	14	electrical	electrical	ADJ
ejde-637	651	15	systems	system	NOUN
ejde-637	651	16	,	,	PUNCT
ejde-637	651	17	interscience	interscience	NOUN
ejde-637	651	18	publishers	publisher	NOUN
ejde-637	651	19	,	,	PUNCT
ejde-637	651	20	inc	inc	PROPN
ejde-637	651	21	.	.	PROPN
ejde-637	651	22	,	,	PUNCT
ejde-637	651	23	new	new	PROPN
ejde-637	651	24	york	york	PROPN
ejde-637	651	25	,	,	PUNCT
ejde-637	651	26	n.y	n.y	PROPN
ejde-637	651	27	.	.	PROPN
ejde-637	651	28	,	,	PUNCT
ejde-637	651	29	1950	1950	NUM
ejde-637	651	30	[	[	X
ejde-637	651	31	52	52	NUM
ejde-637	651	32	]	]	PUNCT
ejde-637	651	33	tonnelier	tonnelier	NOUN
ejde-637	651	34	,	,	PUNCT
ejde-637	651	35	a.	a.	NOUN
ejde-637	651	36	;	;	PUNCT
ejde-637	651	37	gerstner	gerstner	PROPN
ejde-637	651	38	,	,	PUNCT
ejde-637	651	39	w.	w.	PROPN
ejde-637	651	40	;	;	PUNCT
ejde-637	651	41	piecewise	piecewise	NOUN
ejde-637	651	42	linear	linear	PROPN
ejde-637	651	43	differential	differential	NOUN
ejde-637	651	44	equations	equation	NOUN
ejde-637	651	45	and	and	CCONJ
ejde-637	651	46	integrate	integrate	VERB
ejde-637	651	47	-	-	PUNCT
ejde-637	651	48	and	and	CCONJ
ejde-637	651	49	-	-	PUNCT
ejde-637	651	50	fire	fire	NOUN
ejde-637	651	51	neurons	neuron	NOUN
ejde-637	651	52	:	:	PUNCT
ejde-637	651	53	insights	insight	NOUN
ejde-637	651	54	from	from	ADP
ejde-637	651	55	two	two	NUM
ejde-637	651	56	-	-	PUNCT
ejde-637	651	57	dimensional	dimensional	ADJ
ejde-637	651	58	membrane	membrane	NOUN
ejde-637	651	59	models	model	NOUN
ejde-637	651	60	.	.	PUNCT
ejde-637	652	1	phys	phy	NOUN
ejde-637	652	2	.	.	PUNCT
ejde-637	653	1	rev	rev	PROPN
ejde-637	653	2	.	.	PROPN
ejde-637	654	1	e	e	PROPN
ejde-637	654	2	,	,	PUNCT
ejde-637	654	3	67	67	NUM
ejde-637	654	4	(	(	PUNCT
ejde-637	654	5	2003	2003	NUM
ejde-637	654	6	):	):	PUNCT
ejde-637	654	7	021908	021908	NUM
ejde-637	654	8	.	.	PUNCT
ejde-637	655	1	[	[	X
ejde-637	655	2	53	53	NUM
ejde-637	655	3	]	]	X
ejde-637	655	4	xiong	xiong	PROPN
ejde-637	655	5	,	,	PUNCT
ejde-637	655	6	l.	l.	PROPN
ejde-637	655	7	,	,	PUNCT
ejde-637	655	8	wu	wu	PROPN
ejde-637	655	9	,	,	PUNCT
ejde-637	655	10	k.l	k.l	PROPN
ejde-637	655	11	&	&	CCONJ
ejde-637	655	12	li	li	PROPN
ejde-637	655	13	,	,	PUNCT
ejde-637	655	14	s.	s.	PROPN
ejde-637	655	15	m.	m.	PROPN
ejde-637	655	16	;	;	PUNCT
ejde-637	655	17	phase	phase	NOUN
ejde-637	655	18	portraits	portrait	NOUN
ejde-637	655	19	of	of	ADP
ejde-637	655	20	the	the	DET
ejde-637	655	21	discontinuous	discontinuous	ADJ
ejde-637	655	22	planar	planar	ADJ
ejde-637	655	23	piecewise	piecewise	NOUN
ejde-637	655	24	linear	linear	PROPN
ejde-637	655	25	differential	differential	NOUN
ejde-637	655	26	systems	system	NOUN
ejde-637	655	27	of	of	ADP
ejde-637	655	28	focus	focus	NOUN
ejde-637	655	29	-	-	PUNCT
ejde-637	655	30	center	center	NOUN
ejde-637	655	31	type	type	NOUN
ejde-637	655	32	.	.	PUNCT
ejde-637	656	1	qual	qual	X
ejde-637	656	2	.	.	PROPN
ejde-637	656	3	theory	theory	NOUN
ejde-637	656	4	dyn	dyn	PROPN
ejde-637	656	5	.	.	PUNCT
ejde-637	657	1	syst	syst	PROPN
ejde-637	657	2	.	.	PROPN
ejde-637	657	3	,	,	PUNCT
ejde-637	657	4	21	21	NUM
ejde-637	657	5	(	(	PUNCT
ejde-637	657	6	2022	2022	NUM
ejde-637	657	7	):	):	PUNCT
ejde-637	657	8	1	1	NUM
ejde-637	657	9	-	-	SYM
ejde-637	657	10	20	20	NUM
ejde-637	657	11	.	.	PUNCT
ejde-637	658	1	[	[	X
ejde-637	658	2	54	54	NUM
ejde-637	658	3	]	]	X
ejde-637	658	4	zhao	zhao	PROPN
ejde-637	658	5	,	,	PUNCT
ejde-637	658	6	q.	q.	PROPN
ejde-637	658	7	q.	q.	PROPN
ejde-637	658	8	;	;	PUNCT
ejde-637	658	9	yu	yu	PROPN
ejde-637	658	10	,	,	PUNCT
ejde-637	658	11	j.	j.	PROPN
ejde-637	658	12	;	;	PUNCT
ejde-637	658	13	limit	limit	VERB
ejde-637	658	14	cycles	cycle	NOUN
ejde-637	658	15	of	of	ADP
ejde-637	658	16	piecewise	piecewise	NOUN
ejde-637	658	17	linear	linear	ADJ
ejde-637	658	18	dynamical	dynamical	ADJ
ejde-637	658	19	systems	system	NOUN
ejde-637	658	20	with	with	ADP
ejde-637	658	21	three	three	NUM
ejde-637	658	22	zones	zone	NOUN
ejde-637	658	23	and	and	CCONJ
ejde-637	658	24	lateral	lateral	ADJ
ejde-637	658	25	systems	system	NOUN
ejde-637	658	26	.	.	PUNCT
ejde-637	659	1	j.	j.	PROPN
ejde-637	659	2	appl	appl	PROPN
ejde-637	659	3	.	.	PROPN
ejde-637	660	1	anal	anal	PROPN
ejde-637	660	2	.	.	PUNCT
ejde-637	661	1	comput	comput	PROPN
ejde-637	661	2	.	.	PUNCT
ejde-637	661	3	,	,	PUNCT
ejde-637	661	4	9	9	NUM
ejde-637	661	5	(	(	PUNCT
ejde-637	661	6	2019a	2019a	NUM
ejde-637	661	7	):	):	PUNCT
ejde-637	661	8	1822–1837	1822–1837	NUM
ejde-637	661	9	.	.	PUNCT
ejde-637	662	1	[	[	X
ejde-637	662	2	55	55	NUM
ejde-637	662	3	]	]	X
ejde-637	662	4	zhao	zhao	PROPN
ejde-637	662	5	,	,	PUNCT
ejde-637	662	6	q.	q.	PROPN
ejde-637	662	7	q.	q.	PROPN
ejde-637	662	8	;	;	PUNCT
ejde-637	662	9	yu	yu	PROPN
ejde-637	662	10	,	,	PUNCT
ejde-637	662	11	j.	j.	PROPN
ejde-637	662	12	;	;	PUNCT
ejde-637	662	13	poincaré	poincaré	ADJ
ejde-637	662	14	maps	map	NOUN
ejde-637	662	15	of	of	ADP
ejde-637	662	16	’	'	PUNCT
ejde-637	662	17	<	<	NOUN
ejde-637	662	18	’	'	PUNCT
ejde-637	662	19	-shape	-shape	NOUN
ejde-637	662	20	planar	planar	ADJ
ejde-637	662	21	piecewise	piecewise	NOUN
ejde-637	662	22	linear	linear	ADJ
ejde-637	662	23	dynamical	dynamical	ADJ
ejde-637	662	24	systems	system	NOUN
ejde-637	662	25	with	with	ADP
ejde-637	662	26	a	a	DET
ejde-637	662	27	saddle	saddle	NOUN
ejde-637	662	28	.	.	PUNCT
ejde-637	663	1	internat	internat	PROPN
ejde-637	663	2	.	.	PUNCT
ejde-637	664	1	j.	j.	PROPN
ejde-637	664	2	bifur	bifur	PROPN
ejde-637	664	3	.	.	PUNCT
ejde-637	665	1	chaos	chaos	NOUN
ejde-637	665	2	,	,	PUNCT
ejde-637	665	3	29	29	NUM
ejde-637	665	4	(	(	PUNCT
ejde-637	665	5	2019b	2019b	NUM
ejde-637	665	6	):	):	PUNCT
ejde-637	665	7	1950165	1950165	NUM
ejde-637	665	8	-	-	PUNCT
ejde-637	665	9	1–21	1–21	PROPN
ejde-637	665	10	.	.	PUNCT
ejde-637	666	1	[	[	X
ejde-637	666	2	56	56	NUM
ejde-637	666	3	]	]	X
ejde-637	666	4	zhao	zhao	PROPN
ejde-637	666	5	,	,	PUNCT
ejde-637	666	6	q.	q.	PROPN
ejde-637	666	7	q.	q.	PROPN
ejde-637	666	8	;	;	PUNCT
ejde-637	666	9	wang	wang	PROPN
ejde-637	666	10	,	,	PUNCT
ejde-637	666	11	c.	c.	PROPN
ejde-637	666	12	;	;	PUNCT
ejde-637	666	13	yu	yu	PROPN
ejde-637	666	14	,	,	PUNCT
ejde-637	666	15	j.	j.	PROPN
ejde-637	666	16	;	;	PUNCT
ejde-637	666	17	limit	limit	VERB
ejde-637	666	18	cycles	cycle	NOUN
ejde-637	666	19	in	in	ADP
ejde-637	666	20	discontinuous	discontinuous	ADJ
ejde-637	666	21	planar	planar	ADJ
ejde-637	666	22	piecewise	piecewise	NOUN
ejde-637	666	23	linear	linear	NOUN
ejde-637	666	24	systems	system	NOUN
ejde-637	666	25	separated	separate	VERB
ejde-637	666	26	by	by	ADP
ejde-637	666	27	a	a	DET
ejde-637	666	28	nonregular	nonregular	ADJ
ejde-637	666	29	line	line	NOUN
ejde-637	666	30	of	of	ADP
ejde-637	666	31	center	center	ADJ
ejde-637	666	32	-	-	PUNCT
ejde-637	666	33	center	center	NOUN
ejde-637	666	34	type	type	NOUN
ejde-637	666	35	.	.	PUNCT
ejde-637	667	1	internat	internat	PROPN
ejde-637	667	2	.	.	PUNCT
ejde-637	668	1	j.	j.	PROPN
ejde-637	668	2	bifur	bifur	PROPN
ejde-637	668	3	.	.	PUNCT
ejde-637	669	1	chaos	chaos	NOUN
ejde-637	669	2	,	,	PUNCT
ejde-637	669	3	31	31	NUM
ejde-637	669	4	(	(	PUNCT
ejde-637	669	5	2021	2021	NUM
ejde-637	669	6	):	):	PUNCT
ejde-637	669	7	2150136	2150136	NUM
ejde-637	669	8	-	-	SYM
ejde-637	669	9	1–17	1–17	PROPN
ejde-637	669	10	.	.	PUNCT
ejde-637	670	1	qian	qian	PROPN
ejde-637	670	2	-	-	PUNCT
ejde-637	670	3	qian	qian	PROPN
ejde-637	670	4	han	han	PROPN
ejde-637	670	5	(	(	PUNCT
ejde-637	670	6	corresponding	corresponding	ADJ
ejde-637	670	7	author	author	NOUN
ejde-637	670	8	)	)	PUNCT
ejde-637	670	9	school	school	NOUN
ejde-637	670	10	of	of	ADP
ejde-637	670	11	mathematics	mathematic	NOUN
ejde-637	670	12	and	and	CCONJ
ejde-637	670	13	statistics	statistic	NOUN
ejde-637	670	14	,	,	PUNCT
ejde-637	670	15	north	north	PROPN
ejde-637	670	16	china	china	PROPN
ejde-637	670	17	university	university	PROPN
ejde-637	670	18	of	of	ADP
ejde-637	670	19	water	water	NOUN
ejde-637	670	20	resources	resource	NOUN
ejde-637	670	21	and	and	CCONJ
ejde-637	670	22	electric	electric	ADJ
ejde-637	670	23	power	power	NOUN
ejde-637	670	24	,	,	PUNCT
ejde-637	670	25	zhengzhou	zhengzhou	PROPN
ejde-637	670	26	,	,	PUNCT
ejde-637	670	27	henan	henan	PROPN
ejde-637	670	28	450046	450046	NUM
ejde-637	670	29	,	,	PUNCT
ejde-637	670	30	china	china	PROPN
ejde-637	670	31	email	email	NOUN
ejde-637	670	32	address	address	PROPN
ejde-637	670	33	:	:	PUNCT
ejde-637	670	34	hanqianqian@ncwu.edu.cn	hanqianqian@ncwu.edu.cn	ADJ
ejde-637	670	35	song	song	PROPN
ejde-637	670	36	-	-	PUNCT
ejde-637	670	37	mei	mei	PROPN
ejde-637	670	38	huan	huan	PROPN
ejde-637	670	39	school	school	PROPN
ejde-637	670	40	of	of	ADP
ejde-637	670	41	mathematics	mathematic	NOUN
ejde-637	670	42	and	and	CCONJ
ejde-637	670	43	statistics	statistic	NOUN
ejde-637	670	44	,	,	PUNCT
ejde-637	670	45	huazhong	huazhong	PROPN
ejde-637	670	46	university	university	PROPN
ejde-637	670	47	of	of	ADP
ejde-637	670	48	science	science	NOUN
ejde-637	670	49	and	and	CCONJ
ejde-637	670	50	technology	technology	NOUN
ejde-637	670	51	,	,	PUNCT
ejde-637	670	52	hubei	hubei	PROPN
ejde-637	670	53	key	key	PROPN
ejde-637	670	54	laboratory	laboratory	NOUN
ejde-637	670	55	of	of	ADP
ejde-637	670	56	engineering	engineering	NOUN
ejde-637	670	57	modeling	modeling	NOUN
ejde-637	670	58	and	and	CCONJ
ejde-637	670	59	scientific	scientific	ADJ
ejde-637	670	60	computing	computing	NOUN
ejde-637	670	61	,	,	PUNCT
ejde-637	670	62	wuhan	wuhan	PROPN
ejde-637	670	63	,	,	PUNCT
ejde-637	670	64	hubei	hubei	PROPN
ejde-637	670	65	430074	430074	NUM
ejde-637	670	66	,	,	PUNCT
ejde-637	670	67	china	china	PROPN
ejde-637	670	68	email	email	NOUN
ejde-637	670	69	address	address	NOUN
ejde-637	670	70	:	:	PUNCT
ejde-637	670	71	smhuan@hust.edu.cn	smhuan@hust.edu.cn	PROPN
ejde-637	670	72	1	1	NUM
ejde-637	670	73	.	.	PUNCT
ejde-637	671	1	introduction	introduction	NOUN
ejde-637	671	2	2	2	NUM
ejde-637	671	3	.	.	PUNCT
ejde-637	671	4	preliminaries	preliminary	NOUN
ejde-637	671	5	3	3	NUM
ejde-637	671	6	.	.	X
ejde-637	671	7	main	main	ADJ
ejde-637	671	8	results	result	NOUN
ejde-637	671	9	4	4	NUM
ejde-637	671	10	.	.	PUNCT
ejde-637	672	1	proofs	proof	NOUN
ejde-637	672	2	of	of	ADP
ejde-637	672	3	main	main	ADJ
ejde-637	672	4	results	result	NOUN
ejde-637	672	5	5	5	NUM
ejde-637	672	6	.	.	PUNCT
ejde-637	672	7	examples	example	NOUN
ejde-637	672	8	6	6	NUM
ejde-637	672	9	.	.	PUNCT
ejde-637	673	1	conclusions	conclusion	NOUN
ejde-637	673	2	acknowledgments	acknowledgment	NOUN
ejde-637	673	3	references	reference	NOUN