id	sid	tid	token	lemma	pos
ap-1805	1	1	acta	acta	PROPN
ap-1805	1	2	polytechnica	polytechnica	PROPN
ap-1805	1	3	acta	acta	PROPN
ap-1805	1	4	polytechnica	polytechnica	PROPN
ap-1805	1	5	53(3):283–288	53(3):283–288	PROPN
ap-1805	1	6	,	,	PUNCT
ap-1805	1	7	2013	2013	NUM
ap-1805	1	8	©	©	PROPN
ap-1805	1	9	czech	czech	PROPN
ap-1805	1	10	technical	technical	PROPN
ap-1805	1	11	university	university	PROPN
ap-1805	1	12	in	in	ADP
ap-1805	1	13	prague	prague	PROPN
ap-1805	1	14	,	,	PUNCT
ap-1805	1	15	2013	2013	NUM
ap-1805	1	16	available	available	ADJ
ap-1805	1	17	online	online	ADV
ap-1805	1	18	at	at	ADP
ap-1805	1	19	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-1805	1	20	on	on	ADP
ap-1805	1	21	the	the	DET
ap-1805	1	22	solvability	solvability	NOUN
ap-1805	1	23	of	of	ADP
ap-1805	1	24	some	some	DET
ap-1805	1	25	partial	partial	ADJ
ap-1805	1	26	differential	differential	NOUN
ap-1805	1	27	inequality	inequality	NOUN
ap-1805	1	28	martin	martin	PROPN
ap-1805	1	29	himmel∗	himmel∗	PROPN
ap-1805	1	30	fb	fb	INTJ
ap-1805	1	31	08	08	NUM
ap-1805	1	32	—	—	PUNCT
ap-1805	1	33	institut	institut	PROPN
ap-1805	1	34	für	für	PROPN
ap-1805	1	35	mathematik	mathematik	PROPN
ap-1805	1	36	,	,	PUNCT
ap-1805	1	37	johannes	johannes	PROPN
ap-1805	1	38	gutenberg	gutenberg	PROPN
ap-1805	1	39	-	-	PUNCT
ap-1805	1	40	universität	universität	NOUN
ap-1805	1	41	mainz	mainz	NOUN
ap-1805	1	42	,	,	PUNCT
ap-1805	1	43	staudinger	stauding	ADJ
ap-1805	1	44	weg	weg	PROPN
ap-1805	1	45	9	9	NUM
ap-1805	1	46	,	,	PUNCT
ap-1805	1	47	d-55099	d-55099	PROPN
ap-1805	1	48	mainz	mainz	PROPN
ap-1805	1	49	,	,	PUNCT
ap-1805	1	50	germany	germany	PROPN
ap-1805	1	51	∗	∗	NOUN
ap-1805	1	52	corresponding	correspond	VERB
ap-1805	1	53	author	author	NOUN
ap-1805	1	54	:	:	PUNCT
ap-1805	1	55	himmel@mathematik.uni-mainz.de	himmel@mathematik.uni-mainz.de	ADJ
ap-1805	1	56	abstract	abstract	NOUN
ap-1805	1	57	.	.	PUNCT
ap-1805	2	1	the	the	DET
ap-1805	2	2	dulac	dulac	PROPN
ap-1805	2	3	criterion	criterion	NOUN
ap-1805	2	4	is	be	AUX
ap-1805	2	5	a	a	DET
ap-1805	2	6	classical	classical	ADJ
ap-1805	2	7	method	method	NOUN
ap-1805	2	8	for	for	ADP
ap-1805	2	9	ruling	rule	VERB
ap-1805	2	10	out	out	ADP
ap-1805	2	11	the	the	DET
ap-1805	2	12	existence	existence	NOUN
ap-1805	2	13	of	of	ADP
ap-1805	2	14	periodic	periodic	ADJ
ap-1805	2	15	solutions	solution	NOUN
ap-1805	2	16	in	in	ADP
ap-1805	2	17	planar	planar	ADJ
ap-1805	2	18	differential	differential	ADJ
ap-1805	2	19	equations	equation	NOUN
ap-1805	2	20	.	.	PUNCT
ap-1805	3	1	in	in	ADP
ap-1805	3	2	this	this	DET
ap-1805	3	3	paper	paper	NOUN
ap-1805	3	4	the	the	DET
ap-1805	3	5	applicability	applicability	NOUN
ap-1805	3	6	and	and	CCONJ
ap-1805	3	7	therefore	therefore	ADV
ap-1805	3	8	reversibility	reversibility	NOUN
ap-1805	3	9	of	of	ADP
ap-1805	3	10	this	this	DET
ap-1805	3	11	criterion	criterion	NOUN
ap-1805	3	12	is	be	AUX
ap-1805	3	13	under	under	ADP
ap-1805	3	14	consideration	consideration	NOUN
ap-1805	3	15	.	.	PUNCT
ap-1805	4	1	keywords	keyword	NOUN
ap-1805	4	2	:	:	PUNCT
ap-1805	4	3	dynamical	dynamical	ADJ
ap-1805	4	4	systems	system	NOUN
ap-1805	4	5	,	,	PUNCT
ap-1805	4	6	planar	planar	ADJ
ap-1805	4	7	differential	differential	ADJ
ap-1805	4	8	equations	equation	NOUN
ap-1805	4	9	,	,	PUNCT
ap-1805	4	10	limit	limit	NOUN
ap-1805	4	11	cycles	cycle	NOUN
ap-1805	4	12	,	,	PUNCT
ap-1805	4	13	dulac	dulac	PROPN
ap-1805	4	14	’s	’s	PART
ap-1805	4	15	inequality	inequality	NOUN
ap-1805	4	16	,	,	PUNCT
ap-1805	4	17	locally	locally	ADV
ap-1805	4	18	sufficient	sufficient	ADJ
ap-1805	4	19	criteria	criterion	NOUN
ap-1805	4	20	.	.	PUNCT
ap-1805	5	1	1	1	X
ap-1805	5	2	.	.	X
ap-1805	5	3	introduction	introduction	NOUN
ap-1805	5	4	and	and	CCONJ
ap-1805	5	5	motivation	motivation	NOUN
ap-1805	5	6	let	let	VERB
ap-1805	5	7	x	x	PRON
ap-1805	5	8	:	:	PUNCT
ap-1805	5	9	d	d	X
ap-1805	5	10	→	→	SYM
ap-1805	5	11	r2	r2	PROPN
ap-1805	5	12	be	be	AUX
ap-1805	5	13	a	a	DET
ap-1805	5	14	smooth	smooth	ADJ
ap-1805	5	15	vector	vector	NOUN
ap-1805	5	16	-	-	PUNCT
ap-1805	5	17	valued	value	VERB
ap-1805	5	18	function	function	NOUN
ap-1805	5	19	with	with	ADP
ap-1805	5	20	components	component	NOUN
ap-1805	5	21	p	p	NOUN
ap-1805	5	22	and	and	CCONJ
ap-1805	5	23	q	q	NOUN
ap-1805	5	24	,	,	PUNCT
ap-1805	5	25	x	x	SYM
ap-1805	5	26	=	=	PUNCT
ap-1805	5	27	(	(	PUNCT
ap-1805	5	28	p	p	X
ap-1805	5	29	,	,	PUNCT
ap-1805	5	30	q	q	NOUN
ap-1805	5	31	)	)	PUNCT
ap-1805	5	32	,	,	PUNCT
ap-1805	5	33	defined	define	VERB
ap-1805	5	34	on	on	ADP
ap-1805	5	35	some	some	DET
ap-1805	5	36	planar	planar	ADJ
ap-1805	5	37	domain	domain	NOUN
ap-1805	5	38	d	d	NOUN
ap-1805	5	39	⊆	⊆	NUM
ap-1805	5	40	r2	r2	NOUN
ap-1805	5	41	.	.	PUNCT
ap-1805	6	1	now	now	ADV
ap-1805	6	2	,	,	PUNCT
ap-1805	6	3	consider	consider	VERB
ap-1805	6	4	the	the	DET
ap-1805	6	5	system	system	NOUN
ap-1805	6	6	of	of	ADP
ap-1805	6	7	two	two	NUM
ap-1805	6	8	ordinary	ordinary	ADJ
ap-1805	6	9	differential	differential	ADJ
ap-1805	6	10	equations	equation	NOUN
ap-1805	6	11	dx	dx	PROPN
ap-1805	6	12	dt	dt	NOUN
ap-1805	7	1	=	=	PUNCT
ap-1805	7	2	p	p	X
ap-1805	7	3	(	(	PUNCT
ap-1805	7	4	x	x	NOUN
ap-1805	7	5	,	,	PUNCT
ap-1805	7	6	y	y	PROPN
ap-1805	7	7	)	)	PUNCT
ap-1805	7	8	,	,	PUNCT
ap-1805	7	9	dy	dy	NOUN
ap-1805	7	10	dt	dt	NOUN
ap-1805	7	11	=	=	SYM
ap-1805	7	12	q(x	q(x	PROPN
ap-1805	7	13	,	,	PUNCT
ap-1805	7	14	y	y	NOUN
ap-1805	7	15	)	)	PUNCT
ap-1805	7	16	.	.	PUNCT
ap-1805	8	1	(	(	PUNCT
ap-1805	8	2	1	1	X
ap-1805	8	3	)	)	PUNCT
ap-1805	8	4	such	such	ADJ
ap-1805	8	5	systems	system	NOUN
ap-1805	8	6	appear	appear	VERB
ap-1805	8	7	frequently	frequently	ADV
ap-1805	8	8	in	in	ADP
ap-1805	8	9	applications	application	NOUN
ap-1805	8	10	,	,	PUNCT
ap-1805	8	11	e.g.	e.g.	ADV
ap-1805	8	12	in	in	ADP
ap-1805	8	13	electrical	electrical	ADJ
ap-1805	8	14	engineering	engineering	NOUN
ap-1805	8	15	,	,	PUNCT
ap-1805	8	16	physics	physics	NOUN
ap-1805	8	17	,	,	PUNCT
ap-1805	8	18	biology	biology	NOUN
ap-1805	8	19	and	and	CCONJ
ap-1805	8	20	many	many	ADJ
ap-1805	8	21	others	other	NOUN
ap-1805	8	22	,	,	PUNCT
ap-1805	8	23	but	but	CCONJ
ap-1805	8	24	they	they	PRON
ap-1805	8	25	have	have	AUX
ap-1805	8	26	also	also	ADV
ap-1805	8	27	become	become	VERB
ap-1805	8	28	a	a	DET
ap-1805	8	29	field	field	NOUN
ap-1805	8	30	of	of	ADP
ap-1805	8	31	mathematical	mathematical	ADJ
ap-1805	8	32	interest	interest	NOUN
ap-1805	8	33	on	on	ADP
ap-1805	8	34	their	their	PRON
ap-1805	8	35	own	own	ADJ
ap-1805	8	36	.	.	PUNCT
ap-1805	9	1	for	for	ADP
ap-1805	9	2	simplicity	simplicity	NOUN
ap-1805	9	3	,	,	PUNCT
ap-1805	9	4	one	one	PRON
ap-1805	9	5	can	can	AUX
ap-1805	9	6	think	think	VERB
ap-1805	9	7	of	of	ADP
ap-1805	9	8	p	p	NOUN
ap-1805	9	9	and	and	CCONJ
ap-1805	9	10	q	q	NOUN
ap-1805	9	11	either	either	CCONJ
ap-1805	9	12	just	just	ADV
ap-1805	9	13	as	as	ADP
ap-1805	9	14	polynomials	polynomial	NOUN
ap-1805	9	15	of	of	ADP
ap-1805	9	16	two	two	NUM
ap-1805	9	17	real	real	ADJ
ap-1805	9	18	variables	variable	NOUN
ap-1805	9	19	x	x	PUNCT
ap-1805	9	20	and	and	CCONJ
ap-1805	9	21	y	y	PROPN
ap-1805	9	22	,	,	PUNCT
ap-1805	9	23	or	or	CCONJ
ap-1805	9	24	as	as	ADV
ap-1805	9	25	smooth	smooth	ADJ
ap-1805	9	26	or	or	CCONJ
ap-1805	9	27	even	even	ADV
ap-1805	9	28	analytical	analytical	ADJ
ap-1805	9	29	functions	function	NOUN
ap-1805	9	30	given	give	VERB
ap-1805	9	31	by	by	ADP
ap-1805	9	32	some	some	DET
ap-1805	9	33	power	power	NOUN
ap-1805	9	34	series	series	NOUN
ap-1805	9	35	that	that	PRON
ap-1805	9	36	converges	converge	VERB
ap-1805	9	37	in	in	ADP
ap-1805	9	38	d	d	PROPN
ap-1805	9	39	,	,	PUNCT
ap-1805	9	40	i.e.	i.e.	X
ap-1805	9	41	,	,	PUNCT
ap-1805	9	42	x	x	X
ap-1805	9	43	is	be	AUX
ap-1805	9	44	of	of	ADP
ap-1805	9	45	class	class	NOUN
ap-1805	9	46	cr	cr	NOUN
ap-1805	9	47	with	with	ADP
ap-1805	9	48	r	r	PROPN
ap-1805	9	49	∈	∈	PROPN
ap-1805	9	50	{	{	PUNCT
ap-1805	9	51	1	1	NUM
ap-1805	9	52	,	,	PUNCT
ap-1805	9	53	2	2	NUM
ap-1805	9	54	,	,	PUNCT
ap-1805	9	55	.	.	PUNCT
ap-1805	9	56	.	.	PUNCT
ap-1805	10	1	.∞	.∞	PROPN
ap-1805	10	2	,	,	PUNCT
ap-1805	10	3	ω	ω	NOUN
ap-1805	10	4	}	}	PUNCT
ap-1805	10	5	.	.	PUNCT
ap-1805	11	1	geometrically	geometrically	ADV
ap-1805	11	2	speaking	speak	VERB
ap-1805	11	3	,	,	PUNCT
ap-1805	11	4	the	the	DET
ap-1805	11	5	solutions	solution	NOUN
ap-1805	11	6	of	of	ADP
ap-1805	11	7	the	the	DET
ap-1805	11	8	system	system	NOUN
ap-1805	11	9	(	(	PUNCT
ap-1805	11	10	1	1	X
ap-1805	11	11	)	)	PUNCT
ap-1805	11	12	are	be	AUX
ap-1805	11	13	smooth	smooth	ADJ
ap-1805	11	14	curves	curve	NOUN
ap-1805	11	15	in	in	ADP
ap-1805	11	16	the	the	DET
ap-1805	11	17	plane	plane	NOUN
ap-1805	11	18	that	that	PRON
ap-1805	11	19	are	be	AUX
ap-1805	11	20	tangential	tangential	ADJ
ap-1805	11	21	to	to	ADP
ap-1805	11	22	the	the	DET
ap-1805	11	23	function	function	NOUN
ap-1805	11	24	x	x	PUNCT
ap-1805	11	25	at	at	ADP
ap-1805	11	26	each	each	DET
ap-1805	11	27	point	point	NOUN
ap-1805	11	28	z	z	NOUN
ap-1805	11	29	=	=	SYM
ap-1805	11	30	(	(	PUNCT
ap-1805	11	31	x	x	X
ap-1805	11	32	,	,	PUNCT
ap-1805	11	33	y	y	PROPN
ap-1805	11	34	)	)	PUNCT
ap-1805	11	35	∈	∈	PROPN
ap-1805	11	36	d.	d.	NOUN
ap-1805	11	37	if	if	SCONJ
ap-1805	11	38	the	the	DET
ap-1805	11	39	components	component	NOUN
ap-1805	11	40	of	of	ADP
ap-1805	11	41	x	x	SYM
ap-1805	11	42	are	be	AUX
ap-1805	11	43	polynomials	polynomial	NOUN
ap-1805	11	44	in	in	ADP
ap-1805	11	45	x	x	PUNCT
ap-1805	11	46	and	and	CCONJ
ap-1805	11	47	y	y	PROPN
ap-1805	11	48	of	of	ADP
ap-1805	11	49	degree	degree	NOUN
ap-1805	11	50	one	one	NUM
ap-1805	11	51	then	then	ADV
ap-1805	11	52	x(x	x(x	PROPN
ap-1805	11	53	,	,	PUNCT
ap-1805	11	54	y	y	NOUN
ap-1805	11	55	)	)	PUNCT
ap-1805	12	1	=	=	NOUN
ap-1805	12	2	(	(	PUNCT
ap-1805	12	3	ax+	ax+	ADV
ap-1805	12	4	by	by	ADP
ap-1805	12	5	cx+	cx+	NOUN
ap-1805	12	6	dy	dy	NOUN
ap-1805	12	7	)	)	PUNCT
ap-1805	12	8	with	with	ADP
ap-1805	12	9	a	a	DET
ap-1805	12	10	,	,	PUNCT
ap-1805	12	11	b	b	NOUN
ap-1805	12	12	,	,	PUNCT
ap-1805	12	13	c	c	NOUN
ap-1805	12	14	,	,	PUNCT
ap-1805	12	15	d	d	PROPN
ap-1805	12	16	∈	∈	NOUN
ap-1805	12	17	r	r	NOUN
ap-1805	12	18	being	be	AUX
ap-1805	12	19	real	real	ADJ
ap-1805	12	20	constants	constant	NOUN
ap-1805	12	21	,	,	PUNCT
ap-1805	12	22	and	and	CCONJ
ap-1805	12	23	the	the	DET
ap-1805	12	24	analysis	analysis	NOUN
ap-1805	12	25	of	of	ADP
ap-1805	12	26	system	system	NOUN
ap-1805	12	27	(	(	PUNCT
ap-1805	12	28	1	1	X
ap-1805	12	29	)	)	PUNCT
ap-1805	12	30	is	be	AUX
ap-1805	12	31	easy	easy	ADJ
ap-1805	12	32	and	and	CCONJ
ap-1805	12	33	the	the	DET
ap-1805	12	34	solution	solution	NOUN
ap-1805	12	35	curves	curve	NOUN
ap-1805	12	36	of	of	ADP
ap-1805	12	37	system	system	NOUN
ap-1805	12	38	(	(	PUNCT
ap-1805	12	39	1	1	X
ap-1805	12	40	)	)	PUNCT
ap-1805	12	41	are	be	AUX
ap-1805	12	42	given	give	VERB
ap-1805	12	43	explicitly	explicitly	ADV
ap-1805	12	44	in	in	ADP
ap-1805	12	45	terms	term	NOUN
ap-1805	12	46	of	of	ADP
ap-1805	12	47	the	the	DET
ap-1805	12	48	matrix	matrix	NOUN
ap-1805	12	49	exponential	exponential	NOUN
ap-1805	12	50	function	function	NOUN
ap-1805	12	51	ea	ea	NOUN
ap-1805	12	52	:	:	PUNCT
ap-1805	12	53	=	=	SYM
ap-1805	12	54	∑∞	∑∞	NOUN
ap-1805	12	55	k=0	k=0	PROPN
ap-1805	12	56	1	1	NUM
ap-1805	12	57	k!a	k!a	PROPN
ap-1805	12	58	k.	k.	PROPN
ap-1805	13	1	the	the	DET
ap-1805	13	2	situation	situation	NOUN
ap-1805	13	3	changes	change	VERB
ap-1805	13	4	drastically	drastically	ADV
ap-1805	13	5	if	if	SCONJ
ap-1805	13	6	x	x	PRON
ap-1805	13	7	is	be	AUX
ap-1805	13	8	at	at	ADP
ap-1805	13	9	least	least	ADJ
ap-1805	13	10	quadratic	quadratic	ADJ
ap-1805	13	11	,	,	PUNCT
ap-1805	13	12	i.e.	i.e.	X
ap-1805	13	13	,	,	PUNCT
ap-1805	13	14	if	if	SCONJ
ap-1805	13	15	p	p	NOUN
ap-1805	13	16	and/or	and/or	CCONJ
ap-1805	13	17	q	q	NOUN
ap-1805	13	18	are	be	AUX
ap-1805	13	19	polynomials	polynomial	NOUN
ap-1805	13	20	of	of	ADP
ap-1805	13	21	degree	degree	NOUN
ap-1805	13	22	two	two	NUM
ap-1805	13	23	or	or	CCONJ
ap-1805	13	24	higher	high	ADJ
ap-1805	13	25	,	,	PUNCT
ap-1805	13	26	p	p	X
ap-1805	13	27	,	,	PUNCT
ap-1805	13	28	q	q	PROPN
ap-1805	13	29	∈	∈	PROPN
ap-1805	13	30	rn[x	rn[x	PROPN
ap-1805	13	31	,	,	PUNCT
ap-1805	13	32	y	y	PROPN
ap-1805	13	33	]	]	X
ap-1805	13	34	,	,	PUNCT
ap-1805	13	35	n	n	X
ap-1805	13	36	≥	≥	NOUN
ap-1805	13	37	2	2	NUM
ap-1805	13	38	.	.	PUNCT
ap-1805	14	1	many	many	ADJ
ap-1805	14	2	things	thing	NOUN
ap-1805	14	3	are	be	AUX
ap-1805	14	4	known	know	VERB
ap-1805	14	5	about	about	ADP
ap-1805	14	6	quadratic	quadratic	ADJ
ap-1805	14	7	differential	differential	ADJ
ap-1805	14	8	equations	equation	NOUN
ap-1805	14	9	,	,	PUNCT
ap-1805	14	10	see	see	VERB
ap-1805	14	11	[	[	X
ap-1805	14	12	1–3	1–3	NOUN
ap-1805	14	13	]	]	X
ap-1805	14	14	,	,	PUNCT
ap-1805	14	15	but	but	CCONJ
ap-1805	14	16	they	they	PRON
ap-1805	14	17	are	be	AUX
ap-1805	14	18	still	still	ADV
ap-1805	14	19	a	a	DET
ap-1805	14	20	broad	broad	ADJ
ap-1805	14	21	area	area	NOUN
ap-1805	14	22	of	of	ADP
ap-1805	14	23	research	research	NOUN
ap-1805	14	24	.	.	PUNCT
ap-1805	15	1	quite	quite	DET
ap-1805	15	2	a	a	DET
ap-1805	15	3	few	few	ADJ
ap-1805	15	4	people	people	NOUN
ap-1805	15	5	have	have	AUX
ap-1805	15	6	dedicated	dedicate	VERB
ap-1805	15	7	their	their	PRON
ap-1805	15	8	whole	whole	ADJ
ap-1805	15	9	life	life	NOUN
ap-1805	15	10	to	to	ADP
ap-1805	15	11	the	the	DET
ap-1805	15	12	investigation	investigation	NOUN
ap-1805	15	13	of	of	ADP
ap-1805	15	14	quadratic	quadratic	ADJ
ap-1805	15	15	planar	planar	ADJ
ap-1805	15	16	differential	differential	ADJ
ap-1805	15	17	equations	equation	NOUN
ap-1805	15	18	.	.	PUNCT
ap-1805	16	1	interest	interest	NOUN
ap-1805	16	2	in	in	ADP
ap-1805	16	3	this	this	DET
ap-1805	16	4	field	field	NOUN
ap-1805	16	5	is	be	AUX
ap-1805	16	6	related	relate	VERB
ap-1805	16	7	to	to	ADP
ap-1805	16	8	the	the	DET
ap-1805	16	9	16th	16th	ADJ
ap-1805	16	10	hilbert	hilbert	NOUN
ap-1805	16	11	problem	problem	NOUN
ap-1805	16	12	,	,	PUNCT
ap-1805	16	13	which	which	PRON
ap-1805	16	14	is	be	AUX
ap-1805	16	15	still	still	ADV
ap-1805	16	16	unsolved	unsolved	ADJ
ap-1805	16	17	even	even	ADV
ap-1805	16	18	in	in	ADP
ap-1805	16	19	the	the	DET
ap-1805	16	20	quadratic	quadratic	ADJ
ap-1805	16	21	case	case	NOUN
ap-1805	16	22	.	.	PUNCT
ap-1805	17	1	1.1	1.1	NUM
ap-1805	17	2	.	.	PUNCT
ap-1805	18	1	sixteenth	sixteenth	ADJ
ap-1805	18	2	hilbert	hilbert	PROPN
ap-1805	18	3	problem	problem	NOUN
ap-1805	18	4	let	let	VERB
ap-1805	18	5	rd[x	rd[x	PROPN
ap-1805	18	6	,	,	PUNCT
ap-1805	18	7	y	y	NOUN
ap-1805	18	8	]	]	PUNCT
ap-1805	18	9	denote	denote	VERB
ap-1805	18	10	the	the	DET
ap-1805	18	11	space	space	NOUN
ap-1805	18	12	given	give	VERB
ap-1805	18	13	by	by	ADP
ap-1805	18	14	polynomials	polynomial	NOUN
ap-1805	18	15	in	in	ADP
ap-1805	18	16	x	x	PUNCT
ap-1805	18	17	and	and	CCONJ
ap-1805	18	18	y	y	PROPN
ap-1805	18	19	of	of	ADP
ap-1805	18	20	degree	degree	NOUN
ap-1805	18	21	at	at	ADP
ap-1805	18	22	most	most	ADJ
ap-1805	18	23	d	d	NOUN
ap-1805	18	24	,	,	PUNCT
ap-1805	18	25	and	and	CCONJ
ap-1805	18	26	consider	consider	VERB
ap-1805	18	27	a	a	DET
ap-1805	18	28	planar	planar	ADJ
ap-1805	18	29	system	system	NOUN
ap-1805	18	30	(	(	PUNCT
ap-1805	18	31	1	1	NUM
ap-1805	18	32	)	)	PUNCT
ap-1805	18	33	with	with	ADP
ap-1805	18	34	polynomial	polynomial	ADJ
ap-1805	18	35	right	right	ADJ
ap-1805	18	36	-	-	PUNCT
ap-1805	18	37	hand	hand	NOUN
ap-1805	18	38	side	side	NOUN
ap-1805	18	39	x	x	SYM
ap-1805	18	40	∈	∈	PROPN
ap-1805	18	41	r2	r2	PROPN
ap-1805	18	42	d[x	d[x	PROPN
ap-1805	18	43	,	,	PUNCT
ap-1805	18	44	y	y	PROPN
ap-1805	18	45	]	]	PUNCT
ap-1805	18	46	.	.	PUNCT
ap-1805	19	1	the	the	DET
ap-1805	19	2	16th	16th	ADJ
ap-1805	19	3	hilbert	hilbert	NOUN
ap-1805	19	4	problem	problem	NOUN
ap-1805	19	5	consists	consist	VERB
ap-1805	19	6	of	of	ADP
ap-1805	19	7	two	two	NUM
ap-1805	19	8	parts	part	NOUN
ap-1805	19	9	,	,	PUNCT
ap-1805	19	10	the	the	DET
ap-1805	19	11	first	first	ADJ
ap-1805	19	12	of	of	ADP
ap-1805	19	13	which	which	PRON
ap-1805	19	14	is	be	AUX
ap-1805	19	15	a	a	DET
ap-1805	19	16	purely	purely	ADV
ap-1805	19	17	algebraic	algebraic	ADJ
ap-1805	19	18	problem	problem	NOUN
ap-1805	19	19	and	and	CCONJ
ap-1805	19	20	deals	deal	NOUN
ap-1805	19	21	with	with	ADP
ap-1805	19	22	questions	question	NOUN
ap-1805	19	23	related	relate	VERB
ap-1805	19	24	to	to	ADP
ap-1805	19	25	the	the	DET
ap-1805	19	26	topology	topology	NOUN
ap-1805	19	27	of	of	ADP
ap-1805	19	28	algebraic	algebraic	ADJ
ap-1805	19	29	curves	curve	NOUN
ap-1805	19	30	and	and	CCONJ
ap-1805	19	31	surfaces	surface	NOUN
ap-1805	19	32	.	.	PUNCT
ap-1805	20	1	in	in	ADP
ap-1805	20	2	this	this	DET
ap-1805	20	3	paper	paper	NOUN
ap-1805	20	4	,	,	PUNCT
ap-1805	20	5	we	we	PRON
ap-1805	20	6	are	be	AUX
ap-1805	20	7	mainly	mainly	ADV
ap-1805	20	8	concerned	concerned	ADJ
ap-1805	20	9	about	about	ADP
ap-1805	20	10	the	the	DET
ap-1805	20	11	second	second	ADJ
ap-1805	20	12	part	part	NOUN
ap-1805	20	13	of	of	ADP
ap-1805	20	14	the	the	DET
ap-1805	20	15	16th	16th	ADJ
ap-1805	20	16	hilbert	hilbert	NOUN
ap-1805	20	17	problem	problem	NOUN
ap-1805	20	18	,	,	PUNCT
ap-1805	20	19	which	which	PRON
ap-1805	20	20	deals	deal	VERB
ap-1805	20	21	with	with	ADP
ap-1805	20	22	the	the	DET
ap-1805	20	23	curves	curve	NOUN
ap-1805	20	24	that	that	PRON
ap-1805	20	25	arise	arise	VERB
ap-1805	20	26	as	as	ADP
ap-1805	20	27	solutions	solution	NOUN
ap-1805	20	28	of	of	ADP
ap-1805	20	29	the	the	DET
ap-1805	20	30	planar	planar	ADJ
ap-1805	20	31	differential	differential	ADJ
ap-1805	20	32	equation	equation	NOUN
ap-1805	20	33	(	(	PUNCT
ap-1805	20	34	1	1	NUM
ap-1805	20	35	)	)	PUNCT
ap-1805	20	36	with	with	ADP
ap-1805	20	37	polynomial	polynomial	ADJ
ap-1805	20	38	vector	vector	NOUN
ap-1805	20	39	field	field	NOUN
ap-1805	20	40	x.	x.	NOUN
ap-1805	20	41	more	more	ADV
ap-1805	20	42	precisely	precisely	ADV
ap-1805	20	43	,	,	PUNCT
ap-1805	20	44	in	in	ADP
ap-1805	20	45	the	the	DET
ap-1805	20	46	second	second	ADJ
ap-1805	20	47	part	part	NOUN
ap-1805	20	48	of	of	ADP
ap-1805	20	49	his	his	PRON
ap-1805	20	50	problem	problem	NOUN
ap-1805	20	51	hilbert	hilbert	PROPN
ap-1805	20	52	asks	ask	VERB
ap-1805	20	53	for	for	ADP
ap-1805	20	54	the	the	DET
ap-1805	20	55	maximal	maximal	ADJ
ap-1805	20	56	number	number	NOUN
ap-1805	20	57	and	and	CCONJ
ap-1805	20	58	relative	relative	ADJ
ap-1805	20	59	position	position	NOUN
ap-1805	20	60	of	of	ADP
ap-1805	20	61	the	the	DET
ap-1805	20	62	isolated	isolate	VERB
ap-1805	20	63	closed	closed	ADJ
ap-1805	20	64	orbits	orbit	NOUN
ap-1805	20	65	,	,	PUNCT
ap-1805	20	66	called	call	VERB
ap-1805	20	67	limit	limit	NOUN
ap-1805	20	68	cycles,1	cycles,1	VERB
ap-1805	20	69	this	this	DET
ap-1805	20	70	differential	differential	ADJ
ap-1805	20	71	system	system	NOUN
ap-1805	20	72	(	(	PUNCT
ap-1805	20	73	1	1	X
ap-1805	20	74	)	)	PUNCT
ap-1805	20	75	can	can	AUX
ap-1805	20	76	have	have	VERB
ap-1805	20	77	at	at	ADV
ap-1805	20	78	most	most	ADJ
ap-1805	20	79	.	.	PUNCT
ap-1805	21	1	it	it	PRON
ap-1805	21	2	is	be	AUX
ap-1805	21	3	even	even	ADV
ap-1805	21	4	difficult	difficult	ADJ
ap-1805	21	5	to	to	PART
ap-1805	21	6	understand	understand	VERB
ap-1805	21	7	why	why	SCONJ
ap-1805	21	8	fixed	fix	VERB
ap-1805	21	9	planar	planar	ADJ
ap-1805	21	10	differential	differential	ADJ
ap-1805	21	11	equations	equation	NOUN
ap-1805	21	12	with	with	ADP
ap-1805	21	13	polynomial	polynomial	ADJ
ap-1805	21	14	vector	vector	NOUN
ap-1805	21	15	field	field	NOUN
ap-1805	21	16	can	can	AUX
ap-1805	21	17	only	only	ADV
ap-1805	21	18	have	have	VERB
ap-1805	21	19	a	a	DET
ap-1805	21	20	finite	finite	ADJ
ap-1805	21	21	number	number	NOUN
ap-1805	21	22	of	of	ADP
ap-1805	21	23	limit	limit	NOUN
ap-1805	21	24	cycles	cycle	NOUN
ap-1805	21	25	.	.	PUNCT
ap-1805	22	1	a	a	DET
ap-1805	22	2	proof	proof	NOUN
ap-1805	22	3	of	of	ADP
ap-1805	22	4	this	this	DET
ap-1805	22	5	fact	fact	NOUN
ap-1805	22	6	is	be	AUX
ap-1805	22	7	due	due	ADJ
ap-1805	22	8	to	to	ADP
ap-1805	22	9	ilyashenko	ilyashenko	NOUN
ap-1805	22	10	in	in	ADP
ap-1805	22	11	1991	1991	NUM
ap-1805	22	12	[	[	X
ap-1805	22	13	4	4	NUM
ap-1805	22	14	]	]	PUNCT
ap-1805	22	15	,	,	PUNCT
ap-1805	22	16	who	who	PRON
ap-1805	22	17	actually	actually	ADV
ap-1805	22	18	corrected	correct	VERB
ap-1805	22	19	a	a	DET
ap-1805	22	20	very	very	ADV
ap-1805	22	21	complicated	complicated	ADJ
ap-1805	22	22	and	and	CCONJ
ap-1805	22	23	long	long	ADJ
ap-1805	22	24	proof	proof	NOUN
ap-1805	22	25	due	due	ADP
ap-1805	22	26	to	to	ADP
ap-1805	22	27	dulac	dulac	PROPN
ap-1805	22	28	[	[	X
ap-1805	22	29	5	5	NUM
ap-1805	22	30	]	]	PUNCT
ap-1805	22	31	,	,	PUNCT
ap-1805	22	32	a	a	DET
ap-1805	22	33	student	student	NOUN
ap-1805	22	34	of	of	ADP
ap-1805	22	35	poincaré	poincaré	PROPN
ap-1805	22	36	.	.	PUNCT
ap-1805	23	1	écalle	écalle	PROPN
ap-1805	23	2	et	et	PROPN
ap-1805	23	3	al	al	PROPN
ap-1805	23	4	.	.	PROPN
ap-1805	23	5	independently	independently	ADV
ap-1805	23	6	obtained	obtain	VERB
ap-1805	23	7	a	a	DET
ap-1805	23	8	proof	proof	NOUN
ap-1805	23	9	for	for	ADP
ap-1805	23	10	this	this	DET
ap-1805	23	11	theorem	theorem	NOUN
ap-1805	23	12	[	[	X
ap-1805	23	13	6	6	NUM
ap-1805	23	14	]	]	PUNCT
ap-1805	23	15	.	.	PUNCT
ap-1805	24	1	note	note	VERB
ap-1805	24	2	that	that	SCONJ
ap-1805	24	3	this	this	PRON
ap-1805	24	4	does	do	AUX
ap-1805	24	5	not	not	PART
ap-1805	24	6	imply	imply	VERB
ap-1805	24	7	the	the	DET
ap-1805	24	8	existence	existence	NOUN
ap-1805	24	9	of	of	ADP
ap-1805	24	10	an	an	DET
ap-1805	24	11	upper	upper	ADJ
ap-1805	24	12	bound	bind	VERB
ap-1805	24	13	for	for	ADP
ap-1805	24	14	the	the	DET
ap-1805	24	15	maximal	maximal	ADJ
ap-1805	24	16	number	number	NOUN
ap-1805	24	17	of	of	ADP
ap-1805	24	18	limit	limit	NOUN
ap-1805	24	19	cycles	cycle	NOUN
ap-1805	24	20	h(d	h(d	PROPN
ap-1805	24	21	)	)	PUNCT
ap-1805	24	22	which	which	PRON
ap-1805	24	23	a	a	DET
ap-1805	24	24	planar	planar	ADJ
ap-1805	24	25	polynomial	polynomial	ADJ
ap-1805	24	26	system	system	NOUN
ap-1805	24	27	of	of	ADP
ap-1805	24	28	degree	degree	NOUN
ap-1805	24	29	d	d	NOUN
ap-1805	24	30	can	can	AUX
ap-1805	24	31	have	have	VERB
ap-1805	24	32	.	.	PUNCT
ap-1805	25	1	one	one	NUM
ap-1805	25	2	calls	call	VERB
ap-1805	25	3	h(d	h(d	NOUN
ap-1805	25	4	)	)	PUNCT
ap-1805	25	5	the	the	DET
ap-1805	25	6	d	d	PROPN
ap-1805	25	7	-	-	PUNCT
ap-1805	25	8	th	th	VERB
ap-1805	25	9	hilbert	hilbert	NOUN
ap-1805	25	10	number	number	NOUN
ap-1805	25	11	.	.	PUNCT
ap-1805	26	1	linear	linear	ADJ
ap-1805	26	2	vector	vector	NOUN
ap-1805	26	3	fields	field	NOUN
ap-1805	26	4	have	have	VERB
ap-1805	26	5	no	no	DET
ap-1805	26	6	limit	limit	NOUN
ap-1805	26	7	cycles	cycle	NOUN
ap-1805	26	8	;	;	PUNCT
ap-1805	26	9	hence	hence	ADV
ap-1805	26	10	h(1	h(1	PROPN
ap-1805	26	11	)	)	PUNCT
ap-1805	26	12	=	=	SYM
ap-1805	27	1	0	0	X
ap-1805	27	2	.	.	PUNCT
ap-1805	28	1	quadratic	quadratic	ADJ
ap-1805	28	2	systems	system	NOUN
ap-1805	28	3	can	can	AUX
ap-1805	28	4	actually	actually	ADV
ap-1805	28	5	have	have	VERB
ap-1805	28	6	four	four	NUM
ap-1805	28	7	limit	limit	NOUN
ap-1805	28	8	cycles	cycle	NOUN
ap-1805	28	9	and	and	CCONJ
ap-1805	28	10	some	some	DET
ap-1805	28	11	people	people	NOUN
ap-1805	28	12	believe	believe	VERB
ap-1805	28	13	that	that	SCONJ
ap-1805	28	14	this	this	PRON
ap-1805	28	15	is	be	AUX
ap-1805	28	16	the	the	DET
ap-1805	28	17	maximal	maximal	ADJ
ap-1805	28	18	number	number	NOUN
ap-1805	28	19	of	of	ADP
ap-1805	28	20	limit	limit	NOUN
ap-1805	28	21	cycles	cycle	VERB
ap-1805	28	22	a	a	DET
ap-1805	28	23	quadratic	quadratic	ADJ
ap-1805	28	24	system	system	NOUN
ap-1805	28	25	can	can	AUX
ap-1805	28	26	have	have	VERB
ap-1805	28	27	,	,	PUNCT
ap-1805	28	28	but	but	CCONJ
ap-1805	28	29	it	it	PRON
ap-1805	28	30	is	be	AUX
ap-1805	28	31	still	still	ADV
ap-1805	28	32	unknown	unknown	ADJ
ap-1805	28	33	whether	whether	SCONJ
ap-1805	28	34	or	or	CCONJ
ap-1805	28	35	not	not	PART
ap-1805	28	36	h(2	h(2	NOUN
ap-1805	28	37	)	)	PUNCT
ap-1805	28	38	is	be	AUX
ap-1805	28	39	a	a	DET
ap-1805	28	40	finite	finite	ADJ
ap-1805	28	41	number	number	NOUN
ap-1805	28	42	.	.	PUNCT
ap-1805	29	1	usually	usually	ADV
ap-1805	29	2	,	,	PUNCT
ap-1805	29	3	the	the	DET
ap-1805	29	4	first	first	ADJ
ap-1805	29	5	part	part	NOUN
ap-1805	29	6	of	of	ADP
ap-1805	29	7	the	the	DET
ap-1805	29	8	16th	16th	ADJ
ap-1805	29	9	hilbert	hilbert	NOUN
ap-1805	29	10	problem	problem	NOUN
ap-1805	29	11	is	be	AUX
ap-1805	29	12	studied	study	VERB
ap-1805	29	13	by	by	ADP
ap-1805	29	14	researchers	researcher	NOUN
ap-1805	29	15	in	in	ADP
ap-1805	29	16	real	real	ADJ
ap-1805	29	17	algebraic	algebraic	ADJ
ap-1805	29	18	geometry	geometry	NOUN
ap-1805	29	19	,	,	PUNCT
ap-1805	29	20	while	while	SCONJ
ap-1805	29	21	the	the	DET
ap-1805	29	22	second	second	ADJ
ap-1805	29	23	part	part	NOUN
ap-1805	29	24	is	be	AUX
ap-1805	29	25	considered	consider	VERB
ap-1805	29	26	by	by	ADP
ap-1805	29	27	mathematicians	mathematician	NOUN
ap-1805	29	28	working	work	VERB
ap-1805	29	29	in	in	ADP
ap-1805	29	30	dynamical	dynamical	ADJ
ap-1805	29	31	systems	system	NOUN
ap-1805	29	32	or	or	CCONJ
ap-1805	29	33	differential	differential	ADJ
ap-1805	29	34	equations	equation	NOUN
ap-1805	29	35	.	.	PUNCT
ap-1805	30	1	hilbert	hilbert	PROPN
ap-1805	30	2	also	also	ADV
ap-1805	30	3	pointed	point	VERB
ap-1805	30	4	out	out	ADP
ap-1805	30	5	that	that	SCONJ
ap-1805	30	6	there	there	PRON
ap-1805	30	7	exist	exist	VERB
ap-1805	30	8	possibly	possibly	ADV
ap-1805	30	9	connections	connection	NOUN
ap-1805	30	10	between	between	ADP
ap-1805	30	11	these	these	DET
ap-1805	30	12	two	two	NUM
ap-1805	30	13	parts	part	NOUN
ap-1805	30	14	.	.	PUNCT
ap-1805	31	1	see	see	VERB
ap-1805	31	2	paper	paper	NOUN
ap-1805	32	1	[	[	X
ap-1805	32	2	7	7	X
ap-1805	32	3	]	]	PUNCT
ap-1805	32	4	and	and	CCONJ
ap-1805	32	5	[	[	X
ap-1805	32	6	8	8	NUM
ap-1805	32	7	]	]	PUNCT
ap-1805	32	8	for	for	ADP
ap-1805	32	9	the	the	DET
ap-1805	32	10	original	original	ADJ
ap-1805	32	11	paper	paper	NOUN
ap-1805	32	12	in	in	ADP
ap-1805	32	13	russian	russian	NOUN
ap-1805	32	14	by	by	ADP
ap-1805	32	15	ilyashenko	ilyashenko	PROPN
ap-1805	32	16	and	and	CCONJ
ap-1805	32	17	more	more	ADV
ap-1805	32	18	recently	recently	ADV
ap-1805	32	19	a	a	DET
ap-1805	32	20	paper	paper	NOUN
ap-1805	32	21	[	[	X
ap-1805	32	22	9	9	NUM
ap-1805	32	23	]	]	PUNCT
ap-1805	32	24	for	for	ADP
ap-1805	32	25	a	a	DET
ap-1805	32	26	survey	survey	NOUN
ap-1805	32	27	about	about	ADP
ap-1805	32	28	the	the	DET
ap-1805	32	29	second	second	ADJ
ap-1805	32	30	part	part	NOUN
ap-1805	32	31	of	of	ADP
ap-1805	32	32	the	the	DET
ap-1805	32	33	16th	16th	ADJ
ap-1805	32	34	hilbert	hilbert	NOUN
ap-1805	32	35	1	1	NUM
ap-1805	32	36	in	in	ADP
ap-1805	32	37	the	the	DET
ap-1805	32	38	past	past	NOUN
ap-1805	32	39	,	,	PUNCT
ap-1805	32	40	the	the	DET
ap-1805	32	41	term	term	NOUN
ap-1805	32	42	limit	limit	NOUN
ap-1805	32	43	cycle	cycle	NOUN
ap-1805	32	44	was	be	AUX
ap-1805	32	45	used	use	VERB
ap-1805	32	46	for	for	ADP
ap-1805	32	47	a	a	DET
ap-1805	32	48	stable	stable	ADJ
ap-1805	32	49	isolated	isolate	VERB
ap-1805	32	50	closed	closed	ADJ
ap-1805	32	51	orbit	orbit	NOUN
ap-1805	32	52	or	or	CCONJ
ap-1805	32	53	just	just	ADV
ap-1805	32	54	for	for	ADP
ap-1805	32	55	a	a	DET
ap-1805	32	56	closed	closed	ADJ
ap-1805	32	57	orbit	orbit	NOUN
ap-1805	32	58	.	.	PUNCT
ap-1805	33	1	nowadays	nowadays	ADV
ap-1805	33	2	and	and	CCONJ
ap-1805	33	3	in	in	ADP
ap-1805	33	4	this	this	DET
ap-1805	33	5	paper	paper	NOUN
ap-1805	33	6	,	,	PUNCT
ap-1805	33	7	a	a	DET
ap-1805	33	8	limit	limit	NOUN
ap-1805	33	9	cycle	cycle	NOUN
ap-1805	33	10	is	be	AUX
ap-1805	33	11	a	a	DET
ap-1805	33	12	closed	closed	ADJ
ap-1805	33	13	orbit	orbit	NOUN
ap-1805	33	14	that	that	PRON
ap-1805	33	15	is	be	AUX
ap-1805	33	16	isolated	isolate	VERB
ap-1805	33	17	in	in	ADP
ap-1805	33	18	the	the	DET
ap-1805	33	19	set	set	NOUN
ap-1805	33	20	of	of	ADP
ap-1805	33	21	all	all	DET
ap-1805	33	22	periodic	periodic	ADJ
ap-1805	33	23	orbits	orbit	NOUN
ap-1805	33	24	of	of	ADP
ap-1805	33	25	some	some	DET
ap-1805	33	26	differential	differential	ADJ
ap-1805	33	27	equation	equation	NOUN
ap-1805	33	28	.	.	PUNCT
ap-1805	34	1	283	283	NUM
ap-1805	34	2	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-1805	34	3	m.	m.	PROPN
ap-1805	34	4	himmel	himmel	PROPN
ap-1805	34	5	acta	acta	PROPN
ap-1805	34	6	polytechnica	polytechnica	PROPN
ap-1805	34	7	problem	problem	NOUN
ap-1805	34	8	.	.	PUNCT
ap-1805	35	1	1.2	1.2	NUM
ap-1805	35	2	.	.	PUNCT
ap-1805	36	1	dulac	dulac	PROPN
ap-1805	36	2	criterion	criterion	NOUN
ap-1805	36	3	in	in	ADP
ap-1805	36	4	2008	2008	NUM
ap-1805	36	5	,	,	PUNCT
ap-1805	36	6	the	the	DET
ap-1805	36	7	author	author	NOUN
ap-1805	36	8	was	be	AUX
ap-1805	36	9	confronted	confront	VERB
ap-1805	36	10	with	with	ADP
ap-1805	36	11	the	the	DET
ap-1805	36	12	analysis	analysis	NOUN
ap-1805	36	13	of	of	ADP
ap-1805	36	14	a	a	DET
ap-1805	36	15	quadratic	quadratic	ADJ
ap-1805	36	16	polynomial	polynomial	ADJ
ap-1805	36	17	differential	differential	NOUN
ap-1805	36	18	equation	equation	NOUN
ap-1805	36	19	.	.	PUNCT
ap-1805	37	1	in	in	ADP
ap-1805	37	2	literature	literature	NOUN
ap-1805	37	3	there	there	ADV
ap-1805	37	4	existed	exist	VERB
ap-1805	37	5	a	a	DET
ap-1805	37	6	quite	quite	ADV
ap-1805	37	7	technical	technical	ADJ
ap-1805	37	8	proof	proof	NOUN
ap-1805	37	9	showing	show	VERB
ap-1805	37	10	the	the	DET
ap-1805	37	11	uniqueness	uniqueness	NOUN
ap-1805	37	12	of	of	ADP
ap-1805	37	13	a	a	DET
ap-1805	37	14	limit	limit	NOUN
ap-1805	37	15	cycle	cycle	NOUN
ap-1805	37	16	for	for	ADP
ap-1805	37	17	this	this	DET
ap-1805	37	18	system	system	NOUN
ap-1805	37	19	.	.	PUNCT
ap-1805	38	1	then	then	ADV
ap-1805	38	2	,	,	PUNCT
ap-1805	38	3	fortunately	fortunately	ADV
ap-1805	38	4	,	,	PUNCT
ap-1805	38	5	he	he	PRON
ap-1805	38	6	was	be	AUX
ap-1805	38	7	able	able	ADJ
ap-1805	38	8	to	to	PART
ap-1805	38	9	obtain	obtain	VERB
ap-1805	38	10	the	the	DET
ap-1805	38	11	same	same	ADJ
ap-1805	38	12	result	result	NOUN
ap-1805	38	13	by	by	ADP
ap-1805	38	14	applying	apply	VERB
ap-1805	38	15	the	the	DET
ap-1805	38	16	well	well	ADV
ap-1805	38	17	-	-	PUNCT
ap-1805	38	18	known	know	VERB
ap-1805	38	19	theorem	theorem	NOUN
ap-1805	38	20	1	1	NUM
ap-1805	38	21	(	(	PUNCT
ap-1805	38	22	dulac	dulac	PROPN
ap-1805	38	23	criterion	criterion	NOUN
ap-1805	38	24	[	[	X
ap-1805	38	25	5	5	NUM
ap-1805	38	26	]	]	PUNCT
ap-1805	38	27	)	)	PUNCT
ap-1805	38	28	.	.	PUNCT
ap-1805	39	1	let	let	VERB
ap-1805	39	2	ω	ω	NOUN
ap-1805	39	3	⊆	⊆	NUM
ap-1805	39	4	r2	r2	PROPN
ap-1805	39	5	be	be	AUX
ap-1805	39	6	a	a	DET
ap-1805	39	7	simply	simply	ADV
ap-1805	39	8	connected	connected	ADJ
ap-1805	39	9	region	region	NOUN
ap-1805	39	10	,	,	PUNCT
ap-1805	39	11	x	x	X
ap-1805	39	12	:	:	PUNCT
ap-1805	39	13	=	=	SYM
ap-1805	39	14	(	(	PUNCT
ap-1805	39	15	p	p	X
ap-1805	39	16	,	,	PUNCT
ap-1805	39	17	q	q	NOUN
ap-1805	39	18	)	)	PUNCT
ap-1805	39	19	∈	∈	PROPN
ap-1805	39	20	c1(ω	c1(ω	SYM
ap-1805	39	21	,	,	PUNCT
ap-1805	39	22	r2	r2	PROPN
ap-1805	39	23	)	)	PUNCT
ap-1805	39	24	a	a	DET
ap-1805	39	25	smooth	smooth	ADJ
ap-1805	39	26	vector	vector	NOUN
ap-1805	39	27	field	field	NOUN
ap-1805	39	28	and	and	CCONJ
ap-1805	39	29	b	b	X
ap-1805	39	30	∈	∈	PROPN
ap-1805	39	31	c1(ω	c1(ω	NOUN
ap-1805	39	32	,	,	PUNCT
ap-1805	39	33	r	r	NOUN
ap-1805	39	34	)	)	PUNCT
ap-1805	39	35	a	a	DET
ap-1805	39	36	smooth	smooth	ADJ
ap-1805	39	37	real	real	ADV
ap-1805	39	38	-	-	PUNCT
ap-1805	39	39	valued	value	VERB
ap-1805	39	40	function	function	NOUN
ap-1805	39	41	such	such	ADJ
ap-1805	39	42	that	that	SCONJ
ap-1805	39	43	the	the	DET
ap-1805	39	44	partial	partial	ADJ
ap-1805	39	45	differential	differential	NOUN
ap-1805	39	46	inequality	inequality	NOUN
ap-1805	39	47	div(bx	div(bx	PROPN
ap-1805	39	48	)	)	PUNCT
ap-1805	39	49	:	:	PUNCT
ap-1805	40	1	=	=	NOUN
ap-1805	40	2	∂(bp	∂(bp	X
ap-1805	40	3	)	)	PUNCT
ap-1805	41	1	∂x	∂x	PROPN
ap-1805	41	2	+	+	NUM
ap-1805	41	3	∂(bq	∂(bq	NOUN
ap-1805	41	4	)	)	PUNCT
ap-1805	42	1	∂y	∂y	NOUN
ap-1805	42	2	>	>	X
ap-1805	42	3	0	0	PUNCT
ap-1805	43	1	(	(	PUNCT
ap-1805	43	2	2	2	NUM
ap-1805	43	3	)	)	PUNCT
ap-1805	43	4	is	be	AUX
ap-1805	43	5	satisfied	satisfied	ADJ
ap-1805	43	6	in	in	ADP
ap-1805	43	7	ω	ω	PROPN
ap-1805	43	8	.	.	PUNCT
ap-1805	44	1	then	then	ADV
ap-1805	44	2	the	the	DET
ap-1805	44	3	planar	planar	ADJ
ap-1805	44	4	ordinary	ordinary	ADJ
ap-1805	44	5	differential	differential	ADJ
ap-1805	44	6	equation	equation	NOUN
ap-1805	44	7	(	(	PUNCT
ap-1805	44	8	1	1	NUM
ap-1805	44	9	)	)	PUNCT
ap-1805	44	10	with	with	ADP
ap-1805	44	11	x	x	PUNCT
ap-1805	44	12	as	as	ADP
ap-1805	44	13	right	right	ADJ
ap-1805	44	14	-	-	PUNCT
ap-1805	44	15	hand	hand	NOUN
ap-1805	44	16	-	-	PUNCT
ap-1805	44	17	side	side	NOUN
ap-1805	44	18	does	do	AUX
ap-1805	44	19	not	not	PART
ap-1805	44	20	posses	posse	VERB
ap-1805	44	21	any	any	DET
ap-1805	44	22	periodic	periodic	ADJ
ap-1805	44	23	solution	solution	NOUN
ap-1805	44	24	that	that	PRON
ap-1805	44	25	is	be	AUX
ap-1805	44	26	fully	fully	ADV
ap-1805	44	27	contained	contain	VERB
ap-1805	44	28	in	in	ADP
ap-1805	44	29	ω	ω	PROPN
ap-1805	44	30	.	.	PUNCT
ap-1805	44	31	remark	remark	PROPN
ap-1805	44	32	1	1	NUM
ap-1805	44	33	.	.	PUNCT
ap-1805	45	1	(	(	PUNCT
ap-1805	45	2	1	1	NUM
ap-1805	45	3	.	.	PUNCT
ap-1805	45	4	)	)	PUNCT
ap-1805	46	1	the	the	DET
ap-1805	46	2	proof	proof	NOUN
ap-1805	46	3	of	of	ADP
ap-1805	46	4	theorem	theorem	ADJ
ap-1805	46	5	1	1	NUM
ap-1805	46	6	is	be	AUX
ap-1805	46	7	indirect	indirect	ADJ
ap-1805	46	8	:	:	PUNCT
ap-1805	46	9	one	one	NUM
ap-1805	46	10	assumes	assume	VERB
ap-1805	46	11	the	the	DET
ap-1805	46	12	existence	existence	NOUN
ap-1805	46	13	of	of	ADP
ap-1805	46	14	a	a	DET
ap-1805	46	15	closed	closed	ADJ
ap-1805	46	16	orbit	orbit	NOUN
ap-1805	46	17	of	of	ADP
ap-1805	46	18	(	(	PUNCT
ap-1805	46	19	1	1	NUM
ap-1805	46	20	)	)	PUNCT
ap-1805	46	21	in	in	ADP
ap-1805	46	22	ω	ω	PROPN
ap-1805	46	23	and	and	CCONJ
ap-1805	46	24	applies	apply	VERB
ap-1805	46	25	the	the	DET
ap-1805	46	26	divergence	divergence	NOUN
ap-1805	46	27	theorem	theorem	NOUN
ap-1805	46	28	of	of	ADP
ap-1805	46	29	gauß	gauß	NOUN
ap-1805	46	30	.	.	PUNCT
ap-1805	47	1	this	this	PRON
ap-1805	47	2	immediately	immediately	ADV
ap-1805	47	3	gives	give	VERB
ap-1805	47	4	a	a	DET
ap-1805	47	5	contradiction	contradiction	NOUN
ap-1805	47	6	.	.	PUNCT
ap-1805	48	1	(	(	PUNCT
ap-1805	48	2	2	2	NUM
ap-1805	48	3	.	.	PUNCT
ap-1805	48	4	)	)	PUNCT
ap-1805	48	5	in	in	ADP
ap-1805	48	6	2009	2009	NUM
ap-1805	48	7	,	,	PUNCT
ap-1805	48	8	the	the	DET
ap-1805	48	9	author	author	NOUN
ap-1805	48	10	was	be	AUX
ap-1805	48	11	able	able	ADJ
ap-1805	48	12	to	to	PART
ap-1805	48	13	weaken	weaken	VERB
ap-1805	48	14	the	the	DET
ap-1805	48	15	assumptions	assumption	NOUN
ap-1805	48	16	made	make	VERB
ap-1805	48	17	on	on	ADP
ap-1805	48	18	the	the	DET
ap-1805	48	19	function	function	NOUN
ap-1805	48	20	b	b	NOUN
ap-1805	48	21	,	,	PUNCT
ap-1805	48	22	see	see	VERB
ap-1805	48	23	[	[	X
ap-1805	48	24	10	10	NUM
ap-1805	48	25	]	]	PUNCT
ap-1805	48	26	.	.	PUNCT
ap-1805	49	1	essentially	essentially	ADV
ap-1805	49	2	,	,	PUNCT
ap-1805	49	3	the	the	DET
ap-1805	49	4	statement	statement	NOUN
ap-1805	49	5	of	of	ADP
ap-1805	49	6	theorem	theorem	ADJ
ap-1805	49	7	1	1	NUM
ap-1805	49	8	still	still	ADV
ap-1805	49	9	holds	hold	VERB
ap-1805	49	10	if	if	SCONJ
ap-1805	49	11	the	the	DET
ap-1805	49	12	function	function	NOUN
ap-1805	49	13	b	b	NOUN
ap-1805	49	14	is	be	AUX
ap-1805	49	15	only	only	ADV
ap-1805	49	16	weakly	weakly	ADV
ap-1805	49	17	differentiable	differentiable	ADJ
ap-1805	49	18	of	of	ADP
ap-1805	49	19	first	first	ADJ
ap-1805	49	20	degree	degree	NOUN
ap-1805	49	21	and	and	CCONJ
ap-1805	49	22	equation	equation	NOUN
ap-1805	49	23	(	(	PUNCT
ap-1805	49	24	2	2	X
ap-1805	49	25	)	)	PUNCT
ap-1805	49	26	holds	hold	VERB
ap-1805	49	27	only	only	ADV
ap-1805	49	28	almost	almost	ADV
ap-1805	49	29	everywhere	everywhere	ADV
ap-1805	49	30	in	in	ADP
ap-1805	49	31	ω	ω	NOUN
ap-1805	49	32	,	,	PUNCT
ap-1805	49	33	compare	compare	ADJ
ap-1805	49	34	definition	definition	NOUN
ap-1805	49	35	1	1	NUM
ap-1805	49	36	.	.	PUNCT
ap-1805	50	1	(	(	PUNCT
ap-1805	50	2	3	3	NUM
ap-1805	50	3	.	.	PUNCT
ap-1805	50	4	)	)	PUNCT
ap-1805	51	1	if	if	SCONJ
ap-1805	51	2	the	the	DET
ap-1805	51	3	domain	domain	NOUN
ap-1805	51	4	ω	ω	NOUN
ap-1805	51	5	⊆	⊆	NUM
ap-1805	51	6	r2	r2	NOUN
ap-1805	51	7	referred	refer	VERB
ap-1805	51	8	to	to	ADP
ap-1805	51	9	in	in	ADP
ap-1805	51	10	theorem	theorem	NOUN
ap-1805	51	11	1	1	NUM
ap-1805	51	12	is	be	AUX
ap-1805	51	13	not	not	PART
ap-1805	51	14	simply	simply	ADV
ap-1805	51	15	connected	connect	VERB
ap-1805	51	16	,	,	PUNCT
ap-1805	51	17	but	but	CCONJ
ap-1805	51	18	p	p	X
ap-1805	51	19	-	-	PUNCT
ap-1805	51	20	connected	connected	ADJ
ap-1805	51	21	for	for	ADP
ap-1805	51	22	some	some	DET
ap-1805	51	23	p	p	PROPN
ap-1805	51	24	∈	∈	PROPN
ap-1805	51	25	n	n	CCONJ
ap-1805	51	26	,	,	PUNCT
ap-1805	51	27	p	p	PRON
ap-1805	51	28	≥	≥	NUM
ap-1805	51	29	2	2	NUM
ap-1805	51	30	,	,	PUNCT
ap-1805	51	31	then	then	ADV
ap-1805	51	32	there	there	PRON
ap-1805	51	33	can	can	AUX
ap-1805	51	34	be	be	AUX
ap-1805	51	35	at	at	ADP
ap-1805	51	36	most	most	ADJ
ap-1805	51	37	p−1	p−1	PROPN
ap-1805	51	38	closed	closed	ADJ
ap-1805	51	39	orbits	orbit	NOUN
ap-1805	51	40	fully	fully	ADV
ap-1805	51	41	contained	contain	VERB
ap-1805	51	42	in	in	ADP
ap-1805	51	43	ω	ω	PROPN
ap-1805	51	44	.	.	PUNCT
ap-1805	52	1	(	(	PUNCT
ap-1805	52	2	4	4	NUM
ap-1805	52	3	.	.	PUNCT
ap-1805	52	4	)	)	PUNCT
ap-1805	53	1	the	the	DET
ap-1805	53	2	dulac	dulac	PROPN
ap-1805	53	3	criterion	criterion	NOUN
ap-1805	53	4	is	be	AUX
ap-1805	53	5	a	a	DET
ap-1805	53	6	generalization	generalization	NOUN
ap-1805	53	7	of	of	ADP
ap-1805	53	8	the	the	DET
ap-1805	53	9	bendixson	bendixson	NOUN
ap-1805	53	10	criterion	criterion	NOUN
ap-1805	53	11	[	[	X
ap-1805	53	12	11	11	NUM
ap-1805	53	13	]	]	PUNCT
ap-1805	53	14	.	.	PUNCT
ap-1805	54	1	in	in	ADP
ap-1805	54	2	fact	fact	NOUN
ap-1805	54	3	,	,	PUNCT
ap-1805	54	4	the	the	DET
ap-1805	54	5	bendixson	bendixson	NOUN
ap-1805	54	6	criterion	criterion	NOUN
ap-1805	54	7	follows	follow	VERB
ap-1805	54	8	from	from	ADP
ap-1805	54	9	theorem	theorem	ADJ
ap-1805	54	10	1	1	NUM
ap-1805	54	11	if	if	SCONJ
ap-1805	54	12	we	we	PRON
ap-1805	54	13	choose	choose	VERB
ap-1805	54	14	b	b	NOUN
ap-1805	54	15	=	=	SYM
ap-1805	54	16	1	1	NUM
ap-1805	54	17	,	,	PUNCT
ap-1805	54	18	the	the	DET
ap-1805	54	19	function	function	NOUN
ap-1805	54	20	that	that	PRON
ap-1805	54	21	is	be	AUX
ap-1805	54	22	constant	constant	ADJ
ap-1805	54	23	1	1	NUM
ap-1805	54	24	for	for	ADP
ap-1805	54	25	all	all	DET
ap-1805	54	26	z	z	NOUN
ap-1805	54	27	∈	∈	PROPN
ap-1805	54	28	ω	ω	PROPN
ap-1805	54	29	.	.	PUNCT
ap-1805	55	1	definition	definition	NOUN
ap-1805	55	2	1	1	NUM
ap-1805	55	3	(	(	PUNCT
ap-1805	55	4	dulac	dulac	PROPN
ap-1805	55	5	function	function	PROPN
ap-1805	55	6	)	)	PUNCT
ap-1805	55	7	.	.	PUNCT
ap-1805	56	1	the	the	DET
ap-1805	56	2	multiplier	multipli	ADJ
ap-1805	56	3	b	b	X
ap-1805	56	4	∈w	∈w	NOUN
ap-1805	56	5	1,p(ω	1,p(ω	NUM
ap-1805	56	6	,	,	PUNCT
ap-1805	56	7	r	r	NOUN
ap-1805	56	8	)	)	PUNCT
ap-1805	56	9	is	be	AUX
ap-1805	56	10	called	call	VERB
ap-1805	56	11	dulac	dulac	PROPN
ap-1805	56	12	function	function	NOUN
ap-1805	56	13	of	of	ADP
ap-1805	56	14	the	the	DET
ap-1805	56	15	planar	planar	ADJ
ap-1805	56	16	dynamical	dynamical	ADJ
ap-1805	56	17	system	system	NOUN
ap-1805	56	18	(	(	PUNCT
ap-1805	56	19	1	1	NUM
ap-1805	56	20	)	)	PUNCT
ap-1805	56	21	in	in	ADP
ap-1805	56	22	ω	ω	NUM
ap-1805	56	23	⊆	⊆	NUM
ap-1805	56	24	d	d	NOUN
ap-1805	56	25	if	if	SCONJ
ap-1805	57	1	and	and	CCONJ
ap-1805	57	2	only	only	ADV
ap-1805	57	3	if	if	SCONJ
ap-1805	57	4	there	there	PRON
ap-1805	57	5	is	be	VERB
ap-1805	57	6	a	a	DET
ap-1805	57	7	real	real	ADV
ap-1805	57	8	-	-	PUNCT
ap-1805	57	9	valued	value	VERB
ap-1805	57	10	continuous	continuous	ADJ
ap-1805	57	11	function	function	NOUN
ap-1805	57	12	g	g	PROPN
ap-1805	57	13	>	>	X
ap-1805	57	14	0	0	PUNCT
ap-1805	58	1	having	have	VERB
ap-1805	58	2	a	a	DET
ap-1805	58	3	positive	positive	ADJ
ap-1805	58	4	sign	sign	NOUN
ap-1805	58	5	in	in	ADP
ap-1805	58	6	ω	ω	PROPN
ap-1805	58	7	except	except	SCONJ
ap-1805	58	8	on	on	ADP
ap-1805	58	9	a	a	DET
ap-1805	58	10	set	set	NOUN
ap-1805	58	11	of	of	ADP
ap-1805	58	12	lebesgue	lebesgue	ADJ
ap-1805	58	13	measure	measure	NOUN
ap-1805	58	14	zero	zero	NUM
ap-1805	58	15	such	such	ADJ
ap-1805	58	16	that	that	SCONJ
ap-1805	58	17	the	the	DET
ap-1805	58	18	equation	equation	NOUN
ap-1805	58	19	div(bx	div(bx	VERB
ap-1805	58	20	)	)	PUNCT
ap-1805	58	21	=	=	SYM
ap-1805	58	22	b	b	PROPN
ap-1805	58	23	·	·	PUNCT
ap-1805	58	24	divx	divx	PROPN
ap-1805	58	25	+	+	CCONJ
ap-1805	58	26	〈	〈	PROPN
ap-1805	58	27	∇b	∇b	PROPN
ap-1805	58	28	,	,	PUNCT
ap-1805	58	29	x	x	NOUN
ap-1805	58	30	〉	〉	NOUN
ap-1805	58	31	=	=	SYM
ap-1805	58	32	g	g	PROPN
ap-1805	58	33	(	(	PUNCT
ap-1805	58	34	3	3	NUM
ap-1805	58	35	)	)	PUNCT
ap-1805	58	36	holds	hold	VERB
ap-1805	58	37	in	in	ADP
ap-1805	58	38	ω	ω	PROPN
ap-1805	58	39	.	.	PUNCT
ap-1805	59	1	here	here	ADV
ap-1805	59	2	w	w	PROPN
ap-1805	59	3	1,p(ω	1,p(ω	NUM
ap-1805	59	4	,	,	PUNCT
ap-1805	59	5	r	r	NOUN
ap-1805	59	6	)	)	PUNCT
ap-1805	59	7	denotes	denote	VERB
ap-1805	59	8	the	the	DET
ap-1805	59	9	sobolev	sobolev	NOUN
ap-1805	59	10	space	space	NOUN
ap-1805	59	11	of	of	ADP
ap-1805	59	12	lp	lp	PROPN
ap-1805	59	13	functions	function	NOUN
ap-1805	59	14	that	that	PRON
ap-1805	59	15	are	be	AUX
ap-1805	59	16	weakly	weakly	ADV
ap-1805	59	17	differentiable	differentiable	ADJ
ap-1805	59	18	of	of	ADP
ap-1805	59	19	first	first	ADJ
ap-1805	59	20	degree	degree	NOUN
ap-1805	59	21	and	and	CCONJ
ap-1805	59	22	with	with	ADP
ap-1805	59	23	a	a	DET
ap-1805	59	24	weak	weak	ADJ
ap-1805	59	25	derivative	derivative	NOUN
ap-1805	59	26	in	in	ADP
ap-1805	59	27	lp	lp	PROPN
ap-1805	59	28	.	.	PUNCT
ap-1805	60	1	vice	vice	PROPN
ap-1805	60	2	versa	versa	ADV
ap-1805	60	3	,	,	PUNCT
ap-1805	60	4	we	we	PRON
ap-1805	60	5	call	call	VERB
ap-1805	60	6	any	any	DET
ap-1805	60	7	function	function	NOUN
ap-1805	60	8	b	b	PROPN
ap-1805	60	9	of	of	ADP
ap-1805	60	10	class	class	NOUN
ap-1805	60	11	w	w	PROPN
ap-1805	60	12	1,p	1,p	PROPN
ap-1805	60	13	satisfying	satisfying	ADJ
ap-1805	60	14	(	(	PUNCT
ap-1805	60	15	3	3	NUM
ap-1805	60	16	)	)	PUNCT
ap-1805	60	17	a	a	DET
ap-1805	60	18	g	g	PROPN
ap-1805	60	19	-	-	PUNCT
ap-1805	60	20	dulac	dulac	PROPN
ap-1805	60	21	function	function	NOUN
ap-1805	60	22	of	of	ADP
ap-1805	60	23	x	x	PUNCT
ap-1805	60	24	in	in	ADP
ap-1805	60	25	ω	ω	NUM
ap-1805	60	26	.	.	PUNCT
ap-1805	61	1	in	in	ADP
ap-1805	61	2	general	general	ADJ
ap-1805	61	3	,	,	PUNCT
ap-1805	61	4	it	it	PRON
ap-1805	61	5	is	be	AUX
ap-1805	61	6	very	very	ADV
ap-1805	61	7	difficult	difficult	ADJ
ap-1805	61	8	to	to	PART
ap-1805	61	9	find	find	VERB
ap-1805	61	10	a	a	DET
ap-1805	61	11	dulac	dulac	PROPN
ap-1805	61	12	function	function	NOUN
ap-1805	61	13	for	for	ADP
ap-1805	61	14	some	some	DET
ap-1805	61	15	given	give	VERB
ap-1805	61	16	vector	vector	NOUN
ap-1805	61	17	field	field	NOUN
ap-1805	61	18	x	x	NOUN
ap-1805	61	19	,	,	PUNCT
ap-1805	61	20	but	but	CCONJ
ap-1805	61	21	if	if	SCONJ
ap-1805	61	22	one	one	NUM
ap-1805	61	23	incidentally	incidentally	ADV
ap-1805	61	24	guesses	guess	VERB
ap-1805	61	25	such	such	DET
ap-1805	61	26	a	a	DET
ap-1805	61	27	function	function	NOUN
ap-1805	61	28	,	,	PUNCT
ap-1805	61	29	it	it	PRON
ap-1805	61	30	is	be	AUX
ap-1805	61	31	quite	quite	ADV
ap-1805	61	32	easy	easy	ADJ
ap-1805	61	33	to	to	PART
ap-1805	61	34	verify	verify	VERB
ap-1805	61	35	that	that	SCONJ
ap-1805	61	36	it	it	PRON
ap-1805	61	37	obeys	obey	VERB
ap-1805	61	38	condition	condition	NOUN
ap-1805	61	39	(	(	PUNCT
ap-1805	61	40	2).2	2).2	NUM
ap-1805	61	41	just	just	ADV
ap-1805	61	42	for	for	ADP
ap-1805	61	43	curiosity	curiosity	NOUN
ap-1805	61	44	,	,	PUNCT
ap-1805	61	45	the	the	DET
ap-1805	61	46	author	author	NOUN
ap-1805	61	47	wondered	wonder	VERB
ap-1805	61	48	whether	whether	SCONJ
ap-1805	61	49	the	the	DET
ap-1805	61	50	converse	converse	NOUN
ap-1805	61	51	statement	statement	NOUN
ap-1805	61	52	of	of	ADP
ap-1805	61	53	theorem	theorem	NOUN
ap-1805	61	54	1	1	NUM
ap-1805	61	55	is	be	AUX
ap-1805	61	56	also	also	ADV
ap-1805	61	57	true	true	ADJ
ap-1805	61	58	.	.	PUNCT
ap-1805	62	1	question	question	NOUN
ap-1805	62	2	1	1	NUM
ap-1805	62	3	.	.	PUNCT
ap-1805	62	4	given	give	VERB
ap-1805	62	5	a	a	DET
ap-1805	62	6	smooth	smooth	ADJ
ap-1805	62	7	planar	planar	ADJ
ap-1805	62	8	vector	vector	NOUN
ap-1805	62	9	field	field	NOUN
ap-1805	62	10	x	x	PUNCT
ap-1805	62	11	and	and	CCONJ
ap-1805	62	12	assume	assume	VERB
ap-1805	62	13	that	that	SCONJ
ap-1805	62	14	the	the	DET
ap-1805	62	15	planar	planar	ADJ
ap-1805	62	16	differential	differential	ADJ
ap-1805	62	17	equation	equation	NOUN
ap-1805	62	18	(	(	PUNCT
ap-1805	62	19	1	1	X
ap-1805	62	20	)	)	PUNCT
ap-1805	62	21	does	do	AUX
ap-1805	62	22	not	not	PART
ap-1805	62	23	have	have	VERB
ap-1805	62	24	any	any	DET
ap-1805	62	25	periodic	periodic	ADJ
ap-1805	62	26	solution	solution	NOUN
ap-1805	62	27	in	in	ADP
ap-1805	62	28	some	some	DET
ap-1805	62	29	simply	simply	ADV
ap-1805	62	30	connected	connected	ADJ
ap-1805	62	31	domain	domain	NOUN
ap-1805	62	32	ω	ω	X
ap-1805	62	33	.	.	PUNCT
ap-1805	63	1	does	do	AUX
ap-1805	63	2	there	there	PRON
ap-1805	63	3	exist	exist	VERB
ap-1805	63	4	a	a	DET
ap-1805	63	5	dulac	dulac	PROPN
ap-1805	63	6	function	function	NOUN
ap-1805	63	7	in	in	ADP
ap-1805	63	8	ω	ω	PROPN
ap-1805	63	9	?	?	PUNCT
ap-1805	64	1	the	the	DET
ap-1805	64	2	answer	answer	NOUN
ap-1805	64	3	is	be	AUX
ap-1805	64	4	no	no	INTJ
ap-1805	64	5	,	,	PUNCT
ap-1805	64	6	if	if	SCONJ
ap-1805	64	7	the	the	DET
ap-1805	64	8	boundary	boundary	NOUN
ap-1805	64	9	of	of	ADP
ap-1805	64	10	ω	ω	PROPN
ap-1805	64	11	is	be	AUX
ap-1805	64	12	formed	form	VERB
ap-1805	64	13	by	by	ADP
ap-1805	64	14	a	a	DET
ap-1805	64	15	periodic	periodic	ADJ
ap-1805	64	16	solution	solution	NOUN
ap-1805	64	17	of	of	ADP
ap-1805	64	18	the	the	DET
ap-1805	64	19	corresponding	corresponding	ADJ
ap-1805	64	20	system	system	NOUN
ap-1805	64	21	,	,	PUNCT
ap-1805	64	22	but	but	CCONJ
ap-1805	64	23	in	in	ADP
ap-1805	64	24	every	every	DET
ap-1805	64	25	other	other	ADJ
ap-1805	64	26	case	case	NOUN
ap-1805	64	27	considered	consider	VERB
ap-1805	64	28	by	by	ADP
ap-1805	64	29	the	the	DET
ap-1805	64	30	author	author	NOUN
ap-1805	64	31	he	he	PRON
ap-1805	64	32	was	be	AUX
ap-1805	64	33	able	able	ADJ
ap-1805	64	34	to	to	PART
ap-1805	64	35	obtain	obtain	VERB
ap-1805	64	36	an	an	DET
ap-1805	64	37	affirmative	affirmative	ADJ
ap-1805	64	38	answer	answer	NOUN
ap-1805	64	39	to	to	PART
ap-1805	64	40	question	question	VERB
ap-1805	64	41	1	1	NUM
ap-1805	64	42	raised	raise	VERB
ap-1805	64	43	above	above	ADV
ap-1805	64	44	.	.	PUNCT
ap-1805	65	1	in	in	ADP
ap-1805	65	2	the	the	DET
ap-1805	65	3	following	following	NOUN
ap-1805	65	4	we	we	PRON
ap-1805	65	5	quote	quote	VERB
ap-1805	65	6	some	some	PRON
ap-1805	65	7	of	of	ADP
ap-1805	65	8	these	these	DET
ap-1805	65	9	positive	positive	ADJ
ap-1805	65	10	results	result	NOUN
ap-1805	65	11	.	.	PUNCT
ap-1805	66	1	2	2	X
ap-1805	66	2	.	.	X
ap-1805	66	3	local	local	ADJ
ap-1805	66	4	results	result	NOUN
ap-1805	66	5	gradient	gradient	ADJ
ap-1805	66	6	systems	system	NOUN
ap-1805	66	7	never	never	ADV
ap-1805	66	8	possess	possess	VERB
ap-1805	66	9	periodic	periodic	ADJ
ap-1805	66	10	solutions	solution	NOUN
ap-1805	66	11	[	[	X
ap-1805	66	12	12	12	NUM
ap-1805	66	13	]	]	PUNCT
ap-1805	66	14	,	,	PUNCT
ap-1805	66	15	hence	hence	ADV
ap-1805	66	16	we	we	PRON
ap-1805	66	17	expect	expect	VERB
ap-1805	66	18	that	that	SCONJ
ap-1805	66	19	gradient	gradient	ADJ
ap-1805	66	20	fields	field	NOUN
ap-1805	66	21	have	have	VERB
ap-1805	66	22	a	a	DET
ap-1805	66	23	dulac	dulac	PROPN
ap-1805	66	24	function	function	NOUN
ap-1805	66	25	.	.	PUNCT
ap-1805	67	1	indeed	indeed	ADV
ap-1805	67	2	,	,	PUNCT
ap-1805	67	3	this	this	PRON
ap-1805	67	4	is	be	AUX
ap-1805	67	5	the	the	DET
ap-1805	67	6	case	case	NOUN
ap-1805	67	7	.	.	PUNCT
ap-1805	68	1	theorem	theorem	ADJ
ap-1805	68	2	2	2	NUM
ap-1805	68	3	(	(	PUNCT
ap-1805	68	4	gradient	gradient	NOUN
ap-1805	68	5	fields	field	NOUN
ap-1805	68	6	[	[	X
ap-1805	68	7	10	10	NUM
ap-1805	68	8	]	]	NUM
ap-1805	68	9	)	)	PUNCT
ap-1805	68	10	.	.	PUNCT
ap-1805	69	1	let	let	VERB
ap-1805	69	2	x	x	PUNCT
ap-1805	69	3	=	=	PUNCT
ap-1805	69	4	∇v	∇v	ADV
ap-1805	69	5	be	be	AUX
ap-1805	69	6	a	a	DET
ap-1805	69	7	globally	globally	ADV
ap-1805	69	8	defined	define	VERB
ap-1805	69	9	gradient	gradient	ADJ
ap-1805	69	10	field	field	NOUN
ap-1805	69	11	with	with	ADP
ap-1805	69	12	potential	potential	ADJ
ap-1805	69	13	v	v	ADP
ap-1805	69	14	∈	∈	PROPN
ap-1805	69	15	c2(r2,r	c2(r2,r	NOUN
ap-1805	69	16	)	)	PUNCT
ap-1805	69	17	.	.	PUNCT
ap-1805	70	1	then	then	ADV
ap-1805	70	2	b1	b1	NOUN
ap-1805	70	3	=	=	SYM
ap-1805	70	4	exp	exp	PROPN
ap-1805	70	5	(	(	PUNCT
ap-1805	70	6	v	v	NOUN
ap-1805	70	7	)	)	PUNCT
ap-1805	70	8	,	,	PUNCT
ap-1805	70	9	b2	b2	NOUN
ap-1805	70	10	=	=	SYM
ap-1805	70	11	exp	exp	NOUN
ap-1805	70	12	(	(	PUNCT
ap-1805	70	13	−v	−v	NOUN
ap-1805	70	14	)	)	PUNCT
ap-1805	70	15	and	and	CCONJ
ap-1805	70	16	b3	b3	PROPN
ap-1805	70	17	=	=	SYM
ap-1805	70	18	v	v	NOUN
ap-1805	70	19	are	be	AUX
ap-1805	70	20	local	local	ADJ
ap-1805	70	21	dulac	dulac	PROPN
ap-1805	70	22	functions	function	NOUN
ap-1805	70	23	for	for	ADP
ap-1805	70	24	x	x	PUNCT
ap-1805	70	25	in	in	ADP
ap-1805	70	26	ωi	ωi	PROPN
ap-1805	70	27	⊂	⊂	PROPN
ap-1805	70	28	r2	r2	PROPN
ap-1805	70	29	,	,	PUNCT
ap-1805	70	30	i	i	PRON
ap-1805	70	31	=	=	NOUN
ap-1805	70	32	1	1	NUM
ap-1805	70	33	,	,	PUNCT
ap-1805	70	34	2	2	NUM
ap-1805	70	35	,	,	PUNCT
ap-1805	70	36	3	3	NUM
ap-1805	70	37	,	,	PUNCT
ap-1805	70	38	with	with	ADP
ap-1805	70	39	∪3	∪3	ADP
ap-1805	70	40	i=1ωi	i=1ωi	NOUN
ap-1805	70	41	=	=	NOUN
ap-1805	70	42	r2	r2	NOUN
ap-1805	70	43	.	.	PUNCT
ap-1805	71	1	proof	proof	NOUN
ap-1805	71	2	.	.	PUNCT
ap-1805	72	1	define	define	VERB
ap-1805	72	2	b1	b1	NOUN
ap-1805	72	3	=	=	SYM
ap-1805	72	4	exp	exp	X
ap-1805	72	5	(	(	PUNCT
ap-1805	72	6	v	v	NOUN
ap-1805	72	7	)	)	PUNCT
ap-1805	72	8	,	,	PUNCT
ap-1805	72	9	b2	b2	NOUN
ap-1805	72	10	=	=	SYM
ap-1805	72	11	exp	exp	NOUN
ap-1805	72	12	(	(	PUNCT
ap-1805	72	13	−v	−v	NOUN
ap-1805	72	14	)	)	PUNCT
ap-1805	72	15	and	and	CCONJ
ap-1805	72	16	b3	b3	PROPN
ap-1805	72	17	=	=	SYM
ap-1805	72	18	v	v	NOUN
ap-1805	72	19	and	and	CCONJ
ap-1805	72	20	set	set	VERB
ap-1805	72	21	ωi	ωi	NOUN
ap-1805	72	22	:	:	PUNCT
ap-1805	72	23	=	=	SYM
ap-1805	72	24	{	{	PUNCT
ap-1805	72	25	z	z	NOUN
ap-1805	72	26	∈	∈	PROPN
ap-1805	72	27	r2	r2	PROPN
ap-1805	72	28	∣∣	∣∣	X
ap-1805	72	29	div(bix)(z	div(bix)(z	PROPN
ap-1805	72	30	)	)	PUNCT
ap-1805	72	31	>	>	X
ap-1805	72	32	0	0	NUM
ap-1805	72	33	}	}	PUNCT
ap-1805	72	34	.	.	PUNCT
ap-1805	73	1	verify	verify	VERB
ap-1805	73	2	that	that	SCONJ
ap-1805	73	3	∪3	∪3	NOUN
ap-1805	73	4	i=1ωi	i=1ωi	PRON
ap-1805	74	1	=	=	NOUN
ap-1805	74	2	r2	r2	PROPN
ap-1805	74	3	gives	give	VERB
ap-1805	74	4	indeed	indeed	ADV
ap-1805	74	5	the	the	DET
ap-1805	74	6	whole	whole	ADJ
ap-1805	74	7	plane	plane	NOUN
ap-1805	74	8	.	.	PUNCT
ap-1805	75	1	a	a	DET
ap-1805	75	2	standard	standard	ADJ
ap-1805	75	3	result	result	NOUN
ap-1805	75	4	from	from	ADP
ap-1805	75	5	calculus	calculus	NOUN
ap-1805	75	6	says	say	VERB
ap-1805	75	7	that	that	SCONJ
ap-1805	75	8	vector	vector	NOUN
ap-1805	75	9	fields	field	NOUN
ap-1805	75	10	can	can	AUX
ap-1805	75	11	be	be	AUX
ap-1805	75	12	straightened	straighten	VERB
ap-1805	75	13	locally	locally	ADV
ap-1805	75	14	unless	unless	SCONJ
ap-1805	75	15	there	there	PRON
ap-1805	75	16	is	be	VERB
ap-1805	75	17	an	an	DET
ap-1805	75	18	equilibrium	equilibrium	NOUN
ap-1805	75	19	.	.	PUNCT
ap-1805	76	1	this	this	DET
ap-1805	76	2	fact	fact	NOUN
ap-1805	76	3	can	can	AUX
ap-1805	76	4	be	be	AUX
ap-1805	76	5	used	use	VERB
ap-1805	76	6	to	to	PART
ap-1805	76	7	obtain	obtain	VERB
ap-1805	76	8	a	a	DET
ap-1805	76	9	local	local	ADJ
ap-1805	76	10	existence	existence	NOUN
ap-1805	76	11	result	result	NOUN
ap-1805	76	12	in	in	ADP
ap-1805	76	13	domains	domain	NOUN
ap-1805	76	14	not	not	PART
ap-1805	76	15	containing	contain	VERB
ap-1805	76	16	zeros	zero	NOUN
ap-1805	76	17	of	of	ADP
ap-1805	76	18	the	the	DET
ap-1805	76	19	vector	vector	NOUN
ap-1805	76	20	field	field	NOUN
ap-1805	76	21	.	.	PUNCT
ap-1805	77	1	such	such	ADJ
ap-1805	77	2	domains	domain	NOUN
ap-1805	77	3	are	be	AUX
ap-1805	77	4	called	call	VERB
ap-1805	77	5	canonical	canonical	ADJ
ap-1805	77	6	regions	region	NOUN
ap-1805	77	7	.	.	PUNCT
ap-1805	78	1	theorem	theorem	NOUN
ap-1805	78	2	3	3	NUM
ap-1805	78	3	(	(	PUNCT
ap-1805	78	4	parallel	parallel	ADJ
ap-1805	78	5	flow	flow	NOUN
ap-1805	78	6	[	[	X
ap-1805	78	7	13	13	NUM
ap-1805	78	8	]	]	NUM
ap-1805	78	9	)	)	PUNCT
ap-1805	78	10	.	.	PUNCT
ap-1805	79	1	let	let	VERB
ap-1805	79	2	x	x	PRON
ap-1805	79	3	:	:	PUNCT
ap-1805	79	4	d	d	NUM
ap-1805	79	5	⊆	⊆	NUM
ap-1805	79	6	r2	r2	NOUN
ap-1805	79	7	→	→	SYM
ap-1805	79	8	r2	r2	PROPN
ap-1805	79	9	be	be	VERB
ap-1805	79	10	any	any	DET
ap-1805	79	11	smooth	smooth	ADJ
ap-1805	79	12	vector	vector	NOUN
ap-1805	79	13	field	field	NOUN
ap-1805	79	14	and	and	CCONJ
ap-1805	79	15	ω	ω	NUM
ap-1805	79	16	a	a	DET
ap-1805	79	17	canonical	canonical	ADJ
ap-1805	79	18	region	region	NOUN
ap-1805	79	19	of	of	ADP
ap-1805	79	20	x	x	PRON
ap-1805	79	21	,	,	PUNCT
ap-1805	79	22	i.e.	i.e.	X
ap-1805	79	23	,	,	PUNCT
ap-1805	79	24	a	a	DET
ap-1805	79	25	region	region	NOUN
ap-1805	79	26	where	where	SCONJ
ap-1805	79	27	the	the	DET
ap-1805	79	28	flow	flow	NOUN
ap-1805	79	29	of	of	ADP
ap-1805	79	30	system	system	NOUN
ap-1805	79	31	(	(	PUNCT
ap-1805	79	32	1	1	X
ap-1805	79	33	)	)	PUNCT
ap-1805	79	34	is	be	AUX
ap-1805	79	35	equivalent	equivalent	ADJ
ap-1805	79	36	to	to	ADP
ap-1805	79	37	a	a	DET
ap-1805	79	38	parallel	parallel	ADJ
ap-1805	79	39	flow	flow	NOUN
ap-1805	79	40	in	in	ADP
ap-1805	79	41	the	the	DET
ap-1805	79	42	sense	sense	NOUN
ap-1805	79	43	of	of	ADP
ap-1805	79	44	neumann	neumann	PROPN
ap-1805	80	1	[	[	X
ap-1805	80	2	14	14	NUM
ap-1805	80	3	]	]	PUNCT
ap-1805	80	4	.	.	PUNCT
ap-1805	81	1	then	then	ADV
ap-1805	81	2	,	,	PUNCT
ap-1805	81	3	under	under	ADP
ap-1805	81	4	some	some	DET
ap-1805	81	5	integrability	integrability	NOUN
ap-1805	81	6	assumptions	assumption	NOUN
ap-1805	81	7	,	,	PUNCT
ap-1805	81	8	x	x	PRON
ap-1805	81	9	has	have	VERB
ap-1805	81	10	a	a	DET
ap-1805	81	11	dulac	dulac	PROPN
ap-1805	81	12	function	function	NOUN
ap-1805	81	13	in	in	ADP
ap-1805	81	14	ω	ω	PROPN
ap-1805	81	15	.	.	PUNCT
ap-1805	82	1	proof	proof	NOUN
ap-1805	82	2	.	.	PUNCT
ap-1805	83	1	by	by	ADP
ap-1805	83	2	assumption	assumption	NOUN
ap-1805	83	3	there	there	PRON
ap-1805	83	4	are	be	VERB
ap-1805	83	5	no	no	DET
ap-1805	83	6	equilibria	equilibrium	NOUN
ap-1805	83	7	in	in	ADP
ap-1805	83	8	the	the	DET
ap-1805	83	9	domain	domain	NOUN
ap-1805	83	10	,	,	PUNCT
ap-1805	83	11	hence	hence	ADV
ap-1805	83	12	the	the	DET
ap-1805	83	13	vector	vector	NOUN
ap-1805	83	14	field	field	NOUN
ap-1805	83	15	can	can	AUX
ap-1805	83	16	be	be	AUX
ap-1805	83	17	straightened	straighten	VERB
ap-1805	83	18	locally	locally	ADV
ap-1805	83	19	.	.	PUNCT
ap-1805	84	1	observe	observe	VERB
ap-1805	84	2	that	that	SCONJ
ap-1805	84	3	,	,	PUNCT
ap-1805	84	4	by	by	ADP
ap-1805	84	5	this	this	DET
ap-1805	84	6	process	process	NOUN
ap-1805	84	7	of	of	ADP
ap-1805	84	8	straightening	straightening	NOUN
ap-1805	84	9	,	,	PUNCT
ap-1805	84	10	the	the	DET
ap-1805	84	11	planar	planar	ADJ
ap-1805	84	12	system	system	NOUN
ap-1805	84	13	(	(	PUNCT
ap-1805	84	14	1	1	NUM
ap-1805	84	15	)	)	PUNCT
ap-1805	84	16	decouples	decouple	NOUN
ap-1805	84	17	and	and	CCONJ
ap-1805	84	18	the	the	DET
ap-1805	84	19	partial	partial	ADJ
ap-1805	84	20	differential	differential	NOUN
ap-1805	84	21	equation	equation	NOUN
ap-1805	84	22	(	(	PUNCT
ap-1805	84	23	3	3	NUM
ap-1805	84	24	)	)	PUNCT
ap-1805	84	25	from	from	ADP
ap-1805	84	26	the	the	DET
ap-1805	84	27	definition	definition	NOUN
ap-1805	84	28	of	of	ADP
ap-1805	84	29	a	a	DET
ap-1805	84	30	dulac	dulac	PROPN
ap-1805	84	31	function	function	NOUN
ap-1805	84	32	reduces	reduce	VERB
ap-1805	84	33	to	to	ADP
ap-1805	84	34	the	the	DET
ap-1805	84	35	linear	linear	ADJ
ap-1805	84	36	ordinary	ordinary	ADJ
ap-1805	84	37	differential	differential	ADJ
ap-1805	84	38	equation	equation	NOUN
ap-1805	84	39	b	b	PROPN
ap-1805	84	40	divx	divx	PROPN
ap-1805	84	41	+	+	CCONJ
ap-1805	84	42	αbr	αbr	NOUN
ap-1805	84	43	=	=	SYM
ap-1805	84	44	g	g	NOUN
ap-1805	84	45	,	,	PUNCT
ap-1805	84	46	2one	2one	PROPN
ap-1805	84	47	can	can	AUX
ap-1805	84	48	compare	compare	VERB
ap-1805	84	49	this	this	DET
ap-1805	84	50	problem	problem	NOUN
ap-1805	84	51	to	to	ADP
ap-1805	84	52	the	the	DET
ap-1805	84	53	decomposition	decomposition	NOUN
ap-1805	84	54	of	of	ADP
ap-1805	84	55	a	a	DET
ap-1805	84	56	natural	natural	ADJ
ap-1805	84	57	number	number	NOUN
ap-1805	84	58	into	into	ADP
ap-1805	84	59	its	its	PRON
ap-1805	84	60	prime	prime	ADJ
ap-1805	84	61	factors	factor	NOUN
ap-1805	84	62	:	:	PUNCT
ap-1805	84	63	if	if	SCONJ
ap-1805	84	64	some	some	DET
ap-1805	84	65	natural	natural	ADJ
ap-1805	84	66	number	number	NOUN
ap-1805	84	67	n	n	CCONJ
ap-1805	84	68	together	together	ADV
ap-1805	84	69	with	with	ADP
ap-1805	84	70	some	some	DET
ap-1805	84	71	product	product	NOUN
ap-1805	84	72	p	p	X
ap-1805	84	73	:	:	PUNCT
ap-1805	84	74	=	=	SYM
ap-1805	84	75	∏n	∏n	ADJ
ap-1805	84	76	i=1	i=1	X
ap-1805	85	1	p	p	X
ap-1805	85	2	di	di	NOUN
ap-1805	85	3	i	i	PRON
ap-1805	85	4	of	of	ADP
ap-1805	85	5	powers	power	NOUN
ap-1805	85	6	of	of	ADP
ap-1805	85	7	prime	prime	ADJ
ap-1805	85	8	numbers	number	NOUN
ap-1805	85	9	is	be	AUX
ap-1805	85	10	given	give	VERB
ap-1805	85	11	,	,	PUNCT
ap-1805	85	12	it	it	PRON
ap-1805	85	13	is	be	AUX
ap-1805	85	14	quite	quite	ADV
ap-1805	85	15	easy	easy	ADJ
ap-1805	85	16	to	to	PART
ap-1805	85	17	decide	decide	VERB
ap-1805	85	18	whether	whether	SCONJ
ap-1805	85	19	p	p	NOUN
ap-1805	85	20	is	be	AUX
ap-1805	85	21	the	the	DET
ap-1805	85	22	prime	prime	ADJ
ap-1805	85	23	factorization	factorization	NOUN
ap-1805	85	24	of	of	ADP
ap-1805	85	25	n	n	CCONJ
ap-1805	85	26	,	,	PUNCT
ap-1805	85	27	p	p	NOUN
ap-1805	85	28	=	=	NOUN
ap-1805	85	29	n	n	CCONJ
ap-1805	85	30	,	,	PUNCT
ap-1805	85	31	but	but	CCONJ
ap-1805	85	32	,	,	PUNCT
ap-1805	85	33	from	from	ADP
ap-1805	85	34	our	our	PRON
ap-1805	85	35	current	current	ADJ
ap-1805	85	36	state	state	NOUN
ap-1805	85	37	of	of	ADP
ap-1805	85	38	knowledge	knowledge	NOUN
ap-1805	85	39	,	,	PUNCT
ap-1805	85	40	it	it	PRON
ap-1805	85	41	is	be	AUX
ap-1805	85	42	very	very	ADV
ap-1805	85	43	difficult	difficult	ADJ
ap-1805	85	44	to	to	PART
ap-1805	85	45	decompose	decompose	VERB
ap-1805	85	46	a	a	DET
ap-1805	85	47	big	big	ADJ
ap-1805	85	48	natural	natural	ADJ
ap-1805	85	49	number	number	NOUN
ap-1805	85	50	into	into	ADP
ap-1805	85	51	its	its	PRON
ap-1805	85	52	prime	prime	ADJ
ap-1805	85	53	factors	factor	NOUN
ap-1805	85	54	.	.	PUNCT
ap-1805	86	1	284	284	NUM
ap-1805	86	2	vol	vol	NOUN
ap-1805	86	3	.	.	PUNCT
ap-1805	87	1	53	53	NUM
ap-1805	87	2	no	no	NOUN
ap-1805	87	3	.	.	PUNCT
ap-1805	88	1	3/2013	3/2013	PROPN
ap-1805	88	2	on	on	ADP
ap-1805	88	3	the	the	DET
ap-1805	88	4	solvability	solvability	NOUN
ap-1805	88	5	of	of	ADP
ap-1805	88	6	some	some	DET
ap-1805	88	7	partial	partial	ADJ
ap-1805	88	8	differential	differential	NOUN
ap-1805	88	9	inequality	inequality	NOUN
ap-1805	88	10	b20	b20	NOUN
ap-1805	88	11	=	=	SYM
ap-1805	88	12	a4	a4	NOUN
ap-1805	88	13	+	+	CCONJ
ap-1805	88	14	4a3d−	4a3d−	NUM
ap-1805	88	15	a2(2bc−	a2(2bc−	PROPN
ap-1805	88	16	c2	c2	PROPN
ap-1805	88	17	−	−	PROPN
ap-1805	88	18	3d2	3d2	NUM
ap-1805	88	19	)	)	PUNCT
ap-1805	89	1	+	+	CCONJ
ap-1805	89	2	3acd(c−	3acd(c−	NUM
ap-1805	89	3	b	b	NOUN
ap-1805	89	4	)	)	PUNCT
ap-1805	90	1	+	+	CCONJ
ap-1805	90	2	c2(b2	c2(b2	PRON
ap-1805	90	3	−	−	PROPN
ap-1805	90	4	bc+	bc+	PROPN
ap-1805	90	5	d2	d2	PROPN
ap-1805	90	6	)	)	PUNCT
ap-1805	90	7	(	(	PUNCT
ap-1805	90	8	a+	a+	PUNCT
ap-1805	90	9	d)(3a2	d)(3a2	PROPN
ap-1805	90	10	+	+	CCONJ
ap-1805	90	11	10ad−	10ad−	NUM
ap-1805	90	12	4bc+	4bc+	NUM
ap-1805	90	13	3d2	3d2	NUM
ap-1805	90	14	)	)	PUNCT
ap-1805	90	15	,	,	PUNCT
ap-1805	90	16	b02	b02	PROPN
ap-1805	90	17	=	=	SYM
ap-1805	90	18	a2(b2	a2(b2	PROPN
ap-1805	90	19	+	+	CCONJ
ap-1805	90	20	3d2	3d2	NUM
ap-1805	90	21	)	)	PUNCT
ap-1805	90	22	+	+	CCONJ
ap-1805	91	1	ad(3b2	ad(3b2	ADP
ap-1805	91	2	−	−	PROPN
ap-1805	91	3	3bc+	3bc+	PROPN
ap-1805	91	4	4d2)−	4d2)−	NUM
ap-1805	92	1	b3c+	b3c+	NOUN
ap-1805	92	2	b2(c2	b2(c2	PROPN
ap-1805	93	1	+	+	CCONJ
ap-1805	93	2	d2)−	d2)−	ADJ
ap-1805	93	3	2bcd2	2bcd2	PROPN
ap-1805	93	4	+	+	CCONJ
ap-1805	93	5	d4	d4	PROPN
ap-1805	93	6	(	(	PUNCT
ap-1805	93	7	a+	a+	PUNCT
ap-1805	93	8	d)(3a2	d)(3a2	PROPN
ap-1805	93	9	+	+	CCONJ
ap-1805	93	10	10ad−	10ad−	NUM
ap-1805	93	11	4bc+	4bc+	NUM
ap-1805	93	12	3d2	3d2	NUM
ap-1805	93	13	)	)	PUNCT
ap-1805	93	14	,	,	PUNCT
ap-1805	93	15	b11	b11	PROPN
ap-1805	93	16	=	=	SYM
ap-1805	93	17	2a3b+	2a3b+	NUM
ap-1805	93	18	a2d(7b+	a2d(7b+	NOUN
ap-1805	93	19	3c)−	3c)−	NUM
ap-1805	93	20	a(3b2c+	a(3b2c+	NUM
ap-1805	93	21	b(c−3d2)−	b(c−3d2)−	NOUN
ap-1805	93	22	7cd2)−	7cd2)−	NUM
ap-1805	93	23	cd(b2	cd(b2	NOUN
ap-1805	93	24	+	+	CCONJ
ap-1805	93	25	3bc−	3bc−	NUM
ap-1805	93	26	2d2	2d2	NUM
ap-1805	93	27	)	)	PUNCT
ap-1805	93	28	(	(	PUNCT
ap-1805	93	29	a+	a+	PUNCT
ap-1805	93	30	d)(3a2	d)(3a2	PROPN
ap-1805	93	31	+	+	CCONJ
ap-1805	93	32	10ad−	10ad−	NUM
ap-1805	93	33	4bc+	4bc+	NUM
ap-1805	93	34	3d2	3d2	NUM
ap-1805	93	35	)	)	PUNCT
ap-1805	93	36	,	,	PUNCT
ap-1805	93	37	b01	b01	NOUN
ap-1805	93	38	=	=	SYM
ap-1805	93	39	b10	b10	PROPN
ap-1805	93	40	=	=	SYM
ap-1805	93	41	b00	b00	NOUN
ap-1805	93	42	=	=	NOUN
ap-1805	93	43	0	0	X
ap-1805	93	44	.	.	PUNCT
ap-1805	93	45	figure	figure	NOUN
ap-1805	93	46	1	1	NUM
ap-1805	93	47	.	.	PUNCT
ap-1805	94	1	values	value	NOUN
ap-1805	94	2	of	of	ADP
ap-1805	94	3	bij	bij	NOUN
ap-1805	94	4	from	from	ADP
ap-1805	94	5	equation	equation	NOUN
ap-1805	94	6	(	(	PUNCT
ap-1805	94	7	6	6	NUM
ap-1805	94	8	)	)	PUNCT
ap-1805	94	9	.	.	PUNCT
ap-1805	95	1	which	which	PRON
ap-1805	95	2	implies	imply	VERB
ap-1805	95	3	br	br	X
ap-1805	95	4	=	=	SYM
ap-1805	95	5	g	g	PROPN
ap-1805	95	6	−b	−b	PROPN
ap-1805	95	7	divx	divx	PROPN
ap-1805	95	8	α	α	PROPN
ap-1805	95	9	.	.	PUNCT
ap-1805	96	1	this	this	PRON
ap-1805	96	2	is	be	AUX
ap-1805	96	3	an	an	DET
ap-1805	96	4	ordinary	ordinary	ADJ
ap-1805	96	5	differential	differential	ADJ
ap-1805	96	6	equation	equation	NOUN
ap-1805	96	7	with	with	ADP
ap-1805	96	8	the	the	DET
ap-1805	96	9	solution	solution	NOUN
ap-1805	96	10	b	b	NOUN
ap-1805	96	11	=	=	PUNCT
ap-1805	96	12	ea(r	ea(r	PROPN
ap-1805	96	13	)	)	PUNCT
ap-1805	96	14	{	{	PUNCT
ap-1805	96	15	∫	∫	PROPN
ap-1805	96	16	g	g	PROPN
ap-1805	96	17	·	·	PUNCT
ap-1805	96	18	ea(r	ea(r	NUM
ap-1805	96	19	)	)	PUNCT
ap-1805	96	20	dr	dr	PROPN
ap-1805	96	21	+	+	PROPN
ap-1805	96	22	κ	κ	X
ap-1805	96	23	}	}	PUNCT
ap-1805	96	24	,	,	PUNCT
ap-1805	96	25	where	where	SCONJ
ap-1805	96	26	a(r	a(r	NOUN
ap-1805	96	27	)	)	PUNCT
ap-1805	97	1	=	=	SYM
ap-1805	97	2	∫	∫	PROPN
ap-1805	97	3	divx	divx	PROPN
ap-1805	97	4	dr	dr	PROPN
ap-1805	97	5	and	and	CCONJ
ap-1805	97	6	κ	κ	PROPN
ap-1805	97	7	∈	∈	PROPN
ap-1805	97	8	r	r	NOUN
ap-1805	97	9	is	be	AUX
ap-1805	97	10	a	a	DET
ap-1805	97	11	constant	constant	ADJ
ap-1805	97	12	of	of	ADP
ap-1805	97	13	integration	integration	NOUN
ap-1805	97	14	.	.	PUNCT
ap-1805	98	1	for	for	ADP
ap-1805	98	2	linear	linear	PROPN
ap-1805	98	3	vector	vector	NOUN
ap-1805	98	4	fields	field	NOUN
ap-1805	98	5	there	there	PRON
ap-1805	98	6	is	be	VERB
ap-1805	98	7	also	also	ADV
ap-1805	98	8	a	a	DET
ap-1805	98	9	dulac	dulac	PROPN
ap-1805	98	10	function	function	NOUN
ap-1805	98	11	in	in	ADP
ap-1805	98	12	terms	term	NOUN
ap-1805	98	13	of	of	ADP
ap-1805	98	14	a	a	DET
ap-1805	98	15	quadratic	quadratic	ADJ
ap-1805	98	16	function	function	NOUN
ap-1805	98	17	if	if	SCONJ
ap-1805	98	18	some	some	DET
ap-1805	98	19	spectral	spectral	ADJ
ap-1805	98	20	condition	condition	NOUN
ap-1805	98	21	holds	hold	VERB
ap-1805	98	22	.	.	PUNCT
ap-1805	99	1	theorem	theorem	ADJ
ap-1805	99	2	4	4	NUM
ap-1805	99	3	(	(	PUNCT
ap-1805	99	4	linear	linear	PROPN
ap-1805	99	5	case	case	NOUN
ap-1805	99	6	[	[	X
ap-1805	99	7	10	10	NUM
ap-1805	99	8	]	]	NUM
ap-1805	99	9	)	)	PUNCT
ap-1805	99	10	.	.	PUNCT
ap-1805	100	1	let	let	VERB
ap-1805	100	2	x(z	x(z	PROPN
ap-1805	100	3	)	)	PUNCT
ap-1805	101	1	=	=	PUNCT
ap-1805	101	2	az	az	PROPN
ap-1805	101	3	be	be	AUX
ap-1805	101	4	a	a	DET
ap-1805	101	5	linear	linear	ADJ
ap-1805	101	6	vector	vector	NOUN
ap-1805	101	7	field	field	NOUN
ap-1805	101	8	with	with	ADP
ap-1805	101	9	a	a	DET
ap-1805	101	10	having	having	NOUN
ap-1805	101	11	at	at	ADP
ap-1805	101	12	most	most	ADV
ap-1805	101	13	one	one	NUM
ap-1805	101	14	eigenvalue	eigenvalue	NOUN
ap-1805	101	15	zero	zero	NUM
ap-1805	101	16	.	.	PUNCT
ap-1805	102	1	the	the	DET
ap-1805	102	2	linear	linear	ADJ
ap-1805	102	3	system	system	NOUN
ap-1805	102	4	(	(	PUNCT
ap-1805	102	5	1	1	X
ap-1805	102	6	)	)	PUNCT
ap-1805	102	7	does	do	AUX
ap-1805	102	8	not	not	PART
ap-1805	102	9	have	have	VERB
ap-1805	102	10	periodic	periodic	ADJ
ap-1805	102	11	orbits	orbit	NOUN
ap-1805	102	12	if	if	SCONJ
ap-1805	102	13	and	and	CCONJ
ap-1805	102	14	only	only	ADV
ap-1805	102	15	if	if	SCONJ
ap-1805	102	16	the	the	DET
ap-1805	102	17	spectrum	spectrum	NOUN
ap-1805	102	18	of	of	ADP
ap-1805	102	19	the	the	DET
ap-1805	102	20	matrix	matrix	NOUN
ap-1805	102	21	a	a	DET
ap-1805	102	22	consists	consist	NOUN
ap-1805	102	23	only	only	ADV
ap-1805	102	24	of	of	ADP
ap-1805	102	25	eigenvalues	eigenvalue	NOUN
ap-1805	102	26	with	with	ADP
ap-1805	102	27	nonzero	nonzero	PROPN
ap-1805	102	28	real	real	ADJ
ap-1805	102	29	part	part	NOUN
ap-1805	102	30	or	or	CCONJ
ap-1805	102	31	zero	zero	NUM
ap-1805	102	32	,	,	PUNCT
ap-1805	102	33	i.e.	i.e.	X
ap-1805	102	34	,	,	PUNCT
ap-1805	102	35	σ(a	σ(a	PROPN
ap-1805	102	36	)	)	PUNCT
ap-1805	102	37	∩	∩	NOUN
ap-1805	102	38	ir	ir	PROPN
ap-1805	102	39	⊆	⊆	NUM
ap-1805	102	40	{	{	PUNCT
ap-1805	102	41	0	0	NUM
ap-1805	102	42	}	}	PUNCT
ap-1805	102	43	.	.	PUNCT
ap-1805	103	1	proof	proof	NOUN
ap-1805	103	2	.	.	PUNCT
ap-1805	104	1	let	let	VERB
ap-1805	104	2	the	the	DET
ap-1805	104	3	vector	vector	NOUN
ap-1805	104	4	field	field	NOUN
ap-1805	104	5	be	be	AUX
ap-1805	104	6	x(z	x(z	PROPN
ap-1805	104	7	)	)	PUNCT
ap-1805	105	1	=	=	SYM
ap-1805	105	2	az	az	PROPN
ap-1805	105	3	with	with	ADP
ap-1805	105	4	(	(	PUNCT
ap-1805	105	5	a	a	DET
ap-1805	105	6	b	b	NOUN
ap-1805	105	7	c	c	NOUN
ap-1805	105	8	d	d	NOUN
ap-1805	105	9	)	)	PUNCT
ap-1805	105	10	∈	∈	PROPN
ap-1805	105	11	r2×2	r2×2	PROPN
ap-1805	105	12	.	.	PUNCT
ap-1805	106	1	instead	instead	ADV
ap-1805	106	2	of	of	ADP
ap-1805	106	3	the	the	DET
ap-1805	106	4	general	general	ADJ
ap-1805	106	5	partial	partial	ADJ
ap-1805	106	6	differential	differential	NOUN
ap-1805	106	7	inequality	inequality	NOUN
ap-1805	106	8	(	(	PUNCT
ap-1805	106	9	2	2	X
ap-1805	106	10	)	)	PUNCT
ap-1805	106	11	the	the	DET
ap-1805	106	12	author	author	NOUN
ap-1805	106	13	considered	consider	VERB
ap-1805	106	14	div(bx	div(bx	NOUN
ap-1805	106	15	)	)	PUNCT
ap-1805	106	16	=	=	VERB
ap-1805	106	17	‖x‖2	‖x‖2	ADJ
ap-1805	106	18	:	:	PUNCT
ap-1805	106	19	=	=	SYM
ap-1805	106	20	p	p	X
ap-1805	106	21	2	2	NUM
ap-1805	106	22	+	+	NOUN
ap-1805	106	23	q2	q2	NOUN
ap-1805	106	24	(	(	PUNCT
ap-1805	106	25	4	4	NUM
ap-1805	106	26	)	)	PUNCT
ap-1805	106	27	and	and	CCONJ
ap-1805	106	28	made	make	VERB
ap-1805	106	29	a	a	DET
ap-1805	106	30	quadratic	quadratic	ADJ
ap-1805	106	31	ansatz	ansatz	NOUN
ap-1805	106	32	for	for	ADP
ap-1805	106	33	the	the	DET
ap-1805	106	34	dulac	dulac	PROPN
ap-1805	106	35	function	function	PROPN
ap-1805	106	36	b	b	PROPN
ap-1805	106	37	=	=	SYM
ap-1805	106	38	1	1	NUM
ap-1805	106	39	2	2	NUM
ap-1805	106	40	〈	〈	PROPN
ap-1805	106	41	z	z	PROPN
ap-1805	106	42	,	,	PUNCT
ap-1805	106	43	gz	gz	ADP
ap-1805	106	44	〉	〉	NOUN
ap-1805	106	45	with	with	ADP
ap-1805	106	46	some	some	DET
ap-1805	106	47	matrix	matrix	NOUN
ap-1805	106	48	g	g	ADP
ap-1805	106	49	∈	∈	PROPN
ap-1805	106	50	r2×2	r2×2	PROPN
ap-1805	106	51	.	.	PUNCT
ap-1805	107	1	then	then	ADV
ap-1805	107	2	equation	equation	NOUN
ap-1805	107	3	(	(	PUNCT
ap-1805	107	4	4	4	NUM
ap-1805	107	5	)	)	PUNCT
ap-1805	107	6	reduces	reduce	VERB
ap-1805	107	7	to	to	ADP
ap-1805	107	8	atg+ga+	atg+ga+	VERB
ap-1805	107	9	tra	tra	NOUN
ap-1805	107	10	·	·	PUNCT
ap-1805	107	11	g	g	NOUN
ap-1805	107	12	=	=	SYM
ap-1805	107	13	ata	ata	PROPN
ap-1805	107	14	.	.	PUNCT
ap-1805	108	1	letting	let	VERB
ap-1805	108	2	s	s	VERB
ap-1805	108	3	:	:	PUNCT
ap-1805	108	4	=	=	SYM
ap-1805	108	5	a+	a+	X
ap-1805	108	6	tra	tra	PROPN
ap-1805	108	7	,	,	PUNCT
ap-1805	108	8	one	one	NOUN
ap-1805	108	9	obtains	obtain	VERB
ap-1805	108	10	stg+gs	stg+gs	PROPN
ap-1805	108	11	=	=	SYM
ap-1805	108	12	ata	ata	PROPN
ap-1805	108	13	,	,	PUNCT
ap-1805	108	14	(	(	PUNCT
ap-1805	108	15	5	5	X
ap-1805	108	16	)	)	PUNCT
ap-1805	108	17	equation	equation	NOUN
ap-1805	108	18	(	(	PUNCT
ap-1805	108	19	5	5	NUM
ap-1805	108	20	)	)	PUNCT
ap-1805	108	21	is	be	AUX
ap-1805	108	22	the	the	DET
ap-1805	108	23	well	well	ADV
ap-1805	108	24	-	-	PUNCT
ap-1805	108	25	known	know	VERB
ap-1805	108	26	lyapunov	lyapunov	ADJ
ap-1805	108	27	equation	equation	NOUN
ap-1805	108	28	,	,	PUNCT
ap-1805	108	29	a	a	DET
ap-1805	108	30	special	special	ADJ
ap-1805	108	31	case	case	NOUN
ap-1805	108	32	of	of	ADP
ap-1805	108	33	the	the	DET
ap-1805	108	34	more	more	ADV
ap-1805	108	35	general	general	ADJ
ap-1805	108	36	silvester	silvester	NOUN
ap-1805	108	37	equation	equation	NOUN
ap-1805	108	38	.	.	PUNCT
ap-1805	109	1	now	now	ADV
ap-1805	109	2	one	one	PRON
ap-1805	109	3	can	can	AUX
ap-1805	109	4	apply	apply	VERB
ap-1805	109	5	the	the	DET
ap-1805	109	6	well	well	ADV
ap-1805	109	7	-	-	PUNCT
ap-1805	109	8	established	establish	VERB
ap-1805	109	9	solvability	solvability	NOUN
ap-1805	109	10	theory	theory	NOUN
ap-1805	109	11	for	for	ADP
ap-1805	109	12	the	the	DET
ap-1805	109	13	silvester	silvester	NOUN
ap-1805	109	14	equation	equation	NOUN
ap-1805	109	15	[	[	X
ap-1805	109	16	15	15	NUM
ap-1805	109	17	]	]	PUNCT
ap-1805	109	18	and	and	CCONJ
ap-1805	109	19	verify	verify	VERB
ap-1805	109	20	that	that	SCONJ
ap-1805	109	21	the	the	DET
ap-1805	109	22	lyapunov	lyapunov	ADJ
ap-1805	109	23	equation	equation	NOUN
ap-1805	109	24	(	(	PUNCT
ap-1805	109	25	5	5	X
ap-1805	109	26	)	)	PUNCT
ap-1805	109	27	does	do	AUX
ap-1805	109	28	indeed	indeed	ADV
ap-1805	109	29	have	have	VERB
ap-1805	109	30	a	a	DET
ap-1805	109	31	unique	unique	ADJ
ap-1805	109	32	solution	solution	NOUN
ap-1805	109	33	under	under	ADP
ap-1805	109	34	the	the	DET
ap-1805	109	35	spectral	spectral	ADJ
ap-1805	109	36	assumptions	assumption	NOUN
ap-1805	109	37	that	that	PRON
ap-1805	109	38	were	be	AUX
ap-1805	109	39	made	make	VERB
ap-1805	109	40	.	.	PUNCT
ap-1805	110	1	on	on	ADP
ap-1805	110	2	the	the	DET
ap-1805	110	3	other	other	ADJ
ap-1805	110	4	hand	hand	NOUN
ap-1805	110	5	,	,	PUNCT
ap-1805	110	6	one	one	NOUN
ap-1805	110	7	obtains	obtain	VERB
ap-1805	110	8	by	by	ADP
ap-1805	110	9	direct	direct	ADJ
ap-1805	110	10	calculation	calculation	NOUN
ap-1805	110	11	b	b	X
ap-1805	110	12	=	=	SYM
ap-1805	110	13	b20x	b20x	SYM
ap-1805	110	14	2	2	NUM
ap-1805	110	15	+	+	CCONJ
ap-1805	110	16	b02y	b02y	ADP
ap-1805	110	17	2	2	NUM
ap-1805	110	18	+	+	NUM
ap-1805	110	19	b11xy	b11xy	NOUN
ap-1805	110	20	+	+	CCONJ
ap-1805	110	21	b10x+	b10x+	PROPN
ap-1805	110	22	b01y	b01y	NOUN
ap-1805	110	23	+	+	X
ap-1805	110	24	b00	b00	NOUN
ap-1805	110	25	;	;	PUNCT
ap-1805	110	26	(	(	PUNCT
ap-1805	110	27	6	6	X
ap-1805	110	28	)	)	PUNCT
ap-1805	110	29	values	value	NOUN
ap-1805	110	30	of	of	ADP
ap-1805	110	31	bij	bij	NOUN
ap-1805	110	32	are	be	AUX
ap-1805	110	33	shown	show	VERB
ap-1805	110	34	in	in	ADP
ap-1805	110	35	figure	figure	NOUN
ap-1805	110	36	1	1	NUM
ap-1805	110	37	.	.	PUNCT
ap-1805	111	1	the	the	DET
ap-1805	111	2	case	case	NOUN
ap-1805	111	3	tra	tra	NOUN
ap-1805	111	4	=	=	PRON
ap-1805	111	5	a+	a+	PUNCT
ap-1805	111	6	d	d	X
ap-1805	111	7	=	=	SYM
ap-1805	111	8	0	0	PROPN
ap-1805	111	9	has	have	VERB
ap-1805	111	10	to	to	PART
ap-1805	111	11	be	be	AUX
ap-1805	111	12	examined	examine	VERB
ap-1805	111	13	with	with	ADP
ap-1805	111	14	care	care	NOUN
ap-1805	111	15	.	.	PUNCT
ap-1805	112	1	the	the	DET
ap-1805	112	2	reader	reader	NOUN
ap-1805	112	3	may	may	AUX
ap-1805	112	4	verify	verify	VERB
ap-1805	112	5	that	that	SCONJ
ap-1805	112	6	having	having	AUX
ap-1805	112	7	spectrum	spectrum	VERB
ap-1805	112	8	σ(a	σ(a	PROPN
ap-1805	112	9	)	)	PUNCT
ap-1805	112	10	=	=	PRON
ap-1805	112	11	{	{	PUNCT
ap-1805	112	12	0	0	NUM
ap-1805	112	13	,	,	PUNCT
ap-1805	112	14	1	1	NUM
ap-1805	112	15	2	2	NUM
ap-1805	112	16	tra	tra	NOUN
ap-1805	112	17	}	}	PUNCT
ap-1805	112	18	is	be	AUX
ap-1805	112	19	equivalent	equivalent	ADJ
ap-1805	112	20	to	to	PART
ap-1805	112	21	deta	deta	VERB
ap-1805	112	22	=	=	SYM
ap-1805	112	23	(	(	PUNCT
ap-1805	112	24	tra	tra	NOUN
ap-1805	112	25	2	2	NUM
ap-1805	112	26	)	)	PUNCT
ap-1805	112	27	2	2	NUM
ap-1805	112	28	.	.	X
ap-1805	113	1	hence	hence	ADV
ap-1805	113	2	the	the	DET
ap-1805	113	3	quadratic	quadratic	ADJ
ap-1805	113	4	dulac	dulac	PROPN
ap-1805	113	5	function	function	NOUN
ap-1805	113	6	from	from	ADP
ap-1805	113	7	(	(	PUNCT
ap-1805	113	8	6	6	NUM
ap-1805	113	9	)	)	PUNCT
ap-1805	113	10	does	do	VERB
ap-1805	113	11	the	the	DET
ap-1805	113	12	job	job	NOUN
ap-1805	113	13	because	because	SCONJ
ap-1805	113	14	we	we	PRON
ap-1805	113	15	assumed	assume	VERB
ap-1805	113	16	that	that	SCONJ
ap-1805	113	17	at	at	ADP
ap-1805	113	18	most	most	ADV
ap-1805	113	19	one	one	NUM
ap-1805	113	20	eigenvalue	eigenvalue	NOUN
ap-1805	113	21	of	of	ADP
ap-1805	113	22	a	a	PRON
ap-1805	113	23	is	be	AUX
ap-1805	113	24	zero	zero	NUM
ap-1805	113	25	.	.	PUNCT
ap-1805	114	1	the	the	DET
ap-1805	114	2	hartman	hartman	PROPN
ap-1805	114	3	grobman	grobman	PROPN
ap-1805	114	4	theorem	theorem	VERB
ap-1805	114	5	combined	combine	VERB
ap-1805	114	6	with	with	ADP
ap-1805	114	7	the	the	DET
ap-1805	114	8	last	last	ADJ
ap-1805	114	9	two	two	NUM
ap-1805	114	10	results	result	NOUN
ap-1805	114	11	gives	give	VERB
ap-1805	114	12	some	some	DET
ap-1805	114	13	local	local	ADJ
ap-1805	114	14	existence	existence	NOUN
ap-1805	114	15	statement	statement	NOUN
ap-1805	114	16	holding	hold	VERB
ap-1805	114	17	in	in	ADP
ap-1805	114	18	some	some	DET
ap-1805	114	19	neighborhood	neighborhood	NOUN
ap-1805	114	20	of	of	ADP
ap-1805	114	21	hyperbolic	hyperbolic	ADJ
ap-1805	114	22	fixed	fix	VERB
ap-1805	114	23	points	point	NOUN
ap-1805	114	24	.	.	PUNCT
ap-1805	115	1	proposition	proposition	NOUN
ap-1805	115	2	1	1	NUM
ap-1805	115	3	.	.	PUNCT
ap-1805	116	1	let	let	VERB
ap-1805	116	2	x	x	PRON
ap-1805	116	3	be	be	AUX
ap-1805	116	4	a	a	DET
ap-1805	116	5	smooth	smooth	ADJ
ap-1805	116	6	vector	vector	NOUN
ap-1805	116	7	field	field	NOUN
ap-1805	116	8	and	and	CCONJ
ap-1805	116	9	z	z	NOUN
ap-1805	116	10	a	a	DET
ap-1805	116	11	hyperbolic	hyperbolic	ADJ
ap-1805	116	12	zero	zero	NUM
ap-1805	116	13	of	of	ADP
ap-1805	116	14	x	x	PRON
ap-1805	116	15	,	,	PUNCT
ap-1805	116	16	i.e.	i.e.	X
ap-1805	116	17	,	,	PUNCT
ap-1805	116	18	the	the	DET
ap-1805	116	19	real	real	ADJ
ap-1805	116	20	part	part	NOUN
ap-1805	116	21	re	re	NOUN
ap-1805	116	22	z	z	PROPN
ap-1805	116	23	6=	6=	NOUN
ap-1805	116	24	0	0	NUM
ap-1805	116	25	is	be	AUX
ap-1805	116	26	different	different	ADJ
ap-1805	116	27	from	from	ADP
ap-1805	116	28	zero	zero	NUM
ap-1805	116	29	.	.	PUNCT
ap-1805	117	1	then	then	ADV
ap-1805	117	2	there	there	PRON
ap-1805	117	3	is	be	VERB
ap-1805	117	4	a	a	DET
ap-1805	117	5	neighborhood	neighborhood	NOUN
ap-1805	117	6	u	u	NOUN
ap-1805	117	7	of	of	ADP
ap-1805	117	8	z	z	NOUN
ap-1805	117	9	such	such	ADJ
ap-1805	117	10	that	that	SCONJ
ap-1805	117	11	x	x	PRON
ap-1805	117	12	has	have	VERB
ap-1805	117	13	a	a	DET
ap-1805	117	14	dulac	dulac	PROPN
ap-1805	117	15	function	function	NOUN
ap-1805	117	16	on	on	ADP
ap-1805	117	17	u	u	PROPN
ap-1805	117	18	.	.	PUNCT
ap-1805	118	1	remark	remark	PROPN
ap-1805	118	2	2	2	NUM
ap-1805	118	3	.	.	PUNCT
ap-1805	119	1	proposition	proposition	NOUN
ap-1805	119	2	1	1	NUM
ap-1805	119	3	says	say	VERB
ap-1805	119	4	morally	morally	ADV
ap-1805	119	5	that	that	SCONJ
ap-1805	119	6	near	near	ADP
ap-1805	119	7	to	to	ADP
ap-1805	119	8	hyperbolic	hyperbolic	ADJ
ap-1805	119	9	equilibriums	equilibrium	NOUN
ap-1805	119	10	one	one	PRON
ap-1805	119	11	can	can	AUX
ap-1805	119	12	define	define	VERB
ap-1805	119	13	dulac	dulac	PROPN
ap-1805	119	14	functions	function	NOUN
ap-1805	119	15	,	,	PUNCT
ap-1805	119	16	which	which	PRON
ap-1805	119	17	is	be	AUX
ap-1805	119	18	what	what	PRON
ap-1805	119	19	we	we	PRON
ap-1805	119	20	expected	expect	VERB
ap-1805	119	21	since	since	SCONJ
ap-1805	119	22	in	in	ADP
ap-1805	119	23	dimension	dimension	NOUN
ap-1805	119	24	n	n	NOUN
ap-1805	119	25	=	=	SYM
ap-1805	119	26	2	2	NUM
ap-1805	119	27	a	a	DET
ap-1805	119	28	hyperbolic	hyperbolic	ADJ
ap-1805	119	29	equilibrium	equilibrium	NOUN
ap-1805	119	30	is	be	AUX
ap-1805	119	31	either	either	CCONJ
ap-1805	119	32	a	a	DET
ap-1805	119	33	node	node	NOUN
ap-1805	119	34	(	(	PUNCT
ap-1805	119	35	two	two	NUM
ap-1805	119	36	real	real	ADJ
ap-1805	119	37	eigenvalues	eigenvalue	NOUN
ap-1805	119	38	of	of	ADP
ap-1805	119	39	the	the	DET
ap-1805	119	40	same	same	ADJ
ap-1805	119	41	sign	sign	NOUN
ap-1805	119	42	)	)	PUNCT
ap-1805	119	43	,	,	PUNCT
ap-1805	119	44	a	a	DET
ap-1805	119	45	saddle	saddle	NOUN
ap-1805	119	46	(	(	PUNCT
ap-1805	119	47	two	two	NUM
ap-1805	119	48	real	real	ADJ
ap-1805	119	49	eigenvalues	eigenvalue	NOUN
ap-1805	119	50	of	of	ADP
ap-1805	119	51	different	different	ADJ
ap-1805	119	52	sign	sign	NOUN
ap-1805	119	53	)	)	PUNCT
ap-1805	119	54	or	or	CCONJ
ap-1805	119	55	a	a	DET
ap-1805	119	56	focus	focus	NOUN
ap-1805	119	57	,	,	PUNCT
ap-1805	119	58	sometimes	sometimes	ADV
ap-1805	119	59	also	also	ADV
ap-1805	119	60	called	call	VERB
ap-1805	119	61	spiral	spiral	ADJ
ap-1805	119	62	point	point	NOUN
ap-1805	119	63	,	,	PUNCT
ap-1805	119	64	(	(	PUNCT
ap-1805	119	65	two	two	NUM
ap-1805	119	66	complex	complex	ADJ
ap-1805	119	67	conjugate	conjugate	NOUN
ap-1805	119	68	eigenvalues	eigenvalue	NOUN
ap-1805	119	69	with	with	ADP
ap-1805	119	70	non	non	ADJ
ap-1805	119	71	-	-	ADJ
ap-1805	119	72	zero	zero	ADJ
ap-1805	119	73	real	real	ADJ
ap-1805	119	74	part	part	NOUN
ap-1805	119	75	)	)	PUNCT
ap-1805	119	76	.	.	PUNCT
ap-1805	120	1	can	can	AUX
ap-1805	120	2	there	there	PRON
ap-1805	120	3	be	be	AUX
ap-1805	120	4	a	a	DET
ap-1805	120	5	dulac	dulac	PROPN
ap-1805	120	6	function	function	NOUN
ap-1805	120	7	near	near	ADP
ap-1805	120	8	to	to	ADP
ap-1805	120	9	a	a	DET
ap-1805	120	10	non	non	ADJ
ap-1805	120	11	-	-	ADJ
ap-1805	120	12	hyperbolic	hyperbolic	ADJ
ap-1805	120	13	equilibrium	equilibrium	NOUN
ap-1805	120	14	?	?	PUNCT
ap-1805	121	1	we	we	PRON
ap-1805	121	2	believe	believe	VERB
ap-1805	121	3	so	so	ADV
ap-1805	121	4	,	,	PUNCT
ap-1805	121	5	unless	unless	SCONJ
ap-1805	121	6	the	the	DET
ap-1805	121	7	equilibrium	equilibrium	NOUN
ap-1805	121	8	is	be	AUX
ap-1805	121	9	a	a	DET
ap-1805	121	10	center	center	NOUN
ap-1805	121	11	.	.	PUNCT
ap-1805	122	1	recall	recall	VERB
ap-1805	122	2	that	that	SCONJ
ap-1805	122	3	a	a	DET
ap-1805	122	4	non	non	ADJ
ap-1805	122	5	-	-	ADJ
ap-1805	122	6	hyperbolic	hyperbolic	ADJ
ap-1805	122	7	equilibrium	equilibrium	NOUN
ap-1805	122	8	(	(	PUNCT
ap-1805	122	9	two	two	NUM
ap-1805	122	10	purely	purely	ADV
ap-1805	122	11	imaginary	imaginary	ADJ
ap-1805	122	12	eigenvalues	eigenvalue	NOUN
ap-1805	122	13	of	of	ADP
ap-1805	122	14	opposite	opposite	ADJ
ap-1805	122	15	sign	sign	NOUN
ap-1805	122	16	)	)	PUNCT
ap-1805	122	17	can	can	AUX
ap-1805	122	18	be	be	AUX
ap-1805	122	19	either	either	CCONJ
ap-1805	122	20	a	a	DET
ap-1805	122	21	center	center	NOUN
ap-1805	122	22	or	or	CCONJ
ap-1805	122	23	a	a	DET
ap-1805	122	24	focus	focus	NOUN
ap-1805	122	25	.	.	PUNCT
ap-1805	123	1	3	3	X
ap-1805	123	2	.	.	X
ap-1805	123	3	qualitative	qualitative	ADJ
ap-1805	123	4	theory	theory	NOUN
ap-1805	123	5	let	let	VERB
ap-1805	123	6	us	we	PRON
ap-1805	123	7	recall	recall	VERB
ap-1805	123	8	now	now	ADV
ap-1805	123	9	some	some	DET
ap-1805	123	10	basic	basic	ADJ
ap-1805	123	11	definitions	definition	NOUN
ap-1805	123	12	and	and	CCONJ
ap-1805	123	13	results	result	NOUN
ap-1805	123	14	that	that	PRON
ap-1805	123	15	are	be	AUX
ap-1805	123	16	frequently	frequently	ADV
ap-1805	123	17	used	use	VERB
ap-1805	123	18	in	in	ADP
ap-1805	123	19	the	the	DET
ap-1805	123	20	qualitative	qualitative	ADJ
ap-1805	123	21	theory	theory	NOUN
ap-1805	123	22	of	of	ADP
ap-1805	123	23	planar	planar	ADJ
ap-1805	123	24	differential	differential	ADJ
ap-1805	123	25	equations	equation	NOUN
ap-1805	123	26	.	.	PUNCT
ap-1805	124	1	for	for	ADP
ap-1805	124	2	a	a	DET
ap-1805	124	3	more	more	ADV
ap-1805	124	4	detailed	detailed	ADJ
ap-1805	124	5	introduction	introduction	NOUN
ap-1805	124	6	we	we	PRON
ap-1805	124	7	refer	refer	VERB
ap-1805	124	8	to	to	ADP
ap-1805	124	9	[	[	X
ap-1805	124	10	16	16	NUM
ap-1805	124	11	]	]	PUNCT
ap-1805	124	12	and	and	CCONJ
ap-1805	124	13	[	[	X
ap-1805	124	14	13	13	NUM
ap-1805	124	15	]	]	PUNCT
ap-1805	124	16	.	.	PUNCT
ap-1805	125	1	we	we	PRON
ap-1805	125	2	call	call	VERB
ap-1805	125	3	system	system	NOUN
ap-1805	125	4	(	(	PUNCT
ap-1805	125	5	1	1	X
ap-1805	125	6	)	)	PUNCT
ap-1805	125	7	integrable	integrable	ADJ
ap-1805	125	8	in	in	ADP
ap-1805	125	9	domain	domain	NOUN
ap-1805	125	10	d	d	NOUN
ap-1805	125	11	if	if	SCONJ
ap-1805	125	12	it	it	PRON
ap-1805	125	13	has	have	VERB
ap-1805	125	14	a	a	DET
ap-1805	125	15	first	first	ADJ
ap-1805	125	16	integral	integral	ADJ
ap-1805	125	17	defined	define	VERB
ap-1805	125	18	on	on	ADP
ap-1805	125	19	this	this	DET
ap-1805	125	20	domain	domain	NOUN
ap-1805	125	21	,	,	PUNCT
ap-1805	125	22	i.e.	i.e.	X
ap-1805	125	23	,	,	PUNCT
ap-1805	125	24	a	a	DET
ap-1805	125	25	non	non	ADJ
ap-1805	125	26	-	-	ADJ
ap-1805	125	27	constant	constant	ADJ
ap-1805	125	28	smooth	smooth	ADJ
ap-1805	125	29	scalar	scalar	ADV
ap-1805	125	30	-	-	PUNCT
ap-1805	125	31	valued	value	VERB
ap-1805	125	32	function	function	NOUN
ap-1805	125	33	h	h	NOUN
ap-1805	125	34	of	of	ADP
ap-1805	125	35	class	class	NOUN
ap-1805	125	36	ck	ck	INTJ
ap-1805	125	37	which	which	PRON
ap-1805	125	38	is	be	AUX
ap-1805	125	39	constant	constant	ADJ
ap-1805	125	40	285	285	NUM
ap-1805	125	41	m.	m.	NOUN
ap-1805	125	42	himmel	himmel	PROPN
ap-1805	125	43	acta	acta	PROPN
ap-1805	125	44	polytechnica	polytechnica	PROPN
ap-1805	125	45	on	on	ADP
ap-1805	125	46	each	each	DET
ap-1805	125	47	solution	solution	NOUN
ap-1805	125	48	(	(	PUNCT
ap-1805	125	49	x(t	x(t	PROPN
ap-1805	125	50	)	)	PUNCT
ap-1805	125	51	,	,	PUNCT
ap-1805	125	52	y(t	y(t	NOUN
ap-1805	125	53	)	)	PUNCT
ap-1805	125	54	)	)	PUNCT
ap-1805	125	55	of	of	ADP
ap-1805	125	56	(	(	PUNCT
ap-1805	125	57	1	1	X
ap-1805	125	58	)	)	PUNCT
ap-1805	125	59	as	as	ADV
ap-1805	125	60	long	long	ADV
ap-1805	125	61	as	as	SCONJ
ap-1805	125	62	it	it	PRON
ap-1805	125	63	is	be	AUX
ap-1805	125	64	defined	define	VERB
ap-1805	125	65	.	.	PUNCT
ap-1805	126	1	this	this	PRON
ap-1805	126	2	means	mean	VERB
ap-1805	126	3	:	:	PUNCT
ap-1805	126	4	if	if	SCONJ
ap-1805	126	5	(	(	PUNCT
ap-1805	126	6	x(t	x(t	PROPN
ap-1805	126	7	)	)	PUNCT
ap-1805	126	8	,	,	PUNCT
ap-1805	126	9	y(t	y(t	NOUN
ap-1805	126	10	)	)	PUNCT
ap-1805	126	11	)	)	PUNCT
ap-1805	126	12	is	be	AUX
ap-1805	126	13	any	any	DET
ap-1805	126	14	fixed	fix	VERB
ap-1805	126	15	solution	solution	NOUN
ap-1805	126	16	of	of	ADP
ap-1805	126	17	(	(	PUNCT
ap-1805	126	18	1	1	NUM
ap-1805	126	19	)	)	PUNCT
ap-1805	126	20	defined	define	VERB
ap-1805	126	21	for	for	ADP
ap-1805	126	22	t	t	PROPN
ap-1805	126	23	∈	∈	PROPN
ap-1805	127	1	[	[	X
ap-1805	127	2	0	0	NUM
ap-1805	127	3	,	,	PUNCT
ap-1805	127	4	tmax	tmax	PRON
ap-1805	127	5	]	]	X
ap-1805	127	6	=	=	NOUN
ap-1805	127	7	:	:	PUNCT
ap-1805	127	8	imax	imax	NOUN
ap-1805	127	9	,	,	PUNCT
ap-1805	127	10	its	its	PRON
ap-1805	127	11	maximal	maximal	ADJ
ap-1805	127	12	interval	interval	NOUN
ap-1805	127	13	of	of	ADP
ap-1805	127	14	existence	existence	NOUN
ap-1805	127	15	,	,	PUNCT
ap-1805	127	16	and	and	CCONJ
ap-1805	127	17	h	h	NOUN
ap-1805	127	18	∈	∈	PROPN
ap-1805	127	19	c1(d	c1(d	NOUN
ap-1805	127	20	,	,	PUNCT
ap-1805	127	21	r	r	NOUN
ap-1805	127	22	)	)	PUNCT
ap-1805	127	23	a	a	DET
ap-1805	127	24	first	first	ADJ
ap-1805	127	25	integral	integral	ADJ
ap-1805	127	26	of	of	ADP
ap-1805	127	27	system	system	NOUN
ap-1805	127	28	(	(	PUNCT
ap-1805	127	29	1	1	NUM
ap-1805	127	30	)	)	PUNCT
ap-1805	127	31	,	,	PUNCT
ap-1805	127	32	then	then	ADV
ap-1805	127	33	there	there	PRON
ap-1805	127	34	is	be	VERB
ap-1805	127	35	a	a	DET
ap-1805	127	36	real	real	ADJ
ap-1805	127	37	number	number	NOUN
ap-1805	127	38	h	h	NOUN
ap-1805	127	39	such	such	ADJ
ap-1805	127	40	that	that	DET
ap-1805	127	41	h	h	NOUN
ap-1805	127	42	(	(	PUNCT
ap-1805	127	43	x(t	x(t	PROPN
ap-1805	127	44	)	)	PUNCT
ap-1805	127	45	,	,	PUNCT
ap-1805	127	46	y(t	y(t	NOUN
ap-1805	127	47	)	)	PUNCT
ap-1805	127	48	)	)	PUNCT
ap-1805	128	1	=	=	SYM
ap-1805	128	2	h	h	NOUN
ap-1805	128	3	for	for	ADP
ap-1805	128	4	all	all	DET
ap-1805	128	5	t	t	NOUN
ap-1805	128	6	∈	∈	PROPN
ap-1805	128	7	imax	imax	NOUN
ap-1805	128	8	(	(	PUNCT
ap-1805	128	9	7	7	NUM
ap-1805	128	10	)	)	PUNCT
ap-1805	128	11	is	be	AUX
ap-1805	128	12	satisfied	satisfied	ADJ
ap-1805	128	13	.	.	PUNCT
ap-1805	129	1	taking	take	VERB
ap-1805	129	2	the	the	DET
ap-1805	129	3	derivative	derivative	NOUN
ap-1805	129	4	with	with	ADP
ap-1805	129	5	respect	respect	NOUN
ap-1805	129	6	to	to	ADP
ap-1805	129	7	time	time	NOUN
ap-1805	129	8	t	t	PROPN
ap-1805	129	9	of	of	ADP
ap-1805	129	10	equation	equation	NOUN
ap-1805	129	11	(	(	PUNCT
ap-1805	129	12	7	7	NUM
ap-1805	129	13	)	)	PUNCT
ap-1805	129	14	,	,	PUNCT
ap-1805	129	15	we	we	PRON
ap-1805	129	16	see	see	VERB
ap-1805	129	17	that	that	SCONJ
ap-1805	129	18	any	any	DET
ap-1805	129	19	first	first	ADJ
ap-1805	129	20	integral	integral	ADJ
ap-1805	129	21	h	h	NOUN
ap-1805	129	22	∈	∈	PROPN
ap-1805	129	23	c1(d	c1(d	NOUN
ap-1805	129	24	,	,	PUNCT
ap-1805	129	25	r	r	NOUN
ap-1805	129	26	)	)	PUNCT
ap-1805	129	27	of	of	ADP
ap-1805	129	28	(	(	PUNCT
ap-1805	129	29	1	1	X
ap-1805	129	30	)	)	PUNCT
ap-1805	129	31	satisfies	satisfy	VERB
ap-1805	129	32	the	the	DET
ap-1805	129	33	linear	linear	ADJ
ap-1805	129	34	partial	partial	ADJ
ap-1805	129	35	differential	differential	NOUN
ap-1805	129	36	equation	equation	NOUN
ap-1805	129	37	〈	〈	PROPN
ap-1805	129	38	∇h	∇h	PROPN
ap-1805	129	39	,	,	PUNCT
ap-1805	129	40	x	x	NOUN
ap-1805	129	41	〉	〉	NOUN
ap-1805	129	42	=	=	SYM
ap-1805	130	1	p	p	X
ap-1805	130	2	·	·	PUNCT
ap-1805	130	3	hx	hx	PROPN
ap-1805	130	4	+	+	NOUN
ap-1805	130	5	q	q	ADJ
ap-1805	130	6	·	·	SYM
ap-1805	130	7	hy	hy	NOUN
ap-1805	130	8	=	=	SYM
ap-1805	130	9	0	0	PROPN
ap-1805	130	10	.	.	PUNCT
ap-1805	131	1	(	(	PUNCT
ap-1805	131	2	8)	8)	NUM
ap-1805	131	3	conversely	conversely	ADV
ap-1805	131	4	,	,	PUNCT
ap-1805	131	5	every	every	DET
ap-1805	131	6	non	non	ADJ
ap-1805	131	7	-	-	ADJ
ap-1805	131	8	constant	constant	ADJ
ap-1805	131	9	solution	solution	NOUN
ap-1805	131	10	of	of	ADP
ap-1805	131	11	equation	equation	NOUN
ap-1805	131	12	(	(	PUNCT
ap-1805	131	13	8)	8)	NUM
ap-1805	131	14	is	be	AUX
ap-1805	131	15	a	a	DET
ap-1805	131	16	first	first	ADJ
ap-1805	131	17	integral	integral	ADJ
ap-1805	131	18	h	h	NOUN
ap-1805	131	19	:	:	PUNCT
ap-1805	132	1	d	d	X
ap-1805	132	2	→	→	SYM
ap-1805	132	3	r	r	NOUN
ap-1805	132	4	of	of	ADP
ap-1805	132	5	(	(	PUNCT
ap-1805	132	6	1	1	NUM
ap-1805	132	7	)	)	PUNCT
ap-1805	132	8	.	.	PUNCT
ap-1805	133	1	if	if	SCONJ
ap-1805	133	2	h0	h0	PROPN
ap-1805	133	3	is	be	AUX
ap-1805	133	4	a	a	DET
ap-1805	133	5	non	non	ADJ
ap-1805	133	6	-	-	ADJ
ap-1805	133	7	constant	constant	ADJ
ap-1805	133	8	solution	solution	NOUN
ap-1805	133	9	of	of	ADP
ap-1805	133	10	(	(	PUNCT
ap-1805	133	11	8)	8)	NUM
ap-1805	133	12	,	,	PUNCT
ap-1805	133	13	then	then	ADV
ap-1805	133	14	every	every	DET
ap-1805	133	15	other	other	ADJ
ap-1805	133	16	solution	solution	NOUN
ap-1805	133	17	is	be	AUX
ap-1805	133	18	of	of	ADP
ap-1805	133	19	the	the	DET
ap-1805	133	20	form	form	NOUN
ap-1805	133	21	f	f	PROPN
ap-1805	133	22	(	(	PUNCT
ap-1805	133	23	h0	h0	PROPN
ap-1805	133	24	)	)	PUNCT
ap-1805	133	25	,	,	PUNCT
ap-1805	133	26	where	where	SCONJ
ap-1805	133	27	f	f	PROPN
ap-1805	133	28	is	be	AUX
ap-1805	133	29	an	an	DET
ap-1805	133	30	arbitrary	arbitrary	ADJ
ap-1805	133	31	function	function	NOUN
ap-1805	133	32	having	have	VERB
ap-1805	133	33	continuous	continuous	ADJ
ap-1805	133	34	partial	partial	ADJ
ap-1805	133	35	derivatives	derivative	NOUN
ap-1805	133	36	(	(	PUNCT
ap-1805	133	37	use	use	VERB
ap-1805	133	38	the	the	DET
ap-1805	133	39	chain	chain	NOUN
ap-1805	133	40	rule	rule	NOUN
ap-1805	133	41	to	to	PART
ap-1805	133	42	verify	verify	VERB
ap-1805	133	43	this	this	PRON
ap-1805	133	44	)	)	PUNCT
ap-1805	133	45	.	.	PUNCT
ap-1805	134	1	first	first	ADJ
ap-1805	134	2	integrals	integral	NOUN
ap-1805	134	3	are	be	AUX
ap-1805	134	4	strongly	strongly	ADV
ap-1805	134	5	related	relate	VERB
ap-1805	134	6	to	to	ADP
ap-1805	134	7	the	the	DET
ap-1805	134	8	notion	notion	NOUN
ap-1805	134	9	of	of	ADP
ap-1805	134	10	integrating	integrate	VERB
ap-1805	134	11	factors	factor	NOUN
ap-1805	134	12	.	.	PUNCT
ap-1805	135	1	definition	definition	NOUN
ap-1805	135	2	2	2	NUM
ap-1805	135	3	(	(	PUNCT
ap-1805	135	4	integrating	integrating	NOUN
ap-1805	135	5	factor	factor	NOUN
ap-1805	135	6	)	)	PUNCT
ap-1805	135	7	.	.	PUNCT
ap-1805	136	1	an	an	DET
ap-1805	136	2	integrating	integrate	VERB
ap-1805	136	3	factor	factor	NOUN
ap-1805	136	4	µ	µ	NOUN
ap-1805	136	5	of	of	ADP
ap-1805	136	6	the	the	DET
ap-1805	136	7	planar	planar	ADJ
ap-1805	136	8	dynamical	dynamical	ADJ
ap-1805	136	9	system	system	NOUN
ap-1805	136	10	(	(	PUNCT
ap-1805	136	11	1	1	X
ap-1805	136	12	)	)	PUNCT
ap-1805	136	13	is	be	AUX
ap-1805	136	14	a	a	DET
ap-1805	136	15	smooth	smooth	ADJ
ap-1805	136	16	solution	solution	NOUN
ap-1805	136	17	µ	µ	PRON
ap-1805	136	18	∈	∈	PROPN
ap-1805	136	19	c1(ω	c1(ω	SYM
ap-1805	136	20	,	,	PUNCT
ap-1805	136	21	r	r	NOUN
ap-1805	136	22	)	)	PUNCT
ap-1805	136	23	of	of	ADP
ap-1805	136	24	the	the	DET
ap-1805	136	25	linear	linear	ADJ
ap-1805	136	26	partial	partial	ADJ
ap-1805	136	27	differential	differential	NOUN
ap-1805	136	28	equation	equation	NOUN
ap-1805	136	29	div(µ	div(µ	PROPN
ap-1805	136	30	·	·	PUNCT
ap-1805	136	31	x	x	X
ap-1805	136	32	)	)	PUNCT
ap-1805	136	33	=	=	SYM
ap-1805	136	34	µ	µ	X
ap-1805	136	35	·	·	PUNCT
ap-1805	136	36	divx	divx	PROPN
ap-1805	136	37	+	+	CCONJ
ap-1805	136	38	〈	〈	PROPN
ap-1805	136	39	∇µ,x	∇µ,x	NOUN
ap-1805	136	40	〉	〉	NOUN
ap-1805	136	41	=	=	NOUN
ap-1805	136	42	0	0	NUM
ap-1805	136	43	in	in	ADP
ap-1805	136	44	ω	ω	PROPN
ap-1805	136	45	.	.	PUNCT
ap-1805	137	1	(	(	PUNCT
ap-1805	137	2	9	9	X
ap-1805	137	3	)	)	PUNCT
ap-1805	137	4	note	note	NOUN
ap-1805	137	5	that	that	SCONJ
ap-1805	137	6	the	the	DET
ap-1805	137	7	first	first	ADJ
ap-1805	137	8	equality	equality	NOUN
ap-1805	137	9	in	in	ADP
ap-1805	137	10	(	(	PUNCT
ap-1805	137	11	9	9	NUM
ap-1805	137	12	)	)	PUNCT
ap-1805	137	13	is	be	AUX
ap-1805	137	14	due	due	ADJ
ap-1805	137	15	to	to	ADP
ap-1805	137	16	the	the	DET
ap-1805	137	17	leibniz	leibniz	PROPN
ap-1805	137	18	rule	rule	NOUN
ap-1805	137	19	and	and	CCONJ
ap-1805	137	20	divx	divx	PROPN
ap-1805	137	21	,	,	PUNCT
ap-1805	137	22	the	the	DET
ap-1805	137	23	divergence	divergence	NOUN
ap-1805	137	24	of	of	ADP
ap-1805	137	25	the	the	DET
ap-1805	137	26	vector	vector	NOUN
ap-1805	137	27	field	field	NOUN
ap-1805	137	28	x	x	NOUN
ap-1805	137	29	,	,	PUNCT
ap-1805	137	30	denotes	denote	VERB
ap-1805	137	31	the	the	DET
ap-1805	137	32	trace	trace	NOUN
ap-1805	137	33	of	of	ADP
ap-1805	137	34	the	the	DET
ap-1805	137	35	jacobian	jacobian	NOUN
ap-1805	137	36	of	of	ADP
ap-1805	137	37	x	x	PROPN
ap-1805	137	38	,	,	PUNCT
ap-1805	137	39	divx	divx	X
ap-1805	138	1	=	=	PUNCT
ap-1805	138	2	∂p	∂p	PROPN
ap-1805	138	3	∂x	∂x	PROPN
ap-1805	139	1	+	+	CCONJ
ap-1805	140	1	∂q	∂q	PROPN
ap-1805	140	2	∂y	∂y	PROPN
ap-1805	140	3	.	.	PUNCT
ap-1805	141	1	if	if	SCONJ
ap-1805	141	2	instead	instead	ADV
ap-1805	141	3	a	a	DET
ap-1805	141	4	first	first	ADJ
ap-1805	141	5	integral	integral	ADJ
ap-1805	141	6	h	h	NOUN
ap-1805	141	7	:	:	PUNCT
ap-1805	142	1	d	d	X
ap-1805	142	2	→	→	SYM
ap-1805	142	3	r	r	NOUN
ap-1805	142	4	of	of	ADP
ap-1805	142	5	(	(	PUNCT
ap-1805	142	6	1	1	NUM
ap-1805	142	7	)	)	PUNCT
ap-1805	142	8	is	be	AUX
ap-1805	142	9	known	know	VERB
ap-1805	142	10	,	,	PUNCT
ap-1805	142	11	using	use	VERB
ap-1805	142	12	equation	equation	NOUN
ap-1805	142	13	(	(	PUNCT
ap-1805	142	14	8)	8)	NUM
ap-1805	142	15	,	,	PUNCT
ap-1805	142	16	one	one	PRON
ap-1805	142	17	can	can	AUX
ap-1805	142	18	equivalently	equivalently	ADV
ap-1805	142	19	define	define	VERB
ap-1805	142	20	an	an	DET
ap-1805	142	21	integrating	integrating	NOUN
ap-1805	142	22	factor	factor	NOUN
ap-1805	142	23	as	as	SCONJ
ap-1805	142	24	the	the	DET
ap-1805	142	25	common	common	ADJ
ap-1805	142	26	value	value	NOUN
ap-1805	142	27	of	of	ADP
ap-1805	142	28	the	the	DET
ap-1805	142	29	ratios	ratio	NOUN
ap-1805	142	30	µ(x	µ(x	VERB
ap-1805	142	31	,	,	PUNCT
ap-1805	142	32	y	y	NOUN
ap-1805	142	33	)	)	PUNCT
ap-1805	142	34	=	=	SYM
ap-1805	142	35	hy	hy	NOUN
ap-1805	142	36	p	p	NOUN
ap-1805	142	37	!	!	PUNCT
ap-1805	142	38	=	=	PUNCT
ap-1805	143	1	−hx	−hx	PRON
ap-1805	143	2	q	q	NOUN
ap-1805	143	3	,	,	PUNCT
ap-1805	143	4	(	(	PUNCT
ap-1805	143	5	10	10	NUM
ap-1805	143	6	)	)	PUNCT
ap-1805	143	7	i.e.	i.e.	X
ap-1805	143	8	,	,	PUNCT
ap-1805	143	9	an	an	DET
ap-1805	143	10	integrating	integrate	VERB
ap-1805	143	11	factor	factor	NOUN
ap-1805	143	12	must	must	AUX
ap-1805	143	13	satisfy	satisfy	VERB
ap-1805	143	14	both	both	DET
ap-1805	143	15	hy	hy	NOUN
ap-1805	144	1	=	=	PUNCT
ap-1805	144	2	µp	µp	PROPN
ap-1805	144	3	and	and	CCONJ
ap-1805	144	4	hx	hx	PROPN
ap-1805	144	5	=	=	SYM
ap-1805	144	6	−µq	−µq	PROPN
ap-1805	144	7	.	.	PUNCT
ap-1805	145	1	the	the	DET
ap-1805	145	2	latter	latter	ADJ
ap-1805	145	3	two	two	NUM
ap-1805	145	4	relations	relation	NOUN
ap-1805	145	5	can	can	AUX
ap-1805	145	6	be	be	AUX
ap-1805	145	7	read	read	VERB
ap-1805	145	8	as	as	ADP
ap-1805	145	9	dh(x	dh(x	X
ap-1805	145	10	,	,	PUNCT
ap-1805	145	11	y	y	NOUN
ap-1805	145	12	)	)	PUNCT
ap-1805	145	13	=	=	SYM
ap-1805	146	1	µ(x	µ(x	VERB
ap-1805	146	2	,	,	PUNCT
ap-1805	146	3	y	y	NOUN
ap-1805	146	4	)	)	PUNCT
ap-1805	146	5	(	(	PUNCT
ap-1805	146	6	p	p	X
ap-1805	146	7	(	(	PUNCT
ap-1805	146	8	x	x	NOUN
ap-1805	146	9	,	,	PUNCT
ap-1805	146	10	y	y	NOUN
ap-1805	146	11	)	)	PUNCT
ap-1805	146	12	dy	dy	NOUN
ap-1805	146	13	−q(x	−q(x	PROPN
ap-1805	146	14	,	,	PUNCT
ap-1805	146	15	y	y	PROPN
ap-1805	146	16	)	)	PUNCT
ap-1805	146	17	dx	dx	PROPN
ap-1805	146	18	)	)	PUNCT
ap-1805	146	19	,	,	PUNCT
ap-1805	146	20	(	(	PUNCT
ap-1805	146	21	11	11	NUM
ap-1805	146	22	)	)	PUNCT
ap-1805	146	23	where	where	SCONJ
ap-1805	146	24	dh(x	dh(x	PRON
ap-1805	146	25	,	,	PUNCT
ap-1805	146	26	y	y	NOUN
ap-1805	146	27	)	)	PUNCT
ap-1805	146	28	indicates	indicate	VERB
ap-1805	146	29	the	the	DET
ap-1805	146	30	differential	differential	NOUN
ap-1805	146	31	of	of	ADP
ap-1805	146	32	h.	h.	PROPN
ap-1805	146	33	thus	thus	ADV
ap-1805	146	34	,	,	PUNCT
ap-1805	146	35	multiplying	multiply	VERB
ap-1805	146	36	the	the	DET
ap-1805	146	37	right	right	ADJ
ap-1805	146	38	hand	hand	NOUN
ap-1805	146	39	side	side	NOUN
ap-1805	146	40	of	of	ADP
ap-1805	146	41	(	(	PUNCT
ap-1805	146	42	1	1	NUM
ap-1805	146	43	)	)	PUNCT
ap-1805	146	44	by	by	ADP
ap-1805	146	45	an	an	DET
ap-1805	146	46	integrating	integrate	VERB
ap-1805	146	47	factor	factor	NOUN
ap-1805	146	48	makes	make	VERB
ap-1805	146	49	the	the	DET
ap-1805	146	50	equation	equation	NOUN
ap-1805	146	51	an	an	DET
ap-1805	146	52	exact	exact	ADJ
ap-1805	146	53	differential	differential	NOUN
ap-1805	146	54	and	and	CCONJ
ap-1805	146	55	an	an	DET
ap-1805	146	56	exact	exact	ADJ
ap-1805	146	57	equation	equation	NOUN
ap-1805	146	58	)	)	PUNCT
ap-1805	146	59	,	,	PUNCT
ap-1805	146	60	which	which	PRON
ap-1805	146	61	means	mean	VERB
ap-1805	146	62	that	that	SCONJ
ap-1805	146	63	,	,	PUNCT
ap-1805	146	64	whenever	whenever	SCONJ
ap-1805	146	65	an	an	DET
ap-1805	146	66	integrating	integrate	VERB
ap-1805	146	67	factor	factor	NOUN
ap-1805	146	68	is	be	AUX
ap-1805	146	69	available	available	ADJ
ap-1805	146	70	,	,	PUNCT
ap-1805	146	71	the	the	DET
ap-1805	146	72	modified	modify	VERB
ap-1805	146	73	vector	vector	NOUN
ap-1805	146	74	field	field	NOUN
ap-1805	146	75	µx	µx	VERB
ap-1805	146	76	has	have	AUX
ap-1805	146	77	vanishing	vanish	VERB
ap-1805	146	78	divergence	divergence	NOUN
ap-1805	146	79	and	and	CCONJ
ap-1805	146	80	the	the	DET
ap-1805	146	81	problem	problem	NOUN
ap-1805	146	82	of	of	ADP
ap-1805	146	83	solving	solve	VERB
ap-1805	146	84	equation	equation	NOUN
ap-1805	146	85	(	(	PUNCT
ap-1805	146	86	1	1	X
ap-1805	146	87	)	)	PUNCT
ap-1805	146	88	is	be	AUX
ap-1805	146	89	reduced	reduce	VERB
ap-1805	146	90	to	to	ADP
ap-1805	146	91	one	one	NUM
ap-1805	146	92	-	-	PUNCT
ap-1805	146	93	dimensional	dimensional	ADJ
ap-1805	146	94	integration	integration	NOUN
ap-1805	146	95	h(x	h(x	PROPN
ap-1805	146	96	,	,	PUNCT
ap-1805	146	97	y	y	PROPN
ap-1805	146	98	)	)	PUNCT
ap-1805	147	1	=	=	SYM
ap-1805	147	2	∫	∫	PROPN
ap-1805	147	3	(	(	PUNCT
ap-1805	147	4	x	x	PROPN
ap-1805	147	5	,	,	PUNCT
ap-1805	147	6	y	y	PROPN
ap-1805	147	7	)	)	PUNCT
ap-1805	147	8	(	(	PUNCT
ap-1805	147	9	x0,y0	x0,y0	NOUN
ap-1805	147	10	)	)	PUNCT
ap-1805	147	11	µ(x	µ(x	PROPN
ap-1805	147	12	,	,	PUNCT
ap-1805	147	13	y	y	NOUN
ap-1805	147	14	)	)	PUNCT
ap-1805	147	15	(	(	PUNCT
ap-1805	147	16	p	p	X
ap-1805	147	17	(	(	PUNCT
ap-1805	147	18	x	x	NOUN
ap-1805	147	19	,	,	PUNCT
ap-1805	147	20	y	y	NOUN
ap-1805	147	21	)	)	PUNCT
ap-1805	147	22	dy	dy	NOUN
ap-1805	147	23	−q(x	−q(x	PROPN
ap-1805	147	24	,	,	PUNCT
ap-1805	147	25	y	y	PROPN
ap-1805	147	26	)	)	PUNCT
ap-1805	147	27	dx	dx	PROPN
ap-1805	147	28	)	)	PUNCT
ap-1805	147	29	.	.	PUNCT
ap-1805	148	1	note	note	VERB
ap-1805	148	2	that	that	SCONJ
ap-1805	148	3	the	the	DET
ap-1805	148	4	latter	latter	ADJ
ap-1805	148	5	line	line	NOUN
ap-1805	148	6	integral	integral	ADJ
ap-1805	148	7	might	might	AUX
ap-1805	148	8	not	not	PART
ap-1805	148	9	be	be	AUX
ap-1805	148	10	welldefined	welldefine	VERB
ap-1805	148	11	if	if	SCONJ
ap-1805	148	12	domain	domain	NOUN
ap-1805	148	13	d	d	NOUN
ap-1805	148	14	is	be	AUX
ap-1805	148	15	not	not	PART
ap-1805	148	16	simply	simply	ADV
ap-1805	148	17	connected	connect	VERB
ap-1805	148	18	.	.	PUNCT
ap-1805	149	1	for	for	ADP
ap-1805	149	2	this	this	DET
ap-1805	149	3	reason	reason	NOUN
ap-1805	149	4	,	,	PUNCT
ap-1805	149	5	integrating	integrate	VERB
ap-1805	149	6	factors	factor	NOUN
ap-1805	149	7	are	be	AUX
ap-1805	149	8	usually	usually	ADV
ap-1805	149	9	considered	consider	VERB
ap-1805	149	10	only	only	ADV
ap-1805	149	11	in	in	ADP
ap-1805	149	12	connected	connected	ADJ
ap-1805	149	13	components	component	NOUN
ap-1805	149	14	of	of	ADP
ap-1805	149	15	d.	d.	PROPN
ap-1805	149	16	secondly	secondly	ADV
ap-1805	149	17	,	,	PUNCT
ap-1805	149	18	we	we	PRON
ap-1805	149	19	observe	observe	VERB
ap-1805	149	20	that	that	SCONJ
ap-1805	149	21	the	the	DET
ap-1805	149	22	vector	vector	NOUN
ap-1805	149	23	fieldsx	fieldsx	NOUN
ap-1805	149	24	and	and	CCONJ
ap-1805	149	25	µx	µx	AUX
ap-1805	149	26	have	have	VERB
ap-1805	149	27	the	the	DET
ap-1805	149	28	same	same	ADJ
ap-1805	149	29	phase	phase	NOUN
ap-1805	149	30	portrait	portrait	NOUN
ap-1805	149	31	(	(	PUNCT
ap-1805	149	32	with	with	ADP
ap-1805	149	33	maybe	maybe	ADV
ap-1805	149	34	reversed	reverse	VERB
ap-1805	149	35	orientation	orientation	NOUN
ap-1805	149	36	if	if	SCONJ
ap-1805	149	37	µ	µ	NOUN
ap-1805	149	38	is	be	AUX
ap-1805	149	39	negative	negative	ADJ
ap-1805	149	40	)	)	PUNCT
ap-1805	149	41	as	as	ADV
ap-1805	149	42	long	long	ADV
ap-1805	149	43	as	as	SCONJ
ap-1805	149	44	µ	µ	NOUN
ap-1805	149	45	does	do	AUX
ap-1805	149	46	not	not	PART
ap-1805	149	47	vanish	vanish	VERB
ap-1805	149	48	.	.	PUNCT
ap-1805	150	1	for	for	ADP
ap-1805	150	2	this	this	DET
ap-1805	150	3	reason	reason	NOUN
ap-1805	150	4	,	,	PUNCT
ap-1805	150	5	solving	solve	VERB
ap-1805	150	6	system	system	NOUN
ap-1805	150	7	(	(	PUNCT
ap-1805	150	8	1	1	NUM
ap-1805	150	9	)	)	PUNCT
ap-1805	150	10	,	,	PUNCT
ap-1805	150	11	i.e.	i.e.	X
ap-1805	150	12	,	,	PUNCT
ap-1805	150	13	constructing	construct	VERB
ap-1805	150	14	a	a	DET
ap-1805	150	15	first	first	ADJ
ap-1805	150	16	integral	integral	ADJ
ap-1805	150	17	and	and	CCONJ
ap-1805	150	18	finding	find	VERB
ap-1805	150	19	an	an	DET
ap-1805	150	20	integrating	integrating	NOUN
ap-1805	150	21	factor	factor	NOUN
ap-1805	150	22	for	for	ADP
ap-1805	150	23	it	it	PRON
ap-1805	150	24	,	,	PUNCT
ap-1805	150	25	are	be	AUX
ap-1805	150	26	considered	consider	VERB
ap-1805	150	27	to	to	PART
ap-1805	150	28	be	be	AUX
ap-1805	150	29	equivalent	equivalent	ADJ
ap-1805	150	30	problems	problem	NOUN
ap-1805	150	31	.	.	PUNCT
ap-1805	151	1	in	in	ADP
ap-1805	151	2	applications	application	NOUN
ap-1805	151	3	the	the	DET
ap-1805	151	4	notion	notion	NOUN
ap-1805	151	5	of	of	ADP
ap-1805	151	6	inverse	inverse	NOUN
ap-1805	151	7	integrating	integrating	NOUN
ap-1805	151	8	factor	factor	NOUN
ap-1805	151	9	is	be	AUX
ap-1805	151	10	very	very	ADV
ap-1805	151	11	common	common	ADJ
ap-1805	151	12	.	.	PUNCT
ap-1805	152	1	definition	definition	NOUN
ap-1805	152	2	3	3	NUM
ap-1805	152	3	(	(	PUNCT
ap-1805	152	4	inverse	inverse	ADJ
ap-1805	152	5	integrating	integrating	NOUN
ap-1805	152	6	factor	factor	NOUN
ap-1805	152	7	)	)	PUNCT
ap-1805	152	8	.	.	PUNCT
ap-1805	153	1	the	the	DET
ap-1805	153	2	function	function	NOUN
ap-1805	153	3	v	v	ADP
ap-1805	153	4	∈	∈	PROPN
ap-1805	153	5	c1(ω	c1(ω	NOUN
ap-1805	153	6	,	,	PUNCT
ap-1805	153	7	r	r	NOUN
ap-1805	153	8	)	)	PUNCT
ap-1805	153	9	is	be	AUX
ap-1805	153	10	called	call	VERB
ap-1805	153	11	an	an	DET
ap-1805	153	12	inverse	inverse	NOUN
ap-1805	153	13	integrating	integrating	NOUN
ap-1805	153	14	factor	factor	NOUN
ap-1805	153	15	for	for	ADP
ap-1805	153	16	the	the	DET
ap-1805	153	17	planar	planar	ADJ
ap-1805	153	18	system	system	NOUN
ap-1805	153	19	(	(	PUNCT
ap-1805	153	20	1	1	NUM
ap-1805	153	21	)	)	PUNCT
ap-1805	153	22	in	in	ADP
ap-1805	153	23	the	the	DET
ap-1805	153	24	domain	domain	NOUN
ap-1805	153	25	ω	ω	NUM
ap-1805	153	26	⊆	⊆	NUM
ap-1805	153	27	r2	r2	NOUN
ap-1805	153	28	if	if	SCONJ
ap-1805	153	29	µ	µ	NOUN
ap-1805	153	30	=	=	SYM
ap-1805	153	31	1	1	NUM
ap-1805	153	32	v	v	NOUN
ap-1805	153	33	is	be	AUX
ap-1805	153	34	an	an	DET
ap-1805	153	35	integrating	integrate	VERB
ap-1805	153	36	factor	factor	NOUN
ap-1805	153	37	of	of	ADP
ap-1805	153	38	system	system	NOUN
ap-1805	153	39	(	(	PUNCT
ap-1805	153	40	1	1	NUM
ap-1805	153	41	)	)	PUNCT
ap-1805	153	42	in	in	ADP
ap-1805	153	43	ω	ω	PROPN
ap-1805	153	44	\	\	PROPN
ap-1805	153	45	{	{	PUNCT
ap-1805	153	46	v	v	NOUN
ap-1805	153	47	=	=	SYM
ap-1805	153	48	0	0	NUM
ap-1805	153	49	}	}	PUNCT
ap-1805	153	50	.	.	PUNCT
ap-1805	154	1	as	as	ADP
ap-1805	154	2	usual	usual	ADJ
ap-1805	154	3	{	{	PUNCT
ap-1805	154	4	v	v	NOUN
ap-1805	154	5	=	=	SYM
ap-1805	154	6	0	0	NUM
ap-1805	154	7	}	}	PUNCT
ap-1805	154	8	is	be	AUX
ap-1805	154	9	short	short	ADJ
ap-1805	154	10	notation	notation	NOUN
ap-1805	154	11	for	for	ADP
ap-1805	154	12	the	the	DET
ap-1805	154	13	preimage	preimage	NOUN
ap-1805	154	14	of	of	ADP
ap-1805	154	15	zero	zero	NUM
ap-1805	154	16	under	under	ADP
ap-1805	154	17	v	v	NUM
ap-1805	154	18	,	,	PUNCT
ap-1805	154	19	v	v	NUM
ap-1805	154	20	−1(0	−1(0	NOUN
ap-1805	154	21	)	)	PUNCT
ap-1805	155	1	=	=	PRON
ap-1805	155	2	{	{	PUNCT
ap-1805	155	3	z	z	PROPN
ap-1805	155	4	∈	∈	PROPN
ap-1805	156	1	ω	ω	NOUN
ap-1805	156	2	:	:	PUNCT
ap-1805	156	3	v	v	X
ap-1805	156	4	(	(	PUNCT
ap-1805	156	5	z	z	NOUN
ap-1805	156	6	)	)	PUNCT
ap-1805	156	7	=	=	SYM
ap-1805	156	8	0	0	NUM
ap-1805	156	9	}	}	PUNCT
ap-1805	156	10	.	.	PUNCT
ap-1805	157	1	the	the	DET
ap-1805	157	2	method	method	NOUN
ap-1805	157	3	of	of	ADP
ap-1805	157	4	integrating	integrate	VERB
ap-1805	157	5	factors	factor	NOUN
ap-1805	157	6	is	be	AUX
ap-1805	157	7	,	,	PUNCT
ap-1805	157	8	both	both	CCONJ
ap-1805	157	9	historically	historically	ADV
ap-1805	157	10	and	and	CCONJ
ap-1805	157	11	theoretically	theoretically	ADV
ap-1805	157	12	,	,	PUNCT
ap-1805	157	13	a	a	DET
ap-1805	157	14	very	very	ADV
ap-1805	157	15	important	important	ADJ
ap-1805	157	16	technique	technique	NOUN
ap-1805	157	17	in	in	ADP
ap-1805	157	18	the	the	DET
ap-1805	157	19	qualitative	qualitative	ADJ
ap-1805	157	20	analysis	analysis	NOUN
ap-1805	157	21	of	of	ADP
ap-1805	157	22	first	first	ADJ
ap-1805	157	23	order	order	NOUN
ap-1805	157	24	ordinary	ordinary	ADJ
ap-1805	157	25	differential	differential	ADJ
ap-1805	157	26	equations	equation	NOUN
ap-1805	157	27	.	.	PUNCT
ap-1805	158	1	the	the	DET
ap-1805	158	2	use	use	NOUN
ap-1805	158	3	of	of	ADP
ap-1805	158	4	integrating	integrate	VERB
ap-1805	158	5	factors	factor	NOUN
ap-1805	158	6	goes	go	VERB
ap-1805	158	7	back	back	ADV
ap-1805	158	8	to	to	ADP
ap-1805	158	9	leonard	leonard	PROPN
ap-1805	158	10	euler	euler	PROPN
ap-1805	158	11	(	(	PUNCT
ap-1805	158	12	1707–1783	1707–1783	NUM
ap-1805	158	13	)	)	PUNCT
ap-1805	158	14	.	.	PUNCT
ap-1805	159	1	integration	integration	NOUN
ap-1805	159	2	factors	factor	NOUN
ap-1805	159	3	and	and	CCONJ
ap-1805	159	4	first	first	ADJ
ap-1805	159	5	integrals	integral	NOUN
ap-1805	159	6	refer	refer	VERB
ap-1805	159	7	to	to	ADP
ap-1805	159	8	the	the	DET
ap-1805	159	9	problem	problem	NOUN
ap-1805	159	10	of	of	ADP
ap-1805	159	11	integrating	integrate	VERB
ap-1805	159	12	the	the	DET
ap-1805	159	13	planar	planar	ADJ
ap-1805	159	14	system	system	NOUN
ap-1805	159	15	(	(	PUNCT
ap-1805	159	16	1	1	NUM
ap-1805	159	17	)	)	PUNCT
ap-1805	159	18	,	,	PUNCT
ap-1805	159	19	which	which	PRON
ap-1805	159	20	means	mean	VERB
ap-1805	159	21	geometrically	geometrically	ADV
ap-1805	159	22	nothing	nothing	PRON
ap-1805	159	23	but	but	SCONJ
ap-1805	159	24	finding	find	VERB
ap-1805	159	25	smooth	smooth	ADJ
ap-1805	159	26	curves	curve	NOUN
ap-1805	159	27	that	that	PRON
ap-1805	159	28	are	be	AUX
ap-1805	159	29	tangential	tangential	ADJ
ap-1805	159	30	to	to	ADP
ap-1805	159	31	the	the	DET
ap-1805	159	32	vector	vector	NOUN
ap-1805	159	33	field	field	NOUN
ap-1805	159	34	at	at	ADP
ap-1805	159	35	each	each	DET
ap-1805	159	36	point	point	NOUN
ap-1805	159	37	.	.	PUNCT
ap-1805	160	1	then	then	ADV
ap-1805	160	2	,	,	PUNCT
ap-1805	160	3	another	another	DET
ap-1805	160	4	interesting	interesting	ADJ
ap-1805	160	5	problem	problem	NOUN
ap-1805	160	6	is	be	AUX
ap-1805	160	7	deriving	derive	VERB
ap-1805	160	8	the	the	DET
ap-1805	160	9	qualitative	qualitative	ADJ
ap-1805	160	10	behavior	behavior	NOUN
ap-1805	160	11	of	of	ADP
ap-1805	160	12	these	these	DET
ap-1805	160	13	solution	solution	NOUN
ap-1805	160	14	curves	curve	NOUN
ap-1805	160	15	as	as	ADP
ap-1805	160	16	,	,	PUNCT
ap-1805	160	17	for	for	ADP
ap-1805	160	18	instance	instance	NOUN
ap-1805	160	19	,	,	PUNCT
ap-1805	160	20	their	their	PRON
ap-1805	160	21	topology	topology	NOUN
ap-1805	160	22	(	(	PUNCT
ap-1805	160	23	whether	whether	SCONJ
ap-1805	160	24	they	they	PRON
ap-1805	160	25	are	be	AUX
ap-1805	160	26	closed	closed	ADJ
ap-1805	160	27	or	or	CCONJ
ap-1805	160	28	not	not	PART
ap-1805	160	29	)	)	PUNCT
ap-1805	160	30	,	,	PUNCT
ap-1805	160	31	their	their	PRON
ap-1805	160	32	asymptotics	asymptotic	NOUN
ap-1805	160	33	(	(	PUNCT
ap-1805	160	34	whether	whether	SCONJ
ap-1805	160	35	they	they	PRON
ap-1805	160	36	blow	blow	VERB
ap-1805	160	37	up	up	ADP
ap-1805	160	38	in	in	ADP
ap-1805	160	39	finite	finite	ADJ
ap-1805	160	40	time	time	NOUN
ap-1805	160	41	or	or	CCONJ
ap-1805	160	42	remain	remain	VERB
ap-1805	160	43	in	in	ADP
ap-1805	160	44	some	some	DET
ap-1805	160	45	compact	compact	ADJ
ap-1805	160	46	set	set	NOUN
ap-1805	160	47	and	and	CCONJ
ap-1805	160	48	approach	approach	VERB
ap-1805	160	49	a	a	DET
ap-1805	160	50	limit	limit	NOUN
ap-1805	160	51	cycle	cycle	NOUN
ap-1805	160	52	or	or	CCONJ
ap-1805	160	53	an	an	DET
ap-1805	160	54	equilibrium	equilibrium	NOUN
ap-1805	160	55	point	point	NOUN
ap-1805	160	56	)	)	PUNCT
ap-1805	160	57	and	and	CCONJ
ap-1805	160	58	stability	stability	NOUN
ap-1805	160	59	properties	property	NOUN
ap-1805	160	60	.	.	PUNCT
ap-1805	161	1	4	4	X
ap-1805	161	2	.	.	X
ap-1805	161	3	a	a	DET
ap-1805	161	4	unifying	unifying	ADJ
ap-1805	161	5	point	point	NOUN
ap-1805	161	6	of	of	ADP
ap-1805	161	7	view	view	NOUN
ap-1805	161	8	definition	definition	NOUN
ap-1805	161	9	4	4	NUM
ap-1805	161	10	(	(	PUNCT
ap-1805	161	11	invariant	invariant	ADJ
ap-1805	161	12	curve	curve	NOUN
ap-1805	161	13	)	)	PUNCT
ap-1805	161	14	.	.	PUNCT
ap-1805	162	1	let	let	VERB
ap-1805	162	2	ω	ω	NOUN
ap-1805	162	3	⊆	⊆	NUM
ap-1805	162	4	r2	r2	NOUN
ap-1805	162	5	be	be	AUX
ap-1805	162	6	an	an	DET
ap-1805	162	7	open	open	ADJ
ap-1805	162	8	set	set	NOUN
ap-1805	162	9	of	of	ADP
ap-1805	162	10	the	the	DET
ap-1805	162	11	plane	plane	NOUN
ap-1805	162	12	.	.	PUNCT
ap-1805	163	1	an	an	DET
ap-1805	163	2	invariant	invariant	ADJ
ap-1805	163	3	curve	curve	NOUN
ap-1805	163	4	is	be	AUX
ap-1805	163	5	the	the	DET
ap-1805	163	6	vanishing	vanish	VERB
ap-1805	163	7	set	set	NOUN
ap-1805	163	8	or	or	CCONJ
ap-1805	163	9	the	the	DET
ap-1805	163	10	preimage	preimage	NOUN
ap-1805	163	11	of	of	ADP
ap-1805	163	12	zero	zero	NUM
ap-1805	163	13	of	of	ADP
ap-1805	163	14	some	some	DET
ap-1805	163	15	smooth	smooth	ADJ
ap-1805	163	16	function	function	NOUN
ap-1805	163	17	.	.	PUNCT
ap-1805	164	1	more	more	ADV
ap-1805	164	2	precisely	precisely	ADV
ap-1805	164	3	,	,	PUNCT
ap-1805	164	4	to	to	ADP
ap-1805	164	5	a	a	DET
ap-1805	164	6	given	give	VERB
ap-1805	164	7	function	function	NOUN
ap-1805	164	8	f	f	PROPN
ap-1805	164	9	∈	∈	PROPN
ap-1805	164	10	c1(ω	c1(ω	PROPN
ap-1805	164	11	,	,	PUNCT
ap-1805	164	12	c	c	NOUN
ap-1805	164	13	)	)	PUNCT
ap-1805	164	14	we	we	PRON
ap-1805	164	15	associate	associate	VERB
ap-1805	164	16	the	the	DET
ap-1805	164	17	preimage	preimage	NOUN
ap-1805	164	18	of	of	ADP
ap-1805	164	19	zero	zero	NUM
ap-1805	164	20	f−1(0	f−1(0	PROPN
ap-1805	164	21	)	)	PUNCT
ap-1805	164	22	≡	≡	PROPN
ap-1805	164	23	{	{	PUNCT
ap-1805	164	24	f	f	PROPN
ap-1805	164	25	=	=	PUNCT
ap-1805	164	26	0	0	NUM
ap-1805	164	27	}	}	PUNCT
ap-1805	164	28	:	:	PUNCT
ap-1805	164	29	=	=	SYM
ap-1805	164	30	{	{	PUNCT
ap-1805	164	31	z	z	NOUN
ap-1805	164	32	∈	∈	PROPN
ap-1805	164	33	ω	ω	NUM
ap-1805	164	34	∣∣f(z	∣∣f(z	NUM
ap-1805	164	35	)	)	PUNCT
ap-1805	164	36	=	=	SYM
ap-1805	164	37	0	0	X
ap-1805	164	38	}	}	PUNCT
ap-1805	164	39	(	(	PUNCT
ap-1805	164	40	12	12	NUM
ap-1805	164	41	)	)	PUNCT
ap-1805	164	42	and	and	CCONJ
ap-1805	164	43	call	call	VERB
ap-1805	164	44	it	it	PRON
ap-1805	164	45	an	an	DET
ap-1805	164	46	invariant	invariant	ADJ
ap-1805	164	47	curve	curve	NOUN
ap-1805	164	48	of	of	ADP
ap-1805	164	49	the	the	DET
ap-1805	164	50	vector	vector	NOUN
ap-1805	164	51	field	field	NOUN
ap-1805	164	52	x	x	PUNCT
ap-1805	164	53	=	=	PUNCT
ap-1805	164	54	(	(	PUNCT
ap-1805	164	55	p	p	X
ap-1805	164	56	,	,	PUNCT
ap-1805	164	57	q	q	NOUN
ap-1805	164	58	)	)	PUNCT
ap-1805	164	59	∈	∈	PROPN
ap-1805	164	60	c1(d	c1(d	NOUN
ap-1805	164	61	,	,	PUNCT
ap-1805	164	62	r2	r2	NOUN
ap-1805	164	63	)	)	PUNCT
ap-1805	164	64	if	if	SCONJ
ap-1805	164	65	there	there	PRON
ap-1805	164	66	is	be	VERB
ap-1805	164	67	a	a	DET
ap-1805	164	68	smooth	smooth	ADJ
ap-1805	164	69	function	function	NOUN
ap-1805	164	70	k	k	PROPN
ap-1805	164	71	∈	∈	PROPN
ap-1805	164	72	c1(ω	c1(ω	PROPN
ap-1805	164	73	,	,	PUNCT
ap-1805	164	74	c	c	NOUN
ap-1805	164	75	)	)	PUNCT
ap-1805	164	76	,	,	PUNCT
ap-1805	164	77	called	call	VERB
ap-1805	164	78	cofactor	cofactor	NOUN
ap-1805	164	79	of	of	ADP
ap-1805	164	80	f	f	PROPN
ap-1805	164	81	,	,	PUNCT
ap-1805	164	82	satisfying	satisfy	VERB
ap-1805	164	83	the	the	DET
ap-1805	164	84	relation	relation	NOUN
ap-1805	164	85	〈	〈	PROPN
ap-1805	164	86	∇f	∇f	PROPN
ap-1805	164	87	,	,	PUNCT
ap-1805	164	88	x	x	NOUN
ap-1805	164	89	〉	〉	NOUN
ap-1805	164	90	=	=	SYM
ap-1805	164	91	k	k	PROPN
ap-1805	164	92	·	·	PUNCT
ap-1805	164	93	f	f	PROPN
ap-1805	164	94	for	for	ADP
ap-1805	164	95	all	all	DET
ap-1805	164	96	z	z	NOUN
ap-1805	164	97	∈	∈	PROPN
ap-1805	164	98	ω	ω	X
ap-1805	164	99	(	(	PUNCT
ap-1805	164	100	13	13	NUM
ap-1805	164	101	)	)	PUNCT
ap-1805	164	102	or	or	CCONJ
ap-1805	164	103	more	more	ADV
ap-1805	164	104	explicitly	explicitly	ADV
ap-1805	164	105	fx(z	fx(z	NUM
ap-1805	164	106	)	)	PUNCT
ap-1805	164	107	·	·	PUNCT
ap-1805	165	1	p	p	X
ap-1805	165	2	(	(	PUNCT
ap-1805	165	3	z	z	NOUN
ap-1805	165	4	)	)	PUNCT
ap-1805	165	5	+	+	NUM
ap-1805	165	6	fy(z	fy(z	NOUN
ap-1805	165	7	)	)	PUNCT
ap-1805	165	8	·	·	PUNCT
ap-1805	165	9	q(z	q(z	X
ap-1805	165	10	)	)	PUNCT
ap-1805	165	11	=	=	SYM
ap-1805	165	12	k(z	k(z	PROPN
ap-1805	165	13	)	)	PUNCT
ap-1805	165	14	·	·	PUNCT
ap-1805	165	15	f(z	f(z	PROPN
ap-1805	165	16	)	)	PUNCT
ap-1805	165	17	.	.	PUNCT
ap-1805	166	1	here	here	ADV
ap-1805	166	2	∇f	∇f	PROPN
ap-1805	166	3	=	=	PUNCT
ap-1805	166	4	(	(	PUNCT
ap-1805	166	5	∂f	∂f	PROPN
ap-1805	166	6	∂x	∂x	PROPN
ap-1805	166	7	,	,	PUNCT
ap-1805	166	8	∂f	∂f	PROPN
ap-1805	166	9	∂y	∂y	PROPN
ap-1805	166	10	)	)	PUNCT
ap-1805	166	11	t	t	PROPN
ap-1805	166	12	denotes	denote	VERB
ap-1805	166	13	the	the	DET
ap-1805	166	14	gradient	gradient	NOUN
ap-1805	166	15	of	of	ADP
ap-1805	166	16	f	f	PROPN
ap-1805	166	17	,	,	PUNCT
ap-1805	166	18	〈	〈	PROPN
ap-1805	166	19	·	·	SYM
ap-1805	166	20	,	,	PUNCT
ap-1805	166	21	·	·	PUNCT
ap-1805	166	22	〉	〉	PROPN
ap-1805	166	23	is	be	AUX
ap-1805	166	24	the	the	DET
ap-1805	166	25	canonical	canonical	ADJ
ap-1805	166	26	inner	inner	ADJ
ap-1805	166	27	product	product	NOUN
ap-1805	166	28	of	of	ADP
ap-1805	166	29	r2	r2	PROPN
ap-1805	166	30	and	and	CCONJ
ap-1805	166	31	the	the	DET
ap-1805	166	32	subscripts	subscript	NOUN
ap-1805	166	33	of	of	ADP
ap-1805	166	34	f	f	PROPN
ap-1805	166	35	indicate	indicate	VERB
ap-1805	166	36	partial	partial	ADJ
ap-1805	166	37	derivates	derivate	NOUN
ap-1805	166	38	,	,	PUNCT
ap-1805	166	39	fx	fx	NOUN
ap-1805	166	40	=	=	SYM
ap-1805	166	41	∂f	∂f	PROPN
ap-1805	166	42	∂x	∂x	PROPN
ap-1805	166	43	,	,	PUNCT
ap-1805	167	1	fy	fy	PROPN
ap-1805	167	2	=	=	SYM
ap-1805	167	3	∂f	∂f	PROPN
ap-1805	167	4	∂y	∂y	PROPN
ap-1805	167	5	.	.	PUNCT
ap-1805	168	1	note	note	VERB
ap-1805	168	2	that	that	SCONJ
ap-1805	168	3	on	on	ADP
ap-1805	168	4	the	the	DET
ap-1805	168	5	invariant	invariant	ADJ
ap-1805	168	6	curve	curve	NOUN
ap-1805	168	7	{	{	PUNCT
ap-1805	168	8	f	f	NOUN
ap-1805	168	9	=	=	SYM
ap-1805	168	10	0	0	NUM
ap-1805	168	11	}	}	PUNCT
ap-1805	168	12	the	the	DET
ap-1805	168	13	gradient	gradient	NOUN
ap-1805	168	14	of	of	ADP
ap-1805	168	15	f	f	PROPN
ap-1805	168	16	,	,	PUNCT
ap-1805	168	17	∇f	∇f	PROPN
ap-1805	168	18	,	,	PUNCT
ap-1805	168	19	is	be	AUX
ap-1805	168	20	orthogonal	orthogonal	ADJ
ap-1805	168	21	to	to	ADP
ap-1805	168	22	the	the	DET
ap-1805	168	23	vector	vector	NOUN
ap-1805	168	24	field	field	NOUN
ap-1805	168	25	x	x	PUNCT
ap-1805	168	26	by	by	ADP
ap-1805	168	27	the	the	DET
ap-1805	168	28	defining	define	VERB
ap-1805	168	29	286	286	NUM
ap-1805	168	30	vol	vol	NOUN
ap-1805	168	31	.	.	PUNCT
ap-1805	169	1	53	53	NUM
ap-1805	169	2	no	no	NOUN
ap-1805	169	3	.	.	PUNCT
ap-1805	170	1	3/2013	3/2013	PROPN
ap-1805	170	2	on	on	ADP
ap-1805	170	3	the	the	DET
ap-1805	170	4	solvability	solvability	NOUN
ap-1805	170	5	of	of	ADP
ap-1805	170	6	some	some	DET
ap-1805	170	7	partial	partial	ADJ
ap-1805	170	8	differential	differential	NOUN
ap-1805	170	9	inequality	inequality	NOUN
ap-1805	170	10	property	property	NOUN
ap-1805	170	11	of	of	ADP
ap-1805	170	12	invariant	invariant	ADJ
ap-1805	170	13	curves	curve	NOUN
ap-1805	170	14	(	(	PUNCT
ap-1805	170	15	13	13	NUM
ap-1805	170	16	)	)	PUNCT
ap-1805	170	17	.	.	PUNCT
ap-1805	171	1	by	by	ADP
ap-1805	171	2	convention	convention	NOUN
ap-1805	171	3	,	,	PUNCT
ap-1805	171	4	the	the	DET
ap-1805	171	5	function	function	NOUN
ap-1805	171	6	f	f	PROPN
ap-1805	171	7	defining	define	VERB
ap-1805	171	8	the	the	DET
ap-1805	171	9	invariant	invariant	ADJ
ap-1805	171	10	curve	curve	NOUN
ap-1805	171	11	f−1(0	f−1(0	PROPN
ap-1805	171	12	)	)	PUNCT
ap-1805	171	13	⊆	⊆	NUM
ap-1805	171	14	r2	r2	NOUN
ap-1805	171	15	is	be	AUX
ap-1805	171	16	called	call	VERB
ap-1805	171	17	the	the	DET
ap-1805	171	18	invariant	invariant	ADJ
ap-1805	171	19	function	function	NOUN
ap-1805	171	20	.	.	PUNCT
ap-1805	172	1	the	the	DET
ap-1805	172	2	notion	notion	NOUN
ap-1805	172	3	of	of	ADP
ap-1805	172	4	exponential	exponential	ADJ
ap-1805	172	5	factors	factor	NOUN
ap-1805	172	6	,	,	PUNCT
ap-1805	172	7	a	a	DET
ap-1805	172	8	special	special	ADJ
ap-1805	172	9	case	case	NOUN
ap-1805	172	10	of	of	ADP
ap-1805	172	11	invariant	invariant	ADJ
ap-1805	172	12	functions	function	NOUN
ap-1805	172	13	,	,	PUNCT
ap-1805	172	14	is	be	AUX
ap-1805	172	15	useful	useful	ADJ
ap-1805	172	16	for	for	ADP
ap-1805	172	17	studying	study	VERB
ap-1805	172	18	the	the	DET
ap-1805	172	19	multiplicity	multiplicity	NOUN
ap-1805	172	20	of	of	ADP
ap-1805	172	21	invariant	invariant	ADJ
ap-1805	172	22	curves	curve	NOUN
ap-1805	172	23	.	.	PUNCT
ap-1805	173	1	it	it	PRON
ap-1805	173	2	allows	allow	VERB
ap-1805	173	3	the	the	DET
ap-1805	173	4	construction	construction	NOUN
ap-1805	173	5	of	of	ADP
ap-1805	173	6	first	first	ADJ
ap-1805	173	7	integrals	integral	NOUN
ap-1805	173	8	for	for	ADP
ap-1805	173	9	polynomial	polynomial	ADJ
ap-1805	173	10	systems	system	NOUN
ap-1805	173	11	via	via	ADP
ap-1805	173	12	the	the	DET
ap-1805	173	13	same	same	ADJ
ap-1805	173	14	method	method	NOUN
ap-1805	173	15	used	use	VERB
ap-1805	173	16	by	by	ADP
ap-1805	173	17	darboux	darboux	NOUN
ap-1805	173	18	.	.	PUNCT
ap-1805	174	1	definition	definition	NOUN
ap-1805	174	2	5	5	NUM
ap-1805	174	3	(	(	PUNCT
ap-1805	174	4	exponential	exponential	ADJ
ap-1805	174	5	factor	factor	NOUN
ap-1805	174	6	)	)	PUNCT
ap-1805	174	7	.	.	PUNCT
ap-1805	175	1	given	give	VERB
ap-1805	175	2	two	two	NUM
ap-1805	175	3	h	h	NOUN
ap-1805	175	4	,	,	PUNCT
ap-1805	175	5	g	g	PROPN
ap-1805	175	6	∈	∈	PROPN
ap-1805	175	7	r[x	r[x	NOUN
ap-1805	175	8	,	,	PUNCT
ap-1805	175	9	y	y	NOUN
ap-1805	175	10	]	]	X
ap-1805	175	11	coprime	coprime	NOUN
ap-1805	175	12	polynomials	polynomial	NOUN
ap-1805	175	13	,	,	PUNCT
ap-1805	175	14	the	the	DET
ap-1805	175	15	function	function	NOUN
ap-1805	175	16	exp(g	exp(g	PROPN
ap-1805	175	17	/	/	SYM
ap-1805	175	18	h	h	NOUN
ap-1805	175	19	)	)	PUNCT
ap-1805	175	20	is	be	AUX
ap-1805	175	21	called	call	VERB
ap-1805	175	22	an	an	DET
ap-1805	175	23	exponential	exponential	ADJ
ap-1805	175	24	factor	factor	NOUN
ap-1805	175	25	for	for	ADP
ap-1805	175	26	system	system	NOUN
ap-1805	175	27	(	(	PUNCT
ap-1805	175	28	1	1	X
ap-1805	175	29	)	)	PUNCT
ap-1805	175	30	if	if	SCONJ
ap-1805	175	31	there	there	PRON
ap-1805	175	32	is	be	VERB
ap-1805	175	33	a	a	DET
ap-1805	175	34	polynomial	polynomial	ADJ
ap-1805	175	35	k	k	PROPN
ap-1805	175	36	∈	∈	PROPN
ap-1805	175	37	r[x	r[x	PROPN
ap-1805	175	38	,	,	PUNCT
ap-1805	175	39	y	y	PROPN
ap-1805	175	40	]	]	PUNCT
ap-1805	175	41	of	of	ADP
ap-1805	175	42	degree	degree	NOUN
ap-1805	175	43	at	at	ADP
ap-1805	175	44	most	most	ADV
ap-1805	175	45	d−	d−	PROPN
ap-1805	175	46	1	1	NUM
ap-1805	175	47	,	,	PUNCT
ap-1805	175	48	d	d	X
ap-1805	175	49	:	:	PUNCT
ap-1805	175	50	=	=	SYM
ap-1805	175	51	max{degp	max{degp	ADJ
ap-1805	175	52	,	,	PUNCT
ap-1805	175	53	degq	degq	NOUN
ap-1805	175	54	}	}	PUNCT
ap-1805	175	55	being	be	AUX
ap-1805	175	56	the	the	DET
ap-1805	175	57	degree	degree	NOUN
ap-1805	175	58	of	of	ADP
ap-1805	175	59	the	the	DET
ap-1805	175	60	polynomial	polynomial	ADJ
ap-1805	175	61	system	system	NOUN
ap-1805	175	62	(	(	PUNCT
ap-1805	175	63	1	1	NUM
ap-1805	175	64	)	)	PUNCT
ap-1805	175	65	,	,	PUNCT
ap-1805	175	66	satisfying	satisfy	VERB
ap-1805	175	67	the	the	DET
ap-1805	175	68	relation	relation	NOUN
ap-1805	175	69	〈	〈	NOUN
ap-1805	175	70	∇	∇	X
ap-1805	175	71	(	(	PUNCT
ap-1805	175	72	eg	eg	NOUN
ap-1805	175	73	/	/	SYM
ap-1805	175	74	h	h	NOUN
ap-1805	175	75	)	)	PUNCT
ap-1805	175	76	,	,	PUNCT
ap-1805	175	77	x	x	SYM
ap-1805	175	78	〉	〉	NOUN
ap-1805	175	79	=	=	SYM
ap-1805	175	80	k	k	X
ap-1805	175	81	·	·	PUNCT
ap-1805	175	82	eg	eg	PROPN
ap-1805	175	83	/	/	SYM
ap-1805	175	84	h.	h.	PROPN
ap-1805	175	85	(	(	PUNCT
ap-1805	175	86	14	14	NUM
ap-1805	175	87	)	)	PUNCT
ap-1805	175	88	note	note	NOUN
ap-1805	175	89	that	that	SCONJ
ap-1805	175	90	obviously	obviously	ADV
ap-1805	175	91	{	{	PUNCT
ap-1805	175	92	(	(	PUNCT
ap-1805	175	93	eg	eg	NOUN
ap-1805	175	94	/	/	SYM
ap-1805	175	95	h	h	NOUN
ap-1805	175	96	)	)	PUNCT
ap-1805	175	97	=	=	SYM
ap-1805	175	98	0	0	PUNCT
ap-1805	175	99	}	}	PUNCT
ap-1805	175	100	=	=	SYM
ap-1805	175	101	∅	∅	NOUN
ap-1805	175	102	,	,	PUNCT
ap-1805	175	103	but	but	CCONJ
ap-1805	175	104	{	{	PUNCT
ap-1805	176	1	g	g	NOUN
ap-1805	176	2	=	=	SYM
ap-1805	176	3	0	0	NUM
ap-1805	176	4	}	}	PUNCT
ap-1805	176	5	defines	define	VERB
ap-1805	176	6	an	an	DET
ap-1805	176	7	invariant	invariant	ADJ
ap-1805	176	8	curve	curve	NOUN
ap-1805	176	9	for	for	ADP
ap-1805	176	10	system	system	NOUN
ap-1805	176	11	(	(	PUNCT
ap-1805	176	12	1	1	NUM
ap-1805	176	13	)	)	PUNCT
ap-1805	176	14	.	.	PUNCT
ap-1805	177	1	definition	definition	NOUN
ap-1805	177	2	6	6	NUM
ap-1805	177	3	(	(	PUNCT
ap-1805	177	4	darboux	darboux	VERB
ap-1805	177	5	function	function	NOUN
ap-1805	177	6	)	)	PUNCT
ap-1805	177	7	.	.	PUNCT
ap-1805	178	1	any	any	DET
ap-1805	178	2	function	function	NOUN
ap-1805	178	3	of	of	ADP
ap-1805	178	4	the	the	DET
ap-1805	178	5	form	form	NOUN
ap-1805	178	6	r∏	r∏	PROPN
ap-1805	178	7	i=1	i=1	PRON
ap-1805	179	1	fλi	fλi	NOUN
ap-1805	180	1	i	i	X
ap-1805	180	2	l∏	l∏	PROPN
ap-1805	181	1	j=1	j=1	NOUN
ap-1805	181	2	(	(	PUNCT
ap-1805	181	3	exp	exp	X
ap-1805	181	4	{	{	PUNCT
ap-1805	181	5	gj	gj	PROPN
ap-1805	181	6	/	/	SYM
ap-1805	181	7	h	h	PROPN
ap-1805	181	8	nj	nj	PROPN
ap-1805	181	9	j	j	PROPN
ap-1805	181	10	}	}	PUNCT
ap-1805	181	11	)	)	PUNCT
ap-1805	181	12	µj	µj	PROPN
ap-1805	181	13	(	(	PUNCT
ap-1805	181	14	15	15	NUM
ap-1805	181	15	)	)	PUNCT
ap-1805	181	16	where	where	SCONJ
ap-1805	181	17	,	,	PUNCT
ap-1805	181	18	for	for	ADP
ap-1805	181	19	1	1	NUM
ap-1805	181	20	≤	≤	NUM
ap-1805	181	21	i	i	PRON
ap-1805	181	22	≤	≤	ADJ
ap-1805	181	23	r	r	NOUN
ap-1805	181	24	and	and	CCONJ
ap-1805	181	25	1	1	NUM
ap-1805	181	26	≤	≤	NUM
ap-1805	181	27	j	j	PROPN
ap-1805	181	28	≤	≤	PROPN
ap-1805	181	29	l	l	NOUN
ap-1805	181	30	,	,	PUNCT
ap-1805	181	31	fi(z	fi(z	NOUN
ap-1805	181	32	)	)	PUNCT
ap-1805	181	33	=	=	SYM
ap-1805	181	34	0	0	NUM
ap-1805	181	35	and	and	CCONJ
ap-1805	181	36	gj(z	gj(z	NOUN
ap-1805	181	37	)	)	PUNCT
ap-1805	181	38	=	=	SYM
ap-1805	181	39	0	0	NUM
ap-1805	181	40	are	be	AUX
ap-1805	181	41	invariant	invariant	ADJ
ap-1805	181	42	curves	curve	NOUN
ap-1805	181	43	for	for	ADP
ap-1805	181	44	system	system	NOUN
ap-1805	181	45	(	(	PUNCT
ap-1805	181	46	1	1	NUM
ap-1805	181	47	)	)	PUNCT
ap-1805	181	48	,	,	PUNCT
ap-1805	181	49	hj	hj	PROPN
ap-1805	181	50	is	be	AUX
ap-1805	181	51	a	a	DET
ap-1805	181	52	polynomial	polynomial	NOUN
ap-1805	181	53	of	of	ADP
ap-1805	181	54	c[x	c[x	NOUN
ap-1805	181	55	,	,	PUNCT
ap-1805	181	56	y	y	PROPN
ap-1805	181	57	]	]	X
ap-1805	181	58	,	,	PUNCT
ap-1805	181	59	λi	λi	CCONJ
ap-1805	181	60	and	and	CCONJ
ap-1805	181	61	µj	µj	PROPN
ap-1805	181	62	are	be	AUX
ap-1805	181	63	complex	complex	ADJ
ap-1805	181	64	numbers	number	NOUN
ap-1805	181	65	and	and	CCONJ
ap-1805	181	66	nj	nj	PROPN
ap-1805	181	67	is	be	AUX
ap-1805	181	68	a	a	DET
ap-1805	181	69	natural	natural	ADJ
ap-1805	181	70	number	number	NOUN
ap-1805	181	71	or	or	CCONJ
ap-1805	181	72	zero	zero	NUM
ap-1805	181	73	,	,	PUNCT
ap-1805	181	74	is	be	AUX
ap-1805	181	75	called	call	VERB
ap-1805	181	76	darboux	darboux	ADJ
ap-1805	181	77	function	function	NOUN
ap-1805	181	78	.	.	PUNCT
ap-1805	182	1	the	the	DET
ap-1805	182	2	following	follow	VERB
ap-1805	182	3	remark	remark	NOUN
ap-1805	182	4	reminds	remind	VERB
ap-1805	182	5	the	the	DET
ap-1805	182	6	reader	reader	NOUN
ap-1805	182	7	of	of	ADP
ap-1805	182	8	some	some	DET
ap-1805	182	9	facts	fact	NOUN
ap-1805	182	10	about	about	ADP
ap-1805	182	11	invariant	invariant	ADJ
ap-1805	182	12	curves	curve	NOUN
ap-1805	182	13	.	.	PUNCT
ap-1805	183	1	remark	remark	NOUN
ap-1805	183	2	3	3	NUM
ap-1805	183	3	.	.	PUNCT
ap-1805	184	1	(	(	PUNCT
ap-1805	184	2	1	1	NUM
ap-1805	184	3	.	.	PUNCT
ap-1805	184	4	)	)	PUNCT
ap-1805	184	5	invariant	invariant	ADJ
ap-1805	184	6	curves	curve	NOUN
ap-1805	184	7	are	be	AUX
ap-1805	184	8	very	very	ADV
ap-1805	184	9	important	important	ADJ
ap-1805	184	10	in	in	ADP
ap-1805	184	11	the	the	DET
ap-1805	184	12	qualitative	qualitative	ADJ
ap-1805	184	13	study	study	NOUN
ap-1805	184	14	of	of	ADP
ap-1805	184	15	dynamical	dynamical	ADJ
ap-1805	184	16	systems	system	NOUN
ap-1805	184	17	because	because	SCONJ
ap-1805	184	18	they	they	PRON
ap-1805	184	19	generalize	generalize	VERB
ap-1805	184	20	the	the	DET
ap-1805	184	21	notion	notion	NOUN
ap-1805	184	22	of	of	ADP
ap-1805	184	23	integrating	integrate	VERB
ap-1805	184	24	factors	factor	NOUN
ap-1805	184	25	and	and	CCONJ
ap-1805	184	26	dulac	dulac	PROPN
ap-1805	184	27	functions	function	NOUN
ap-1805	184	28	.	.	PUNCT
ap-1805	185	1	thus	thus	ADV
ap-1805	185	2	,	,	PUNCT
ap-1805	185	3	it	it	PRON
ap-1805	185	4	is	be	AUX
ap-1805	185	5	possible	possible	ADJ
ap-1805	185	6	to	to	PART
ap-1805	185	7	interpret	interpret	VERB
ap-1805	185	8	integrating	integrate	VERB
ap-1805	185	9	factors	factor	NOUN
ap-1805	185	10	and	and	CCONJ
ap-1805	185	11	dulac	dulac	PROPN
ap-1805	185	12	functions	function	NOUN
ap-1805	185	13	as	as	ADP
ap-1805	185	14	invariant	invariant	ADJ
ap-1805	185	15	functions	function	NOUN
ap-1805	185	16	to	to	ADP
ap-1805	185	17	certain	certain	ADJ
ap-1805	185	18	cofactors	cofactor	NOUN
ap-1805	185	19	:	:	PUNCT
ap-1805	185	20	an	an	DET
ap-1805	185	21	integrating	integrate	VERB
ap-1805	185	22	factor	factor	NOUN
ap-1805	185	23	is	be	AUX
ap-1805	185	24	nothing	nothing	PRON
ap-1805	185	25	but	but	SCONJ
ap-1805	185	26	an	an	DET
ap-1805	185	27	invariant	invariant	ADJ
ap-1805	185	28	function	function	NOUN
ap-1805	185	29	having	have	VERB
ap-1805	185	30	cofactor	cofactor	NOUN
ap-1805	185	31	k	k	NOUN
ap-1805	185	32	=	=	PUNCT
ap-1805	185	33	−divx	−divx	PROPN
ap-1805	185	34	(	(	PUNCT
ap-1805	185	35	16	16	NUM
ap-1805	185	36	)	)	PUNCT
ap-1805	185	37	and	and	CCONJ
ap-1805	185	38	a	a	DET
ap-1805	185	39	dulac	dulac	PROPN
ap-1805	185	40	function	function	NOUN
ap-1805	185	41	is	be	AUX
ap-1805	185	42	an	an	DET
ap-1805	185	43	invariant	invariant	ADJ
ap-1805	185	44	function	function	NOUN
ap-1805	185	45	with	with	ADP
ap-1805	185	46	cofactor	cofactor	NOUN
ap-1805	186	1	k	k	NOUN
ap-1805	186	2	=	=	PUNCT
ap-1805	187	1	−	−	PROPN
ap-1805	187	2	divx	divx	NOUN
ap-1805	187	3	+	+	CCONJ
ap-1805	187	4	1	1	NUM
ap-1805	187	5	f	f	X
ap-1805	187	6	·	·	PUNCT
ap-1805	187	7	g	g	NOUN
ap-1805	187	8	,	,	PUNCT
ap-1805	187	9	(	(	PUNCT
ap-1805	187	10	17	17	NUM
ap-1805	187	11	)	)	PUNCT
ap-1805	187	12	g	g	NOUN
ap-1805	187	13	being	be	AUX
ap-1805	187	14	a	a	DET
ap-1805	187	15	continuous	continuous	ADJ
ap-1805	187	16	function	function	NOUN
ap-1805	187	17	with	with	ADP
ap-1805	187	18	g	g	PROPN
ap-1805	187	19	>	>	X
ap-1805	187	20	0	0	PUNCT
ap-1805	187	21	for	for	ADP
ap-1805	187	22	almost	almost	ADV
ap-1805	187	23	every	every	PRON
ap-1805	187	24	z	z	NOUN
ap-1805	187	25	∈	∈	PROPN
ap-1805	187	26	ω	ω	PROPN
ap-1805	187	27	.	.	PUNCT
ap-1805	188	1	note	note	VERB
ap-1805	188	2	that	that	SCONJ
ap-1805	188	3	the	the	DET
ap-1805	188	4	latter	latter	ADJ
ap-1805	188	5	interpretation	interpretation	NOUN
ap-1805	188	6	of	of	ADP
ap-1805	188	7	a	a	DET
ap-1805	188	8	dulac	dulac	PROPN
ap-1805	188	9	function	function	NOUN
ap-1805	188	10	as	as	ADP
ap-1805	188	11	an	an	DET
ap-1805	188	12	invariant	invariant	ADJ
ap-1805	188	13	function	function	NOUN
ap-1805	188	14	to	to	ADP
ap-1805	188	15	a	a	DET
ap-1805	188	16	specific	specific	ADJ
ap-1805	188	17	cofactor	cofactor	NOUN
ap-1805	188	18	makes	make	VERB
ap-1805	188	19	sense	sense	NOUN
ap-1805	188	20	only	only	ADV
ap-1805	188	21	when	when	SCONJ
ap-1805	188	22	f	f	PROPN
ap-1805	188	23	does	do	AUX
ap-1805	188	24	not	not	PART
ap-1805	188	25	vanish	vanish	VERB
ap-1805	188	26	,	,	PUNCT
ap-1805	188	27	i.e.	i.e.	X
ap-1805	188	28	,	,	PUNCT
ap-1805	188	29	the	the	DET
ap-1805	188	30	dulac	dulac	PROPN
ap-1805	188	31	function	function	NOUN
ap-1805	188	32	is	be	AUX
ap-1805	188	33	not	not	PART
ap-1805	188	34	defined	define	VERB
ap-1805	188	35	respectively	respectively	ADV
ap-1805	188	36	singular	singular	ADJ
ap-1805	188	37	on	on	ADP
ap-1805	188	38	the	the	DET
ap-1805	188	39	invariant	invariant	ADJ
ap-1805	188	40	curve	curve	NOUN
ap-1805	188	41	,	,	PUNCT
ap-1805	188	42	the	the	DET
ap-1805	188	43	vanishing	vanish	VERB
ap-1805	188	44	set	set	NOUN
ap-1805	188	45	of	of	ADP
ap-1805	188	46	the	the	DET
ap-1805	188	47	invariant	invariant	ADJ
ap-1805	188	48	function	function	NOUN
ap-1805	188	49	.	.	PUNCT
ap-1805	189	1	this	this	PRON
ap-1805	189	2	already	already	ADV
ap-1805	189	3	gives	give	VERB
ap-1805	189	4	a	a	DET
ap-1805	189	5	clue	clue	NOUN
ap-1805	189	6	to	to	ADP
ap-1805	189	7	the	the	DET
ap-1805	189	8	natural	natural	ADJ
ap-1805	189	9	boundaries	boundary	NOUN
ap-1805	189	10	on	on	ADP
ap-1805	189	11	the	the	DET
ap-1805	189	12	maximal	maximal	ADJ
ap-1805	189	13	domain	domain	NOUN
ap-1805	189	14	of	of	ADP
ap-1805	189	15	definition	definition	NOUN
ap-1805	189	16	of	of	ADP
ap-1805	189	17	dulac	dulac	PROPN
ap-1805	189	18	functions	function	NOUN
ap-1805	189	19	.	.	PUNCT
ap-1805	190	1	(	(	PUNCT
ap-1805	190	2	2	2	NUM
ap-1805	190	3	.	.	PUNCT
ap-1805	190	4	)	)	PUNCT
ap-1805	191	1	an	an	DET
ap-1805	191	2	easy	easy	ADJ
ap-1805	191	3	observation	observation	NOUN
ap-1805	191	4	is	be	AUX
ap-1805	191	5	that	that	SCONJ
ap-1805	191	6	,	,	PUNCT
ap-1805	191	7	if	if	SCONJ
ap-1805	191	8	f	f	PROPN
ap-1805	191	9	and	and	CCONJ
ap-1805	191	10	g	g	PROPN
ap-1805	191	11	are	be	AUX
ap-1805	191	12	invariant	invariant	ADJ
ap-1805	191	13	functions	function	NOUN
ap-1805	191	14	with	with	ADP
ap-1805	191	15	cofactor	cofactor	NOUN
ap-1805	191	16	kf	kf	PROPN
ap-1805	191	17	and	and	CCONJ
ap-1805	191	18	kg	kg	PROPN
ap-1805	191	19	,	,	PUNCT
ap-1805	191	20	respectively	respectively	ADV
ap-1805	191	21	,	,	PUNCT
ap-1805	191	22	then	then	ADV
ap-1805	191	23	their	their	PRON
ap-1805	191	24	pointwise	pointwise	ADJ
ap-1805	191	25	product	product	NOUN
ap-1805	191	26	f	f	PROPN
ap-1805	191	27	·	·	PUNCT
ap-1805	191	28	g	g	PROPN
ap-1805	191	29	also	also	ADV
ap-1805	191	30	defines	define	VERB
ap-1805	191	31	an	an	DET
ap-1805	191	32	invariant	invariant	ADJ
ap-1805	191	33	curve	curve	NOUN
ap-1805	191	34	with	with	ADP
ap-1805	191	35	cofactor	cofactor	NOUN
ap-1805	191	36	kf	kf	NOUN
ap-1805	192	1	+	+	CCONJ
ap-1805	192	2	kg	kg	NOUN
ap-1805	192	3	.	.	PUNCT
ap-1805	193	1	(	(	PUNCT
ap-1805	193	2	3	3	NUM
ap-1805	193	3	.	.	PUNCT
ap-1805	193	4	)	)	PUNCT
ap-1805	194	1	without	without	ADP
ap-1805	194	2	loss	loss	NOUN
ap-1805	194	3	of	of	ADP
ap-1805	194	4	generality	generality	NOUN
ap-1805	194	5	,	,	PUNCT
ap-1805	194	6	we	we	PRON
ap-1805	194	7	will	will	AUX
ap-1805	194	8	always	always	ADV
ap-1805	194	9	consider	consider	VERB
ap-1805	194	10	complex	complex	ADJ
ap-1805	194	11	-	-	PUNCT
ap-1805	194	12	valued	value	VERB
ap-1805	194	13	invariant	invariant	ADJ
ap-1805	194	14	functions	function	NOUN
ap-1805	194	15	because	because	SCONJ
ap-1805	194	16	,	,	PUNCT
ap-1805	194	17	if	if	SCONJ
ap-1805	194	18	f	f	PROPN
ap-1805	194	19	is	be	AUX
ap-1805	194	20	an	an	DET
ap-1805	194	21	invariant	invariant	ADJ
ap-1805	194	22	function	function	NOUN
ap-1805	194	23	with	with	ADP
ap-1805	194	24	cofactor	cofactor	NOUN
ap-1805	194	25	k	k	PROPN
ap-1805	194	26	(	(	PUNCT
ap-1805	194	27	with	with	ADP
ap-1805	194	28	respect	respect	NOUN
ap-1805	194	29	to	to	ADP
ap-1805	194	30	some	some	DET
ap-1805	194	31	vector	vector	NOUN
ap-1805	194	32	field	field	NOUN
ap-1805	194	33	in	in	ADP
ap-1805	194	34	some	some	DET
ap-1805	194	35	domain	domain	NOUN
ap-1805	194	36	)	)	PUNCT
ap-1805	194	37	,	,	PUNCT
ap-1805	194	38	then	then	ADV
ap-1805	194	39	its	its	PRON
ap-1805	194	40	conjugate	conjugate	ADJ
ap-1805	194	41	function	function	NOUN
ap-1805	194	42	f̄	f̄	PROPN
ap-1805	194	43	is	be	AUX
ap-1805	194	44	also	also	ADV
ap-1805	194	45	an	an	DET
ap-1805	194	46	invariant	invariant	ADJ
ap-1805	194	47	function	function	NOUN
ap-1805	194	48	having	have	VERB
ap-1805	194	49	cofactor	cofactor	NOUN
ap-1805	194	50	k̄	k̄	NOUN
ap-1805	194	51	,	,	PUNCT
ap-1805	194	52	and	and	CCONJ
ap-1805	194	53	therefore	therefore	ADV
ap-1805	194	54	the	the	DET
ap-1805	194	55	product	product	NOUN
ap-1805	194	56	f	f	PROPN
ap-1805	194	57	·	·	PUNCT
ap-1805	194	58	f̄	f̄	PROPN
ap-1805	194	59	is	be	AUX
ap-1805	194	60	a	a	DET
ap-1805	194	61	real	real	ADV
ap-1805	194	62	-	-	PUNCT
ap-1805	194	63	valued	value	VERB
ap-1805	194	64	invariant	invariant	ADJ
ap-1805	194	65	function	function	NOUN
ap-1805	194	66	with	with	ADP
ap-1805	194	67	cofactor	cofactor	NOUN
ap-1805	194	68	k+	k+	NOUN
ap-1805	194	69	k̄.	k̄.	PUNCT
ap-1805	194	70	the	the	DET
ap-1805	194	71	same	same	ADJ
ap-1805	194	72	holds	hold	VERB
ap-1805	194	73	for	for	ADP
ap-1805	194	74	exponential	exponential	ADJ
ap-1805	194	75	factors	factor	NOUN
ap-1805	194	76	.	.	PUNCT
ap-1805	195	1	(	(	PUNCT
ap-1805	195	2	4	4	NUM
ap-1805	195	3	.	.	PUNCT
ap-1805	195	4	)	)	PUNCT
ap-1805	196	1	in	in	ADP
ap-1805	196	2	the	the	DET
ap-1805	196	3	case	case	NOUN
ap-1805	196	4	of	of	ADP
ap-1805	196	5	polynomial	polynomial	ADJ
ap-1805	196	6	planar	planar	ADJ
ap-1805	196	7	vector	vector	NOUN
ap-1805	196	8	fields	field	NOUN
ap-1805	196	9	,	,	PUNCT
ap-1805	196	10	the	the	DET
ap-1805	196	11	algebraic	algebraic	ADJ
ap-1805	196	12	part	part	NOUN
ap-1805	196	13	of	of	ADP
ap-1805	196	14	invariant	invariant	ADJ
ap-1805	196	15	curves	curve	NOUN
ap-1805	196	16	and	and	CCONJ
ap-1805	196	17	exponential	exponential	ADJ
ap-1805	196	18	factors	factor	NOUN
ap-1805	196	19	has	have	AUX
ap-1805	196	20	already	already	ADV
ap-1805	196	21	been	be	AUX
ap-1805	196	22	developed	develop	VERB
ap-1805	196	23	.	.	PUNCT
ap-1805	197	1	we	we	PRON
ap-1805	197	2	quote	quote	VERB
ap-1805	197	3	some	some	PRON
ap-1805	197	4	of	of	ADP
ap-1805	197	5	these	these	DET
ap-1805	197	6	results	result	NOUN
ap-1805	197	7	and	and	CCONJ
ap-1805	197	8	refer	refer	VERB
ap-1805	197	9	to	to	ADP
ap-1805	197	10	[	[	X
ap-1805	197	11	17	17	NUM
ap-1805	197	12	]	]	PUNCT
ap-1805	197	13	,	,	PUNCT
ap-1805	197	14	[	[	X
ap-1805	197	15	18	18	NUM
ap-1805	197	16	]	]	PUNCT
ap-1805	197	17	and	and	CCONJ
ap-1805	197	18	[	[	X
ap-1805	197	19	19	19	NUM
ap-1805	197	20	]	]	PUNCT
ap-1805	197	21	for	for	ADP
ap-1805	197	22	further	further	ADJ
ap-1805	197	23	reading	reading	NOUN
ap-1805	197	24	.	.	PUNCT
ap-1805	198	1	therefore	therefore	ADV
ap-1805	198	2	,	,	PUNCT
ap-1805	198	3	let	let	VERB
ap-1805	198	4	the	the	DET
ap-1805	198	5	vector	vector	NOUN
ap-1805	198	6	field	field	NOUN
ap-1805	198	7	x	x	SYM
ap-1805	198	8	∈	∈	PROPN
ap-1805	198	9	r2	r2	PROPN
ap-1805	198	10	d[x	d[x	PROPN
ap-1805	198	11	,	,	PUNCT
ap-1805	198	12	y	y	PROPN
ap-1805	198	13	]	]	PUNCT
ap-1805	198	14	be	be	AUX
ap-1805	198	15	a	a	DET
ap-1805	198	16	polynomial	polynomial	ADJ
ap-1805	198	17	vector	vector	NOUN
ap-1805	198	18	field	field	NOUN
ap-1805	198	19	of	of	ADP
ap-1805	198	20	degree	degree	NOUN
ap-1805	198	21	d.	d.	PROPN
ap-1805	198	22	furthermore	furthermore	ADV
ap-1805	198	23	,	,	PUNCT
ap-1805	198	24	assume	assume	VERB
ap-1805	198	25	that	that	SCONJ
ap-1805	198	26	d(d+1	d(d+1	PROPN
ap-1805	198	27	)	)	PUNCT
ap-1805	198	28	2	2	NUM
ap-1805	199	1	+	+	SYM
ap-1805	199	2	1	1	NUM
ap-1805	199	3	different	different	ADJ
ap-1805	199	4	irreducible	irreducible	ADJ
ap-1805	199	5	invariant	invariant	ADJ
ap-1805	199	6	algebraic	algebraic	ADJ
ap-1805	199	7	curves	curve	NOUN
ap-1805	199	8	are	be	AUX
ap-1805	199	9	known	know	VERB
ap-1805	199	10	.	.	PUNCT
ap-1805	200	1	then	then	ADV
ap-1805	200	2	one	one	PRON
ap-1805	200	3	can	can	AUX
ap-1805	200	4	construct	construct	VERB
ap-1805	200	5	a	a	DET
ap-1805	200	6	first	first	ADJ
ap-1805	200	7	integral	integral	ADJ
ap-1805	200	8	of	of	ADP
ap-1805	200	9	the	the	DET
ap-1805	200	10	form	form	NOUN
ap-1805	200	11	h	h	NOUN
ap-1805	200	12	=	=	NOUN
ap-1805	200	13	fλ1	fλ1	NOUN
ap-1805	200	14	1	1	NUM
ap-1805	200	15	·	·	PUNCT
ap-1805	200	16	.	.	PUNCT
ap-1805	200	17	.	.	PUNCT
ap-1805	200	18	.	.	PUNCT
ap-1805	201	1	·	·	PUNCT
ap-1805	202	1	fλs	fλs	NOUN
ap-1805	202	2	s	s	X
ap-1805	202	3	(	(	PUNCT
ap-1805	202	4	18	18	NUM
ap-1805	202	5	)	)	PUNCT
ap-1805	202	6	where	where	SCONJ
ap-1805	202	7	each	each	DET
ap-1805	202	8	fi(x	fi(x	PROPN
ap-1805	202	9	,	,	PUNCT
ap-1805	202	10	y	y	NOUN
ap-1805	202	11	)	)	PUNCT
ap-1805	202	12	defines	define	VERB
ap-1805	202	13	an	an	DET
ap-1805	202	14	invariant	invariant	ADJ
ap-1805	202	15	algebraic	algebraic	ADJ
ap-1805	202	16	curve	curve	NOUN
ap-1805	202	17	fi(x	fi(x	PROPN
ap-1805	202	18	,	,	PUNCT
ap-1805	202	19	y	y	NOUN
ap-1805	202	20	)	)	PUNCT
ap-1805	202	21	=	=	SYM
ap-1805	202	22	0	0	NUM
ap-1805	202	23	(	(	PUNCT
ap-1805	202	24	19	19	NUM
ap-1805	202	25	)	)	PUNCT
ap-1805	202	26	for	for	ADP
ap-1805	202	27	system	system	NOUN
ap-1805	202	28	(	(	PUNCT
ap-1805	202	29	1	1	NUM
ap-1805	202	30	)	)	PUNCT
ap-1805	202	31	and	and	CCONJ
ap-1805	202	32	λi	λi	ADP
ap-1805	202	33	∈	∈	PROPN
ap-1805	202	34	c	c	NOUN
ap-1805	202	35	,	,	PUNCT
ap-1805	202	36	not	not	PART
ap-1805	202	37	all	all	PRON
ap-1805	202	38	of	of	ADP
ap-1805	202	39	them	they	PRON
ap-1805	202	40	null	null	ADJ
ap-1805	202	41	,	,	PUNCT
ap-1805	202	42	for	for	ADP
ap-1805	202	43	i	i	PROPN
ap-1805	202	44	=	=	SYM
ap-1805	202	45	1	1	NUM
ap-1805	202	46	,	,	PUNCT
ap-1805	202	47	2	2	NUM
ap-1805	202	48	,	,	PUNCT
ap-1805	202	49	.	.	PUNCT
ap-1805	202	50	.	.	PUNCT
ap-1805	202	51	.	.	PUNCT
ap-1805	203	1	,	,	PUNCT
ap-1805	203	2	s	s	X
ap-1805	203	3	,	,	PUNCT
ap-1805	203	4	s	s	PROPN
ap-1805	203	5	∈	∈	PROPN
ap-1805	203	6	n.	n.	NOUN
ap-1805	203	7	the	the	DET
ap-1805	203	8	functions	function	NOUN
ap-1805	203	9	of	of	ADP
ap-1805	203	10	type	type	NOUN
ap-1805	203	11	(	(	PUNCT
ap-1805	203	12	15	15	NUM
ap-1805	203	13	)	)	PUNCT
ap-1805	203	14	are	be	AUX
ap-1805	203	15	called	call	VERB
ap-1805	203	16	darboux	darboux	NOUN
ap-1805	203	17	functions	function	NOUN
ap-1805	203	18	.	.	PUNCT
ap-1805	204	1	(	(	PUNCT
ap-1805	204	2	5	5	NUM
ap-1805	204	3	.	.	PUNCT
ap-1805	204	4	)	)	PUNCT
ap-1805	205	1	the	the	DET
ap-1805	205	2	irreducibility	irreducibility	NOUN
ap-1805	205	3	of	of	ADP
ap-1805	205	4	the	the	DET
ap-1805	205	5	invariant	invariant	ADJ
ap-1805	205	6	functions	function	NOUN
ap-1805	205	7	in	in	ADP
ap-1805	205	8	the	the	DET
ap-1805	205	9	algebraic	algebraic	ADJ
ap-1805	205	10	case	case	NOUN
ap-1805	205	11	must	must	AUX
ap-1805	205	12	be	be	AUX
ap-1805	205	13	replaced	replace	VERB
ap-1805	205	14	by	by	ADP
ap-1805	205	15	the	the	DET
ap-1805	205	16	condition	condition	NOUN
ap-1805	205	17	{	{	PUNCT
ap-1805	205	18	p	p	PROPN
ap-1805	205	19	∈	∈	PROPN
ap-1805	205	20	ω	ω	NOUN
ap-1805	205	21	:	:	PUNCT
ap-1805	205	22	f(p	f(p	X
ap-1805	205	23	)	)	PUNCT
ap-1805	206	1	=	=	SYM
ap-1805	206	2	0	0	NUM
ap-1805	206	3	and	and	CCONJ
ap-1805	206	4	∇f(p	∇f(p	NOUN
ap-1805	206	5	)	)	PUNCT
ap-1805	207	1	=	=	SYM
ap-1805	207	2	0	0	X
ap-1805	207	3	}	}	PUNCT
ap-1805	207	4	⊆	⊆	NUM
ap-1805	207	5	{	{	PUNCT
ap-1805	207	6	p	p	PROPN
ap-1805	207	7	∈	∈	PROPN
ap-1805	207	8	ω	ω	NOUN
ap-1805	207	9	:	:	PUNCT
ap-1805	207	10	x(p	x(p	PROPN
ap-1805	207	11	)	)	PUNCT
ap-1805	207	12	=	=	SYM
ap-1805	207	13	0	0	X
ap-1805	207	14	}	}	PUNCT
ap-1805	207	15	in	in	ADP
ap-1805	207	16	the	the	DET
ap-1805	207	17	non	non	ADJ
ap-1805	207	18	-	-	ADJ
ap-1805	207	19	algebraic	algebraic	ADJ
ap-1805	207	20	case	case	NOUN
ap-1805	207	21	.	.	PUNCT
ap-1805	208	1	(	(	PUNCT
ap-1805	208	2	6	6	NUM
ap-1805	208	3	.	.	PUNCT
ap-1805	208	4	)	)	PUNCT
ap-1805	209	1	an	an	DET
ap-1805	209	2	easy	easy	ADJ
ap-1805	209	3	observation	observation	NOUN
ap-1805	209	4	:	:	PUNCT
ap-1805	209	5	any	any	DET
ap-1805	209	6	invariant	invariant	ADJ
ap-1805	209	7	curve	curve	NOUN
ap-1805	209	8	{	{	PUNCT
ap-1805	209	9	f	f	NOUN
ap-1805	209	10	=	=	SYM
ap-1805	209	11	0	0	NUM
ap-1805	209	12	}	}	PUNCT
ap-1805	209	13	has	have	VERB
ap-1805	209	14	exactly	exactly	ADV
ap-1805	209	15	one	one	NUM
ap-1805	209	16	cofactor	cofactor	NOUN
ap-1805	209	17	k	k	NOUN
ap-1805	209	18	=	=	SYM
ap-1805	209	19	〈	〈	PROPN
ap-1805	209	20	∇f	∇f	NOUN
ap-1805	209	21	,	,	PUNCT
ap-1805	209	22	x	x	NOUN
ap-1805	209	23	〉	〉	NUM
ap-1805	209	24	f	f	NOUN
ap-1805	209	25	.	.	PUNCT
ap-1805	210	1	5	5	X
ap-1805	210	2	.	.	X
ap-1805	210	3	open	open	ADJ
ap-1805	210	4	questions	question	NOUN
ap-1805	210	5	in	in	ADP
ap-1805	210	6	section	section	NOUN
ap-1805	210	7	2	2	NUM
ap-1805	210	8	,	,	PUNCT
ap-1805	210	9	proposition	proposition	NOUN
ap-1805	210	10	1	1	NUM
ap-1805	210	11	,	,	PUNCT
ap-1805	210	12	we	we	PRON
ap-1805	210	13	obtained	obtain	VERB
ap-1805	210	14	a	a	DET
ap-1805	210	15	local	local	ADJ
ap-1805	210	16	existence	existence	NOUN
ap-1805	210	17	result	result	NOUN
ap-1805	210	18	for	for	ADP
ap-1805	210	19	dulac	dulac	PROPN
ap-1805	210	20	functions	function	NOUN
ap-1805	210	21	near	near	ADP
ap-1805	210	22	to	to	ADP
ap-1805	210	23	a	a	DET
ap-1805	210	24	hyperbolic	hyperbolic	ADJ
ap-1805	210	25	equilibrium	equilibrium	NOUN
ap-1805	210	26	.	.	PUNCT
ap-1805	211	1	the	the	DET
ap-1805	211	2	proof	proof	NOUN
ap-1805	211	3	was	be	AUX
ap-1805	211	4	based	base	VERB
ap-1805	211	5	on	on	ADP
ap-1805	211	6	theorem	theorem	ADJ
ap-1805	211	7	4	4	NUM
ap-1805	211	8	,	,	PUNCT
ap-1805	211	9	where	where	SCONJ
ap-1805	211	10	we	we	PRON
ap-1805	211	11	calculated	calculate	VERB
ap-1805	211	12	a	a	DET
ap-1805	211	13	dulac	dulac	PROPN
ap-1805	211	14	function	function	NOUN
ap-1805	211	15	explicitly	explicitly	ADV
ap-1805	211	16	in	in	ADP
ap-1805	211	17	terms	term	NOUN
ap-1805	211	18	of	of	ADP
ap-1805	211	19	a	a	DET
ap-1805	211	20	quadratic	quadratic	ADJ
ap-1805	211	21	polynomial	polynomial	NOUN
ap-1805	211	22	.	.	PUNCT
ap-1805	212	1	in	in	ADP
ap-1805	212	2	this	this	DET
ap-1805	212	3	proof	proof	NOUN
ap-1805	212	4	we	we	PRON
ap-1805	212	5	observed	observe	VERB
ap-1805	212	6	,	,	PUNCT
ap-1805	212	7	in	in	ADP
ap-1805	212	8	fact	fact	NOUN
ap-1805	212	9	,	,	PUNCT
ap-1805	212	10	why	why	SCONJ
ap-1805	212	11	one	one	PRON
ap-1805	212	12	needs	need	VERB
ap-1805	212	13	to	to	PART
ap-1805	212	14	impose	impose	VERB
ap-1805	212	15	that	that	SCONJ
ap-1805	212	16	at	at	ADP
ap-1805	212	17	most	most	ADV
ap-1805	212	18	one	one	NUM
ap-1805	212	19	eigenvalue	eigenvalue	NOUN
ap-1805	212	20	of	of	ADP
ap-1805	212	21	matrix	matrix	NOUN
ap-1805	212	22	a	a	PRON
ap-1805	212	23	is	be	AUX
ap-1805	212	24	zero	zero	NUM
ap-1805	212	25	,	,	PUNCT
ap-1805	212	26	because	because	SCONJ
ap-1805	212	27	,	,	PUNCT
ap-1805	212	28	if	if	SCONJ
ap-1805	212	29	we	we	PRON
ap-1805	212	30	had	have	VERB
ap-1805	212	31	two	two	NUM
ap-1805	212	32	such	such	ADJ
ap-1805	212	33	eigenvalues	eigenvalue	NOUN
ap-1805	212	34	σ(a	σ(a	PROPN
ap-1805	212	35	)	)	PUNCT
ap-1805	212	36	=	=	PRON
ap-1805	212	37	{	{	PUNCT
ap-1805	212	38	0	0	NUM
ap-1805	212	39	}	}	PUNCT
ap-1805	212	40	,	,	PUNCT
ap-1805	212	41	the	the	DET
ap-1805	212	42	matrix	matrix	NOUN
ap-1805	212	43	would	would	AUX
ap-1805	212	44	have	have	VERB
ap-1805	212	45	trace	trace	NOUN
ap-1805	212	46	zero	zero	NUM
ap-1805	212	47	and	and	CCONJ
ap-1805	212	48	we	we	PRON
ap-1805	212	49	would	would	AUX
ap-1805	212	50	have	have	AUX
ap-1805	212	51	divided	divide	VERB
ap-1805	212	52	by	by	ADP
ap-1805	212	53	it	it	PRON
ap-1805	212	54	.	.	PUNCT
ap-1805	213	1	then	then	ADV
ap-1805	213	2	,	,	PUNCT
ap-1805	213	3	by	by	ADP
ap-1805	213	4	applying	apply	VERB
ap-1805	213	5	the	the	DET
ap-1805	213	6	hartman	hartman	PROPN
ap-1805	213	7	grobman	grobman	PROPN
ap-1805	213	8	theorem	theorem	PROPN
ap-1805	213	9	,	,	PUNCT
ap-1805	213	10	the	the	DET
ap-1805	213	11	result	result	NOUN
ap-1805	213	12	carried	carry	VERB
ap-1805	213	13	over	over	ADP
ap-1805	213	14	to	to	ADP
ap-1805	213	15	hyperbolic	hyperbolic	ADJ
ap-1805	213	16	fixed	fix	VERB
ap-1805	213	17	points	point	NOUN
ap-1805	213	18	.	.	PUNCT
ap-1805	214	1	observe	observe	VERB
ap-1805	214	2	that	that	SCONJ
ap-1805	214	3	neither	neither	CCONJ
ap-1805	214	4	does	do	AUX
ap-1805	214	5	the	the	DET
ap-1805	214	6	hartman	hartman	PROPN
ap-1805	214	7	grobman	grobman	PROPN
ap-1805	214	8	theorem	theorem	VERB
ap-1805	214	9	hold	hold	NOUN
ap-1805	214	10	for	for	ADP
ap-1805	214	11	equilibria	equilibrium	NOUN
ap-1805	214	12	p	p	NOUN
ap-1805	214	13	with	with	ADP
ap-1805	214	14	linearization	linearization	NOUN
ap-1805	214	15	having	have	VERB
ap-1805	214	16	a	a	DET
ap-1805	214	17	purely	purely	ADV
ap-1805	214	18	imaginary	imaginary	ADJ
ap-1805	214	19	or	or	CCONJ
ap-1805	214	20	zero	zero	NUM
ap-1805	214	21	spectrum	spectrum	NOUN
ap-1805	214	22	,	,	PUNCT
ap-1805	214	23	nor	nor	CCONJ
ap-1805	214	24	could	could	AUX
ap-1805	214	25	we	we	PRON
ap-1805	214	26	make	make	VERB
ap-1805	214	27	any	any	DET
ap-1805	214	28	use	use	NOUN
ap-1805	214	29	287	287	NUM
ap-1805	214	30	m.	m.	NOUN
ap-1805	214	31	himmel	himmel	PROPN
ap-1805	214	32	acta	acta	PROPN
ap-1805	214	33	polytechnica	polytechnica	PROPN
ap-1805	214	34	figure	figure	NOUN
ap-1805	214	35	2	2	NUM
ap-1805	214	36	.	.	PUNCT
ap-1805	214	37	gluing	glue	VERB
ap-1805	214	38	three	three	NUM
ap-1805	214	39	different	different	ADJ
ap-1805	214	40	diffeomorphisms	diffeomorphism	NOUN
ap-1805	214	41	of	of	ADP
ap-1805	214	42	it	it	PRON
ap-1805	214	43	,	,	PUNCT
ap-1805	214	44	because	because	SCONJ
ap-1805	214	45	in	in	SCONJ
ap-1805	214	46	both	both	DET
ap-1805	214	47	cases	case	NOUN
ap-1805	214	48	divx(p	divx(p	VERB
ap-1805	214	49	)	)	PUNCT
ap-1805	214	50	=	=	SYM
ap-1805	214	51	0	0	NUM
ap-1805	214	52	holds	hold	NOUN
ap-1805	214	53	and	and	CCONJ
ap-1805	214	54	our	our	PRON
ap-1805	214	55	dulac	dulac	PROPN
ap-1805	214	56	function	function	NOUN
ap-1805	214	57	blows	blow	VERB
ap-1805	214	58	up	up	ADP
ap-1805	214	59	.	.	PUNCT
ap-1805	215	1	hence	hence	ADV
ap-1805	215	2	,	,	PUNCT
ap-1805	215	3	in	in	ADP
ap-1805	215	4	future	future	NOUN
ap-1805	215	5	the	the	DET
ap-1805	215	6	following	follow	VERB
ap-1805	215	7	question	question	NOUN
ap-1805	215	8	for	for	ADP
ap-1805	215	9	nonlinear	nonlinear	ADJ
ap-1805	215	10	vector	vector	NOUN
ap-1805	215	11	fields	field	NOUN
ap-1805	215	12	has	have	VERB
ap-1805	215	13	to	to	PART
ap-1805	215	14	be	be	AUX
ap-1805	215	15	addressed	address	VERB
ap-1805	215	16	:	:	PUNCT
ap-1805	215	17	question	question	NOUN
ap-1805	215	18	2	2	NUM
ap-1805	215	19	.	.	PUNCT
ap-1805	215	20	when	when	SCONJ
ap-1805	215	21	does	do	AUX
ap-1805	215	22	a	a	DET
ap-1805	215	23	dulac	dulac	PROPN
ap-1805	215	24	function	function	NOUN
ap-1805	215	25	exist	exist	VERB
ap-1805	215	26	near	near	ADV
ap-1805	215	27	to	to	ADP
ap-1805	215	28	non	non	ADJ
ap-1805	215	29	-	-	ADJ
ap-1805	215	30	hyperbolic	hyperbolic	ADJ
ap-1805	215	31	fixed	fix	VERB
ap-1805	215	32	points	point	NOUN
ap-1805	215	33	?	?	PUNCT
ap-1805	216	1	this	this	DET
ap-1805	216	2	question	question	NOUN
ap-1805	216	3	is	be	AUX
ap-1805	216	4	somehow	somehow	ADV
ap-1805	216	5	naive	naive	ADJ
ap-1805	216	6	,	,	PUNCT
ap-1805	216	7	because	because	SCONJ
ap-1805	216	8	one	one	PRON
ap-1805	216	9	has	have	VERB
ap-1805	216	10	to	to	PART
ap-1805	216	11	deal	deal	VERB
ap-1805	216	12	here	here	ADV
ap-1805	216	13	with	with	ADP
ap-1805	216	14	the	the	DET
ap-1805	216	15	center	center	ADJ
ap-1805	216	16	-	-	PUNCT
ap-1805	216	17	focus	focus	NOUN
ap-1805	216	18	-	-	PUNCT
ap-1805	216	19	problem	problem	NOUN
ap-1805	216	20	,	,	PUNCT
ap-1805	216	21	which	which	PRON
ap-1805	216	22	is	be	AUX
ap-1805	216	23	still	still	ADV
ap-1805	216	24	not	not	PART
ap-1805	216	25	completely	completely	ADV
ap-1805	216	26	solved	solve	VERB
ap-1805	216	27	in	in	ADP
ap-1805	216	28	general	general	ADJ
ap-1805	216	29	.	.	PUNCT
ap-1805	217	1	however	however	ADV
ap-1805	217	2	,	,	PUNCT
ap-1805	217	3	this	this	DET
ap-1805	217	4	dulac	dulac	PROPN
ap-1805	217	5	approach	approach	NOUN
ap-1805	217	6	may	may	AUX
ap-1805	217	7	give	give	VERB
ap-1805	217	8	a	a	DET
ap-1805	217	9	new	new	ADJ
ap-1805	217	10	perspective	perspective	NOUN
ap-1805	217	11	on	on	ADP
ap-1805	217	12	it	it	PRON
ap-1805	217	13	.	.	PUNCT
ap-1805	218	1	why	why	SCONJ
ap-1805	218	2	do	do	AUX
ap-1805	218	3	we	we	PRON
ap-1805	218	4	bother	bother	VERB
ap-1805	218	5	about	about	ADP
ap-1805	218	6	all	all	DET
ap-1805	218	7	these	these	DET
ap-1805	218	8	local	local	ADJ
ap-1805	218	9	existence	existence	NOUN
ap-1805	218	10	statements	statement	NOUN
ap-1805	218	11	for	for	ADP
ap-1805	218	12	dulac	dulac	PROPN
ap-1805	218	13	functions	function	NOUN
ap-1805	218	14	?	?	PUNCT
ap-1805	219	1	in	in	ADP
ap-1805	219	2	principle	principle	NOUN
ap-1805	219	3	,	,	PUNCT
ap-1805	219	4	the	the	DET
ap-1805	219	5	motivation	motivation	NOUN
ap-1805	219	6	arose	arise	VERB
ap-1805	219	7	from	from	ADP
ap-1805	219	8	the	the	DET
ap-1805	219	9	following	follow	VERB
ap-1805	219	10	algorithm	algorithm	NOUN
ap-1805	219	11	1	1	NUM
ap-1805	219	12	.	.	PUNCT
ap-1805	220	1	input	input	NOUN
ap-1805	220	2	:	:	PUNCT
ap-1805	220	3	a	a	DET
ap-1805	220	4	nonlinear	nonlinear	ADJ
ap-1805	220	5	planar	planar	ADJ
ap-1805	220	6	vector	vector	NOUN
ap-1805	220	7	field	field	NOUN
ap-1805	220	8	x	x	NOUN
ap-1805	220	9	;	;	PUNCT
ap-1805	220	10	output	output	NOUN
ap-1805	220	11	:	:	PUNCT
ap-1805	220	12	number	number	NOUN
ap-1805	220	13	and	and	CCONJ
ap-1805	220	14	position	position	NOUN
ap-1805	220	15	of	of	ADP
ap-1805	220	16	periodic	periodic	ADJ
ap-1805	220	17	orbits	orbit	NOUN
ap-1805	220	18	together	together	ADV
ap-1805	220	19	with	with	ADP
ap-1805	220	20	phase	phase	NOUN
ap-1805	220	21	portrait	portrait	NOUN
ap-1805	220	22	.	.	PUNCT
ap-1805	221	1	step1	step1	PROPN
ap-1805	221	2	:	:	PUNCT
ap-1805	221	3	determine	determine	VERB
ap-1805	221	4	the	the	DET
ap-1805	221	5	zeros	zero	NOUN
ap-1805	221	6	of	of	ADP
ap-1805	221	7	x.	x.	PROPN
ap-1805	221	8	step2	step2	PROPN
ap-1805	221	9	:	:	PUNCT
ap-1805	221	10	at	at	ADP
ap-1805	221	11	each	each	DET
ap-1805	221	12	zero	zero	NUM
ap-1805	221	13	,	,	PUNCT
ap-1805	221	14	define	define	VERB
ap-1805	221	15	locally	locally	ADV
ap-1805	221	16	a	a	DET
ap-1805	221	17	dulac	dulac	PROPN
ap-1805	221	18	function	function	NOUN
ap-1805	221	19	.	.	PUNCT
ap-1805	222	1	step3	step3	PROPN
ap-1805	222	2	:	:	PUNCT
ap-1805	222	3	extend	extend	VERB
ap-1805	222	4	them	they	PRON
ap-1805	222	5	as	as	ADV
ap-1805	222	6	long	long	ADV
ap-1805	222	7	as	as	ADP
ap-1805	222	8	possible	possible	ADJ
ap-1805	222	9	.	.	PUNCT
ap-1805	223	1	if	if	SCONJ
ap-1805	223	2	no	no	DET
ap-1805	223	3	further	further	ADJ
ap-1805	223	4	extension	extension	NOUN
ap-1805	223	5	is	be	AUX
ap-1805	223	6	possible	possible	ADJ
ap-1805	223	7	,	,	PUNCT
ap-1805	223	8	one	one	PRON
ap-1805	223	9	has	have	AUX
ap-1805	223	10	found	find	VERB
ap-1805	223	11	the	the	DET
ap-1805	223	12	limit	limit	NOUN
ap-1805	223	13	cycles	cycle	NOUN
ap-1805	223	14	and	and	CCONJ
ap-1805	223	15	determined	determine	VERB
ap-1805	223	16	the	the	DET
ap-1805	223	17	phase	phase	NOUN
ap-1805	223	18	portrait	portrait	NOUN
ap-1805	223	19	.	.	PUNCT
ap-1805	224	1	of	of	ADP
ap-1805	224	2	course	course	NOUN
ap-1805	224	3	,	,	PUNCT
ap-1805	224	4	this	this	PRON
ap-1805	224	5	is	be	AUX
ap-1805	224	6	rather	rather	ADV
ap-1805	224	7	a	a	DET
ap-1805	224	8	pseudo	pseudo	NOUN
ap-1805	224	9	algorithm	algorithm	NOUN
ap-1805	224	10	,	,	PUNCT
ap-1805	224	11	because	because	SCONJ
ap-1805	224	12	one	one	PRON
ap-1805	224	13	can	can	AUX
ap-1805	224	14	not	not	PART
ap-1805	224	15	accomplish	accomplish	VERB
ap-1805	224	16	any	any	PRON
ap-1805	224	17	of	of	ADP
ap-1805	224	18	its	its	PRON
ap-1805	224	19	steps	step	NOUN
ap-1805	224	20	.	.	PUNCT
ap-1805	225	1	one	one	NUM
ap-1805	225	2	more	more	ADV
ap-1805	225	3	approachable	approachable	ADJ
ap-1805	225	4	but	but	CCONJ
ap-1805	225	5	somehow	somehow	ADV
ap-1805	225	6	technical	technical	ADJ
ap-1805	225	7	step	step	NOUN
ap-1805	225	8	is	be	AUX
ap-1805	225	9	to	to	PART
ap-1805	225	10	combine	combine	VERB
ap-1805	225	11	these	these	DET
ap-1805	225	12	local	local	ADJ
ap-1805	225	13	results	result	NOUN
ap-1805	225	14	in	in	ADP
ap-1805	225	15	a	a	DET
ap-1805	225	16	global	global	ADJ
ap-1805	225	17	one	one	NUM
ap-1805	225	18	.	.	PUNCT
ap-1805	226	1	technically	technically	ADV
ap-1805	226	2	,	,	PUNCT
ap-1805	226	3	this	this	PRON
ap-1805	226	4	means	mean	VERB
ap-1805	226	5	,	,	PUNCT
ap-1805	226	6	as	as	SCONJ
ap-1805	226	7	one	one	PRON
ap-1805	226	8	has	have	VERB
ap-1805	226	9	to	to	PART
ap-1805	226	10	deal	deal	VERB
ap-1805	226	11	here	here	ADV
ap-1805	226	12	with	with	ADP
ap-1805	226	13	different	different	ADJ
ap-1805	226	14	local	local	ADJ
ap-1805	226	15	coordinate	coordinate	NOUN
ap-1805	226	16	representations	representation	NOUN
ap-1805	226	17	,	,	PUNCT
ap-1805	226	18	that	that	SCONJ
ap-1805	226	19	one	one	PRON
ap-1805	226	20	has	have	VERB
ap-1805	226	21	to	to	PART
ap-1805	226	22	glue	glue	VERB
ap-1805	226	23	together	together	ADP
ap-1805	226	24	different	different	ADJ
ap-1805	226	25	diffeomorphisms	diffeomorphism	NOUN
ap-1805	226	26	.	.	PUNCT
ap-1805	227	1	summing	sum	VERB
ap-1805	227	2	up	up	ADP
ap-1805	227	3	,	,	PUNCT
ap-1805	227	4	we	we	PRON
ap-1805	227	5	claim	claim	VERB
ap-1805	227	6	that	that	SCONJ
ap-1805	227	7	the	the	DET
ap-1805	227	8	dulac	dulac	PROPN
ap-1805	227	9	method	method	NOUN
ap-1805	227	10	in	in	ADP
ap-1805	227	11	the	the	DET
ap-1805	227	12	spirit	spirit	NOUN
ap-1805	227	13	of	of	ADP
ap-1805	227	14	algorithm	algorithm	PROPN
ap-1805	227	15	1	1	NUM
ap-1805	227	16	will	will	AUX
ap-1805	227	17	give	give	VERB
ap-1805	227	18	new	new	ADJ
ap-1805	227	19	insights	insight	NOUN
ap-1805	227	20	in	in	ADP
ap-1805	227	21	the	the	DET
ap-1805	227	22	qualitative	qualitative	ADJ
ap-1805	227	23	theory	theory	NOUN
ap-1805	227	24	of	of	ADP
ap-1805	227	25	planar	planar	ADJ
ap-1805	227	26	differential	differential	ADJ
ap-1805	227	27	equations	equation	NOUN
ap-1805	227	28	.	.	PUNCT
ap-1805	228	1	references	reference	NOUN
ap-1805	228	2	[	[	X
ap-1805	228	3	1	1	NUM
ap-1805	228	4	]	]	PUNCT
ap-1805	228	5	i.	i.	NOUN
ap-1805	228	6	burdujan	burdujan	PROPN
ap-1805	228	7	.	.	PUNCT
ap-1805	229	1	some	some	DET
ap-1805	229	2	geometrical	geometrical	ADJ
ap-1805	229	3	aspects	aspect	NOUN
ap-1805	229	4	of	of	ADP
ap-1805	229	5	the	the	DET
ap-1805	229	6	theory	theory	NOUN
ap-1805	229	7	of	of	ADP
ap-1805	229	8	quadratic	quadratic	ADJ
ap-1805	229	9	differential	differential	ADJ
ap-1805	229	10	equations	equation	NOUN
ap-1805	229	11	.	.	PUNCT
ap-1805	230	1	bul	bul	PROPN
ap-1805	230	2	inst	inst	PROPN
ap-1805	230	3	politehn	politehn	PROPN
ap-1805	230	4	iaşi	iaşi	PROPN
ap-1805	230	5	secţ	secţ	PROPN
ap-1805	230	6	i	i	PROPN
ap-1805	230	7	37(41)(1	37(41)(1	NOUN
ap-1805	230	8	-	-	PUNCT
ap-1805	230	9	4):39–44	4):39–44	NUM
ap-1805	230	10	,	,	PUNCT
ap-1805	230	11	1991	1991	NUM
ap-1805	230	12	.	.	PUNCT
ap-1805	231	1	[	[	X
ap-1805	231	2	2	2	X
ap-1805	231	3	]	]	PUNCT
ap-1805	231	4	d.	d.	PROPN
ap-1805	231	5	k.	k.	PROPN
ap-1805	231	6	kayumov	kayumov	PROPN
ap-1805	231	7	.	.	PUNCT
ap-1805	232	1	limit	limit	VERB
ap-1805	232	2	cycles	cycle	NOUN
ap-1805	232	3	of	of	ADP
ap-1805	232	4	a	a	DET
ap-1805	232	5	class	class	NOUN
ap-1805	232	6	of	of	ADP
ap-1805	232	7	quadratic	quadratic	ADJ
ap-1805	232	8	differential	differential	ADJ
ap-1805	232	9	equations	equation	NOUN
ap-1805	232	10	.	.	PUNCT
ap-1805	233	1	in	in	ADP
ap-1805	233	2	problems	problem	NOUN
ap-1805	233	3	in	in	ADP
ap-1805	233	4	the	the	DET
ap-1805	233	5	theory	theory	NOUN
ap-1805	233	6	of	of	ADP
ap-1805	233	7	ordinary	ordinary	ADJ
ap-1805	233	8	differential	differential	ADJ
ap-1805	233	9	equations	equation	NOUN
ap-1805	233	10	(	(	PUNCT
ap-1805	233	11	russian	russian	PROPN
ap-1805	233	12	)	)	PUNCT
ap-1805	233	13	,	,	PUNCT
ap-1805	233	14	pp	pp	ADJ
ap-1805	233	15	.	.	PUNCT
ap-1805	234	1	25–29	25–29	NUM
ap-1805	234	2	,	,	PUNCT
ap-1805	234	3	109–110	109–110	NUM
ap-1805	234	4	.	.	PUNCT
ap-1805	235	1	samarkand	samarkand	PROPN
ap-1805	235	2	.	.	PUNCT
ap-1805	236	1	gos	gos	PROPN
ap-1805	236	2	.	.	PUNCT
ap-1805	237	1	univ	univ	PROPN
ap-1805	237	2	.	.	PROPN
ap-1805	237	3	,	,	PUNCT
ap-1805	237	4	samarkand	samarkand	PROPN
ap-1805	237	5	,	,	PUNCT
ap-1805	237	6	1984	1984	NUM
ap-1805	237	7	.	.	PUNCT
ap-1805	238	1	[	[	X
ap-1805	238	2	3	3	X
ap-1805	238	3	]	]	X
ap-1805	238	4	d.	d.	PROPN
ap-1805	238	5	e.	e.	PROPN
ap-1805	238	6	koditschek	koditschek	PROPN
ap-1805	238	7	,	,	PUNCT
ap-1805	238	8	et	et	PROPN
ap-1805	238	9	al	al	PROPN
ap-1805	238	10	.	.	PROPN
ap-1805	238	11	limit	limit	PROPN
ap-1805	238	12	cycles	cycle	NOUN
ap-1805	238	13	of	of	ADP
ap-1805	238	14	planar	planar	ADJ
ap-1805	238	15	quadratic	quadratic	ADJ
ap-1805	238	16	differential	differential	ADJ
ap-1805	238	17	equations	equation	NOUN
ap-1805	238	18	.	.	PUNCT
ap-1805	239	1	j	j	PROPN
ap-1805	239	2	differential	differential	PROPN
ap-1805	239	3	equations	equation	NOUN
ap-1805	239	4	54(2):181–195	54(2):181–195	NOUN
ap-1805	239	5	,	,	PUNCT
ap-1805	239	6	1984	1984	NUM
ap-1805	239	7	.	.	PUNCT
ap-1805	240	1	[	[	X
ap-1805	240	2	4	4	X
ap-1805	240	3	]	]	X
ap-1805	240	4	y.	y.	PROPN
ap-1805	240	5	s.	s.	PROPN
ap-1805	240	6	il′yashenko	il′yashenko	PROPN
ap-1805	240	7	.	.	PUNCT
ap-1805	241	1	finiteness	finiteness	PROPN
ap-1805	241	2	theorems	theorem	NOUN
ap-1805	241	3	for	for	ADP
ap-1805	241	4	limit	limit	NOUN
ap-1805	241	5	cycles	cycle	NOUN
ap-1805	241	6	,	,	PUNCT
ap-1805	241	7	vol	vol	NOUN
ap-1805	241	8	.	.	PROPN
ap-1805	242	1	94	94	NUM
ap-1805	242	2	of	of	ADP
ap-1805	242	3	translations	translation	NOUN
ap-1805	242	4	of	of	ADP
ap-1805	242	5	mathematical	mathematical	ADJ
ap-1805	242	6	monographs	monograph	NOUN
ap-1805	242	7	.	.	PUNCT
ap-1805	243	1	american	american	PROPN
ap-1805	243	2	mathematical	mathematical	PROPN
ap-1805	243	3	society	society	NOUN
ap-1805	243	4	,	,	PUNCT
ap-1805	243	5	providence	providence	NOUN
ap-1805	243	6	,	,	PUNCT
ap-1805	243	7	ri	ri	NOUN
ap-1805	243	8	,	,	PUNCT
ap-1805	243	9	1991	1991	NUM
ap-1805	243	10	.	.	PUNCT
ap-1805	244	1	translated	translate	VERB
ap-1805	244	2	from	from	ADP
ap-1805	244	3	the	the	DET
ap-1805	244	4	russian	russian	NOUN
ap-1805	244	5	by	by	ADP
ap-1805	244	6	h.	h.	PROPN
ap-1805	244	7	h.	h.	PROPN
ap-1805	244	8	mcfaden	mcfaden	PROPN
ap-1805	244	9	.	.	PUNCT
ap-1805	245	1	[	[	X
ap-1805	245	2	5	5	X
ap-1805	245	3	]	]	PUNCT
ap-1805	245	4	h.	h.	PROPN
ap-1805	245	5	dulac	dulac	PROPN
ap-1805	245	6	.	.	PUNCT
ap-1805	246	1	sur	sur	PROPN
ap-1805	246	2	les	les	PROPN
ap-1805	246	3	cycles	cycle	NOUN
ap-1805	246	4	limites	limes	NOUN
ap-1805	246	5	.	.	PUNCT
ap-1805	247	1	bull	bull	PROPN
ap-1805	247	2	soc	soc	PROPN
ap-1805	247	3	math	math	PROPN
ap-1805	247	4	france	france	PROPN
ap-1805	247	5	51:45–188	51:45–188	NUM
ap-1805	247	6	,	,	PUNCT
ap-1805	247	7	1923	1923	NUM
ap-1805	247	8	.	.	PUNCT
ap-1805	248	1	[	[	X
ap-1805	248	2	6	6	X
ap-1805	248	3	]	]	PUNCT
ap-1805	248	4	j.	j.	PROPN
ap-1805	248	5	écalle	écalle	PROPN
ap-1805	248	6	,	,	PUNCT
ap-1805	248	7	et	et	PROPN
ap-1805	248	8	al	al	PROPN
ap-1805	248	9	.	.	PUNCT
ap-1805	248	10	non	non	ADJ
ap-1805	248	11	-	-	ADJ
ap-1805	248	12	accumulation	accumulation	ADJ
ap-1805	248	13	des	des	PROPN
ap-1805	248	14	cycles	cycle	NOUN
ap-1805	248	15	-	-	PUNCT
ap-1805	248	16	limites	limes	NOUN
ap-1805	248	17	.	.	PUNCT
ap-1805	249	1	i.	i.	PROPN
ap-1805	249	2	c	c	PROPN
ap-1805	249	3	r	r	PROPN
ap-1805	249	4	acad	acad	PROPN
ap-1805	249	5	sci	sci	PROPN
ap-1805	249	6	paris	paris	PROPN
ap-1805	249	7	sér	sér	VERB
ap-1805	249	8	i	i	PRON
ap-1805	249	9	math	math	PROPN
ap-1805	249	10	304(13):375–377	304(13):375–377	PROPN
ap-1805	249	11	,	,	PUNCT
ap-1805	249	12	1987	1987	NUM
ap-1805	249	13	.	.	PUNCT
ap-1805	250	1	[	[	X
ap-1805	250	2	7	7	X
ap-1805	250	3	]	]	X
ap-1805	250	4	y.	y.	PROPN
ap-1805	250	5	ilyashenko	ilyashenko	PROPN
ap-1805	250	6	.	.	PUNCT
ap-1805	251	1	centennial	centennial	NOUN
ap-1805	251	2	history	history	NOUN
ap-1805	251	3	of	of	ADP
ap-1805	251	4	hilbert	hilbert	PROPN
ap-1805	251	5	’s	’s	PART
ap-1805	251	6	16th	16th	ADJ
ap-1805	251	7	problem	problem	NOUN
ap-1805	251	8	.	.	PUNCT
ap-1805	252	1	bull	bull	PROPN
ap-1805	252	2	amer	amer	PROPN
ap-1805	252	3	math	math	PROPN
ap-1805	252	4	soc	soc	PROPN
ap-1805	252	5	(	(	PUNCT
ap-1805	252	6	ns	ns	ADJ
ap-1805	252	7	)	)	PUNCT
ap-1805	252	8	39(3):301–354	39(3):301–354	NUM
ap-1805	252	9	,	,	PUNCT
ap-1805	252	10	2002	2002	NUM
ap-1805	252	11	.	.	PUNCT
ap-1805	253	1	[	[	X
ap-1805	253	2	8	8	NUM
ap-1805	253	3	]	]	X
ap-1805	253	4	y.	y.	PROPN
ap-1805	253	5	s.	s.	PROPN
ap-1805	253	6	il′yashenko	il′yashenko	PROPN
ap-1805	253	7	.	.	PROPN
ap-1805	253	8	centennial	centennial	NOUN
ap-1805	253	9	history	history	NOUN
ap-1805	253	10	of	of	ADP
ap-1805	253	11	hilbert	hilbert	PROPN
ap-1805	253	12	’s	’s	PART
ap-1805	253	13	16th	16th	ADJ
ap-1805	253	14	problem	problem	NOUN
ap-1805	253	15	.	.	PUNCT
ap-1805	254	1	in	in	ADP
ap-1805	254	2	fundamental	fundamental	ADJ
ap-1805	254	3	mathematics	mathematic	NOUN
ap-1805	254	4	today	today	NOUN
ap-1805	254	5	(	(	PUNCT
ap-1805	254	6	russian	russian	PROPN
ap-1805	254	7	)	)	PUNCT
ap-1805	254	8	,	,	PUNCT
ap-1805	254	9	pp	pp	ADP
ap-1805	254	10	.	.	PUNCT
ap-1805	255	1	135–213	135–213	NUM
ap-1805	255	2	.	.	PUNCT
ap-1805	256	1	nezavis	nezavis	PROPN
ap-1805	256	2	.	.	PUNCT
ap-1805	257	1	mosk	mosk	PROPN
ap-1805	257	2	.	.	PUNCT
ap-1805	258	1	univ	univ	PROPN
ap-1805	258	2	.	.	PROPN
ap-1805	258	3	,	,	PUNCT
ap-1805	258	4	moscow	moscow	PROPN
ap-1805	258	5	,	,	PUNCT
ap-1805	258	6	2003	2003	NUM
ap-1805	258	7	.	.	PUNCT
ap-1805	259	1	[	[	X
ap-1805	259	2	9	9	NUM
ap-1805	259	3	]	]	X
ap-1805	259	4	j.	j.	PROPN
ap-1805	259	5	llibre	llibre	PROPN
ap-1805	259	6	.	.	PUNCT
ap-1805	260	1	on	on	ADP
ap-1805	260	2	the	the	DET
ap-1805	260	3	16	16	NUM
ap-1805	260	4	-	-	PUNCT
ap-1805	260	5	hilbert	hilbert	NOUN
ap-1805	260	6	problem	problem	NOUN
ap-1805	260	7	.	.	PUNCT
ap-1805	261	1	gac	gac	PROPN
ap-1805	261	2	r	r	NOUN
ap-1805	261	3	soc	soc	NOUN
ap-1805	261	4	mat	mat	NOUN
ap-1805	261	5	esp	esp	ADJ
ap-1805	261	6	preprint	preprint	NOUN
ap-1805	261	7	2012	2012	NUM
ap-1805	261	8	.	.	PUNCT
ap-1805	262	1	[	[	X
ap-1805	262	2	10	10	NUM
ap-1805	262	3	]	]	PUNCT
ap-1805	262	4	m.	m.	NOUN
ap-1805	262	5	himmel	himmel	PROPN
ap-1805	262	6	.	.	PUNCT
ap-1805	263	1	on	on	ADP
ap-1805	263	2	the	the	DET
ap-1805	263	3	existence	existence	NOUN
ap-1805	263	4	of	of	ADP
ap-1805	263	5	periodic	periodic	ADJ
ap-1805	263	6	orbits	orbit	NOUN
ap-1805	263	7	of	of	ADP
ap-1805	263	8	ordinary	ordinary	ADJ
ap-1805	263	9	differential	differential	ADJ
ap-1805	263	10	equations	equation	NOUN
ap-1805	263	11	(	(	PUNCT
ap-1805	263	12	transl	transl	PROPN
ap-1805	263	13	.	.	PUNCT
ap-1805	263	14	)	)	PUNCT
ap-1805	264	1	pp	pp	ADV
ap-1805	264	2	.	.	PUNCT
ap-1805	265	1	43–46	43–46	NUM
ap-1805	265	2	,	,	PUNCT
ap-1805	265	3	2009	2009	NUM
ap-1805	265	4	.	.	PUNCT
ap-1805	266	1	[	[	X
ap-1805	266	2	11	11	NUM
ap-1805	266	3	]	]	PUNCT
ap-1805	266	4	a.	a.	NOUN
ap-1805	266	5	a.	a.	NOUN
ap-1805	266	6	andronov	andronov	PROPN
ap-1805	266	7	,	,	PUNCT
ap-1805	266	8	et	et	PROPN
ap-1805	266	9	al	al	PROPN
ap-1805	266	10	.	.	PROPN
ap-1805	266	11	qualitative	qualitative	ADJ
ap-1805	266	12	theory	theory	NOUN
ap-1805	266	13	of	of	ADP
ap-1805	266	14	second	second	ADJ
ap-1805	266	15	-	-	PUNCT
ap-1805	266	16	order	order	NOUN
ap-1805	266	17	dynamic	dynamic	ADJ
ap-1805	266	18	systems	system	NOUN
ap-1805	266	19	.	.	PUNCT
ap-1805	267	1	halsted	halsted	ADJ
ap-1805	267	2	press	press	NOUN
ap-1805	267	3	(	(	PUNCT
ap-1805	267	4	a	a	DET
ap-1805	267	5	division	division	NOUN
ap-1805	267	6	of	of	ADP
ap-1805	267	7	john	john	PROPN
ap-1805	267	8	wiley	wiley	PROPN
ap-1805	267	9	&	&	CCONJ
ap-1805	267	10	sons	son	NOUN
ap-1805	267	11	)	)	PUNCT
ap-1805	267	12	,	,	PUNCT
ap-1805	267	13	new	new	PROPN
ap-1805	267	14	york	york	PROPN
ap-1805	267	15	-	-	PUNCT
ap-1805	267	16	toronto	toronto	PROPN
ap-1805	267	17	,	,	PUNCT
ap-1805	267	18	ont	ont	PROPN
ap-1805	267	19	.	.	PROPN
ap-1805	267	20	,	,	PUNCT
ap-1805	267	21	1973	1973	NUM
ap-1805	267	22	.	.	PUNCT
ap-1805	268	1	translated	translate	VERB
ap-1805	268	2	from	from	ADP
ap-1805	268	3	the	the	DET
ap-1805	268	4	russian	russian	NOUN
ap-1805	268	5	by	by	ADP
ap-1805	268	6	d.	d.	PROPN
ap-1805	268	7	louvish	louvish	PROPN
ap-1805	268	8	.	.	PUNCT
ap-1805	269	1	[	[	X
ap-1805	269	2	12	12	NUM
ap-1805	269	3	]	]	PUNCT
ap-1805	269	4	h.	h.	PROPN
ap-1805	269	5	p.	p.	PROPN
ap-1805	269	6	guckenheimer	guckenheimer	PROPN
ap-1805	269	7	,	,	PUNCT
ap-1805	269	8	john	john	PROPN
ap-1805	269	9	.	.	PUNCT
ap-1805	270	1	nonlinear	nonlinear	PROPN
ap-1805	270	2	oscillations	oscillation	NOUN
ap-1805	270	3	,	,	PUNCT
ap-1805	270	4	dynamical	dynamical	ADJ
ap-1805	270	5	systems	system	NOUN
ap-1805	270	6	,	,	PUNCT
ap-1805	270	7	and	and	CCONJ
ap-1805	270	8	bifurcations	bifurcation	NOUN
ap-1805	270	9	of	of	ADP
ap-1805	270	10	vector	vector	NOUN
ap-1805	270	11	fields	field	NOUN
ap-1805	270	12	.	.	PUNCT
ap-1805	271	1	springer	springer	NOUN
ap-1805	271	2	-	-	PUNCT
ap-1805	271	3	verlag	verlag	PROPN
ap-1805	271	4	.	.	PUNCT
ap-1805	272	1	[	[	X
ap-1805	272	2	13	13	NUM
ap-1805	272	3	]	]	PUNCT
ap-1805	272	4	f.	f.	PROPN
ap-1805	272	5	dumortier	dumortier	PROPN
ap-1805	272	6	,	,	PUNCT
ap-1805	272	7	et	et	PROPN
ap-1805	273	1	al	al	PROPN
ap-1805	273	2	.	.	PROPN
ap-1805	273	3	qualitative	qualitative	PROPN
ap-1805	273	4	theory	theory	NOUN
ap-1805	273	5	of	of	ADP
ap-1805	273	6	planar	planar	ADJ
ap-1805	273	7	differential	differential	NOUN
ap-1805	273	8	systems	system	NOUN
ap-1805	273	9	.	.	PUNCT
ap-1805	274	1	universitext	universitext	PROPN
ap-1805	274	2	.	.	PUNCT
ap-1805	274	3	springer	springer	NOUN
ap-1805	274	4	-	-	PUNCT
ap-1805	274	5	verlag	verlag	PROPN
ap-1805	274	6	,	,	PUNCT
ap-1805	274	7	berlin	berlin	PROPN
ap-1805	274	8	,	,	PUNCT
ap-1805	274	9	2006	2006	NUM
ap-1805	274	10	.	.	PUNCT
ap-1805	275	1	[	[	X
ap-1805	275	2	14	14	NUM
ap-1805	275	3	]	]	X
ap-1805	275	4	d.	d.	PROPN
ap-1805	275	5	a.	a.	PROPN
ap-1805	275	6	neumann	neumann	PROPN
ap-1805	275	7	.	.	PUNCT
ap-1805	276	1	classification	classification	NOUN
ap-1805	276	2	of	of	ADP
ap-1805	276	3	continuous	continuous	ADJ
ap-1805	276	4	flows	flow	NOUN
ap-1805	276	5	on	on	ADP
ap-1805	276	6	2	2	NUM
ap-1805	276	7	-	-	PUNCT
ap-1805	276	8	manifolds	manifold	NOUN
ap-1805	276	9	.	.	PUNCT
ap-1805	277	1	proc	proc	PROPN
ap-1805	277	2	amer	amer	PROPN
ap-1805	277	3	math	math	PROPN
ap-1805	277	4	soc	soc	PROPN
ap-1805	277	5	48:73–81	48:73–81	NUM
ap-1805	277	6	,	,	PUNCT
ap-1805	277	7	1975	1975	NUM
ap-1805	277	8	.	.	PUNCT
ap-1805	278	1	[	[	X
ap-1805	278	2	15	15	NUM
ap-1805	278	3	]	]	X
ap-1805	278	4	r.	r.	PROPN
ap-1805	278	5	bhatia	bhatia	PROPN
ap-1805	278	6	,	,	PUNCT
ap-1805	278	7	et	et	PROPN
ap-1805	278	8	al	al	PROPN
ap-1805	278	9	.	.	PUNCT
ap-1805	279	1	how	how	SCONJ
ap-1805	279	2	and	and	CCONJ
ap-1805	279	3	why	why	SCONJ
ap-1805	279	4	to	to	PART
ap-1805	279	5	solve	solve	VERB
ap-1805	279	6	the	the	DET
ap-1805	279	7	operator	operator	NOUN
ap-1805	279	8	equation	equation	NOUN
ap-1805	279	9	ax	ax	NOUN
ap-1805	279	10	−	−	PROPN
ap-1805	279	11	xb	xb	PROPN
ap-1805	279	12	=	=	PUNCT
ap-1805	279	13	y	y	PROPN
ap-1805	279	14	29:1–21	29:1–21	NUM
ap-1805	279	15	,	,	PUNCT
ap-1805	279	16	1997	1997	NUM
ap-1805	279	17	.	.	PUNCT
ap-1805	280	1	[	[	X
ap-1805	280	2	16	16	NUM
ap-1805	280	3	]	]	X
ap-1805	280	4	i.	i.	PROPN
ap-1805	280	5	a.	a.	PROPN
ap-1805	280	6	garcía	garcía	PROPN
ap-1805	280	7	,	,	PUNCT
ap-1805	280	8	et	et	PROPN
ap-1805	280	9	al	al	PROPN
ap-1805	280	10	.	.	PUNCT
ap-1805	281	1	a	a	DET
ap-1805	281	2	survey	survey	NOUN
ap-1805	281	3	on	on	ADP
ap-1805	281	4	the	the	DET
ap-1805	281	5	inverse	inverse	NOUN
ap-1805	281	6	integrating	integrating	NOUN
ap-1805	281	7	factor	factor	NOUN
ap-1805	281	8	.	.	PUNCT
ap-1805	282	1	qual	qual	PROPN
ap-1805	282	2	theory	theory	PROPN
ap-1805	282	3	dyn	dyn	PROPN
ap-1805	282	4	syst	syst	PROPN
ap-1805	282	5	9(1	9(1	PROPN
ap-1805	282	6	-	-	PUNCT
ap-1805	282	7	2):115–166	2):115–166	NUM
ap-1805	282	8	,	,	PUNCT
ap-1805	282	9	2010	2010	NUM
ap-1805	282	10	.	.	PUNCT
ap-1805	283	1	[	[	X
ap-1805	283	2	17	17	NUM
ap-1805	283	3	]	]	X
ap-1805	283	4	j.	j.	PROPN
ap-1805	283	5	llibre	llibre	PROPN
ap-1805	283	6	.	.	PUNCT
ap-1805	284	1	integrability	integrability	NOUN
ap-1805	284	2	of	of	ADP
ap-1805	284	3	polynomial	polynomial	ADJ
ap-1805	284	4	differential	differential	NOUN
ap-1805	284	5	systems	system	NOUN
ap-1805	284	6	.	.	PUNCT
ap-1805	285	1	in	in	ADP
ap-1805	285	2	handbook	handbook	NOUN
ap-1805	285	3	of	of	ADP
ap-1805	285	4	differential	differential	ADJ
ap-1805	285	5	equations	equation	NOUN
ap-1805	285	6	,	,	PUNCT
ap-1805	285	7	pp	pp	ADP
ap-1805	285	8	.	.	PUNCT
ap-1805	286	1	437–532	437–532	NUM
ap-1805	286	2	.	.	PUNCT
ap-1805	286	3	elsevier	elsevier	NOUN
ap-1805	286	4	/	/	SYM
ap-1805	286	5	north	north	PROPN
ap-1805	286	6	-	-	PUNCT
ap-1805	286	7	holland	holland	PROPN
ap-1805	286	8	,	,	PUNCT
ap-1805	286	9	amsterdam	amsterdam	PROPN
ap-1805	286	10	,	,	PUNCT
ap-1805	286	11	2004	2004	NUM
ap-1805	286	12	.	.	PUNCT
ap-1805	287	1	[	[	X
ap-1805	287	2	18	18	NUM
ap-1805	287	3	]	]	X
ap-1805	287	4	d.	d.	NOUN
ap-1805	287	5	schlomiuk	schlomiuk	NOUN
ap-1805	287	6	.	.	PUNCT
ap-1805	288	1	algebraic	algebraic	ADJ
ap-1805	288	2	particular	particular	ADJ
ap-1805	288	3	integrals	integral	NOUN
ap-1805	288	4	,	,	PUNCT
ap-1805	288	5	integrability	integrability	NOUN
ap-1805	288	6	and	and	CCONJ
ap-1805	288	7	the	the	DET
ap-1805	288	8	problem	problem	NOUN
ap-1805	288	9	of	of	ADP
ap-1805	288	10	the	the	DET
ap-1805	288	11	center	center	NOUN
ap-1805	288	12	.	.	PUNCT
ap-1805	289	1	trans	trans	PROPN
ap-1805	289	2	amer	amer	PROPN
ap-1805	289	3	math	math	PROPN
ap-1805	289	4	soc	soc	PROPN
ap-1805	289	5	338(2):799–841	338(2):799–841	PROPN
ap-1805	289	6	,	,	PUNCT
ap-1805	289	7	1993	1993	NUM
ap-1805	289	8	.	.	PUNCT
ap-1805	290	1	[	[	X
ap-1805	290	2	19	19	NUM
ap-1805	290	3	]	]	X
ap-1805	290	4	d.	d.	NOUN
ap-1805	290	5	schlomiuk	schlomiuk	NOUN
ap-1805	290	6	.	.	PUNCT
ap-1805	291	1	algebraic	algebraic	ADJ
ap-1805	291	2	and	and	CCONJ
ap-1805	291	3	geometric	geometric	ADJ
ap-1805	291	4	aspects	aspect	NOUN
ap-1805	291	5	of	of	ADP
ap-1805	291	6	the	the	DET
ap-1805	291	7	theory	theory	NOUN
ap-1805	291	8	of	of	ADP
ap-1805	291	9	polynomial	polynomial	ADJ
ap-1805	291	10	vector	vector	NOUN
ap-1805	291	11	fields	field	NOUN
ap-1805	291	12	.	.	PUNCT
ap-1805	292	1	in	in	ADP
ap-1805	292	2	bifurcations	bifurcation	NOUN
ap-1805	292	3	and	and	CCONJ
ap-1805	292	4	periodic	periodic	ADJ
ap-1805	292	5	orbits	orbit	NOUN
ap-1805	292	6	of	of	ADP
ap-1805	292	7	vector	vector	NOUN
ap-1805	292	8	fields	field	NOUN
ap-1805	292	9	(	(	PUNCT
ap-1805	292	10	montreal	montreal	PROPN
ap-1805	292	11	,	,	PUNCT
ap-1805	292	12	pq	pq	PROPN
ap-1805	292	13	,	,	PUNCT
ap-1805	292	14	1992	1992	NUM
ap-1805	292	15	)	)	PUNCT
ap-1805	292	16	,	,	PUNCT
ap-1805	292	17	vol	vol	NOUN
ap-1805	292	18	.	.	PROPN
ap-1805	293	1	408	408	NUM
ap-1805	293	2	of	of	ADP
ap-1805	293	3	nato	nato	PROPN
ap-1805	293	4	adv	adv	PROPN
ap-1805	293	5	.	.	PUNCT
ap-1805	294	1	sci	sci	PROPN
ap-1805	294	2	.	.	PROPN
ap-1805	294	3	inst	inst	PROPN
ap-1805	294	4	.	.	PUNCT
ap-1805	295	1	ser	ser	PROPN
ap-1805	295	2	.	.	PUNCT
ap-1805	296	1	c	c	PROPN
ap-1805	296	2	math	math	NOUN
ap-1805	296	3	.	.	PUNCT
ap-1805	297	1	phys	phy	NOUN
ap-1805	297	2	.	.	PUNCT
ap-1805	298	1	sci	sci	PROPN
ap-1805	298	2	.	.	PROPN
ap-1805	298	3	,	,	PUNCT
ap-1805	298	4	pp	pp	ADJ
ap-1805	298	5	.	.	PUNCT
ap-1805	299	1	429–467	429–467	NUM
ap-1805	299	2	.	.	PUNCT
ap-1805	299	3	kluwer	kluwer	PROPN
ap-1805	299	4	acad	acad	PROPN
ap-1805	299	5	.	.	PUNCT
ap-1805	300	1	publ	publ	PROPN
ap-1805	300	2	.	.	PUNCT
ap-1805	300	3	,	,	PUNCT
ap-1805	300	4	dordrecht	dordrecht	PROPN
ap-1805	300	5	,	,	PUNCT
ap-1805	300	6	1993	1993	NUM
ap-1805	300	7	.	.	PUNCT
ap-1805	301	1	288	288	NUM
ap-1805	301	2	acta	acta	PROPN
ap-1805	301	3	polytechnica	polytechnica	PROPN
ap-1805	301	4	53(3):283–288	53(3):283–288	PROPN
ap-1805	301	5	,	,	PUNCT
ap-1805	301	6	2013	2013	NUM
ap-1805	301	7	1	1	NUM
ap-1805	301	8	introduction	introduction	NOUN
ap-1805	301	9	and	and	CCONJ
ap-1805	301	10	motivation	motivation	NOUN
ap-1805	301	11	1.1	1.1	NUM
ap-1805	301	12	sixteenth	sixteenth	ADJ
ap-1805	301	13	hilbert	hilbert	PROPN
ap-1805	301	14	problem	problem	NOUN
ap-1805	301	15	1.2	1.2	NUM
ap-1805	301	16	dulac	dulac	PROPN
ap-1805	301	17	criterion	criterion	NOUN
ap-1805	301	18	2	2	NUM
ap-1805	301	19	local	local	ADJ
ap-1805	301	20	results	result	NOUN
ap-1805	301	21	3	3	NUM
ap-1805	301	22	qualitative	qualitative	NOUN
ap-1805	301	23	theory	theory	NOUN
ap-1805	301	24	4	4	NUM
ap-1805	301	25	a	a	DET
ap-1805	301	26	unifying	unifying	ADJ
ap-1805	301	27	point	point	NOUN
ap-1805	301	28	of	of	ADP
ap-1805	301	29	view	view	NOUN
ap-1805	301	30	5	5	NUM
ap-1805	301	31	open	open	ADJ
ap-1805	301	32	questions	question	NOUN
ap-1805	301	33	references	reference	NOUN