id	sid	tid	token	lemma	pos
ijassa-2051	1	1	adv	adv	PROPN
ijassa-2051	1	2	syst	syst	PROPN
ijassa-2051	1	3	sci	sci	PROPN
ijassa-2051	1	4	appl	appl	PROPN
ijassa-2051	1	5	2025	2025	NUM
ijassa-2051	1	6	;	;	PUNCT
ijassa-2051	1	7	02:92–104	02:92–104	NOUN
ijassa-2051	1	8	published	publish	VERB
ijassa-2051	1	9	online	online	ADV
ijassa-2051	1	10	at	at	ADP
ijassa-2051	1	11	https://ijassa.ipu.ru	https://ijassa.ipu.ru	ADV
ijassa-2051	1	12	.	.	PUNCT
ijassa-2051	2	1	vector	vector	NOUN
ijassa-2051	2	2	fields	field	NOUN
ijassa-2051	2	3	with	with	ADP
ijassa-2051	2	4	non	non	ADJ
ijassa-2051	2	5	-	-	ADJ
ijassa-2051	2	6	isolated	isolated	ADJ
ijassa-2051	2	7	singular	singular	NOUN
ijassa-2051	2	8	points	point	NOUN
ijassa-2051	2	9	viewed	view	VERB
ijassa-2051	2	10	from	from	ADP
ijassa-2051	2	11	the	the	DET
ijassa-2051	2	12	inside	inside	NOUN
ijassa-2051	2	13	and	and	CCONJ
ijassa-2051	2	14	outside	outside	ADP
ijassa-2051	2	15	natalia	natalia	PROPN
ijassa-2051	2	16	pavlova1,2	pavlova1,2	PROPN
ijassa-2051	2	17	alexey	alexey	PROPN
ijassa-2051	2	18	remizov1	remizov1	PROPN
ijassa-2051	2	19	*	*	PROPN
ijassa-2051	2	20	1moscow	1moscow	PROPN
ijassa-2051	2	21	institute	institute	PROPN
ijassa-2051	2	22	of	of	ADP
ijassa-2051	2	23	physics	physics	PROPN
ijassa-2051	2	24	and	and	CCONJ
ijassa-2051	2	25	technology	technology	NOUN
ijassa-2051	2	26	(	(	PUNCT
ijassa-2051	2	27	state	state	NOUN
ijassa-2051	2	28	university	university	NOUN
ijassa-2051	2	29	)	)	PUNCT
ijassa-2051	2	30	,	,	PUNCT
ijassa-2051	2	31	dolgoprudnyi	dolgoprudnyi	PROPN
ijassa-2051	2	32	,	,	PUNCT
ijassa-2051	2	33	russia	russia	PROPN
ijassa-2051	2	34	2rudn	2rudn	NUM
ijassa-2051	2	35	university	university	NOUN
ijassa-2051	2	36	,	,	PUNCT
ijassa-2051	2	37	moscow	moscow	PROPN
ijassa-2051	2	38	,	,	PUNCT
ijassa-2051	2	39	russia	russia	PROPN
ijassa-2051	2	40	abstract	abstract	NOUN
ijassa-2051	2	41	:	:	PUNCT
ijassa-2051	2	42	we	we	PRON
ijassa-2051	2	43	present	present	VERB
ijassa-2051	2	44	a	a	DET
ijassa-2051	2	45	brief	brief	ADJ
ijassa-2051	2	46	survey	survey	NOUN
ijassa-2051	2	47	of	of	ADP
ijassa-2051	2	48	recent	recent	ADJ
ijassa-2051	2	49	results	result	NOUN
ijassa-2051	2	50	about	about	ADP
ijassa-2051	2	51	vector	vector	NOUN
ijassa-2051	2	52	fields	field	NOUN
ijassa-2051	2	53	with	with	ADP
ijassa-2051	2	54	non	non	ADJ
ijassa-2051	2	55	-	-	ADJ
ijassa-2051	2	56	isolated	isolated	ADJ
ijassa-2051	2	57	singular	singular	ADJ
ijassa-2051	2	58	points	point	NOUN
ijassa-2051	2	59	and	and	CCONJ
ijassa-2051	2	60	their	their	PRON
ijassa-2051	2	61	applications	application	NOUN
ijassa-2051	2	62	.	.	PUNCT
ijassa-2051	3	1	one	one	NUM
ijassa-2051	3	2	of	of	ADP
ijassa-2051	3	3	the	the	DET
ijassa-2051	3	4	most	most	ADV
ijassa-2051	3	5	interesting	interesting	ADJ
ijassa-2051	3	6	and	and	CCONJ
ijassa-2051	3	7	promising	promising	ADJ
ijassa-2051	3	8	application	application	NOUN
ijassa-2051	3	9	is	be	AUX
ijassa-2051	3	10	connected	connect	VERB
ijassa-2051	3	11	with	with	ADP
ijassa-2051	3	12	quasi	quasi	ADJ
ijassa-2051	3	13	-	-	ADJ
ijassa-2051	3	14	linear	linear	ADJ
ijassa-2051	3	15	differential	differential	ADJ
ijassa-2051	3	16	equations	equation	NOUN
ijassa-2051	3	17	of	of	ADP
ijassa-2051	3	18	the	the	DET
ijassa-2051	3	19	second	second	ADJ
ijassa-2051	3	20	order	order	NOUN
ijassa-2051	3	21	,	,	PUNCT
ijassa-2051	3	22	including	include	VERB
ijassa-2051	3	23	the	the	DET
ijassa-2051	3	24	equation	equation	NOUN
ijassa-2051	3	25	of	of	ADP
ijassa-2051	3	26	geodesics	geodesic	NOUN
ijassa-2051	3	27	in	in	ADP
ijassa-2051	3	28	signature	signature	NOUN
ijassa-2051	3	29	varying	vary	VERB
ijassa-2051	3	30	(	(	PUNCT
ijassa-2051	3	31	pseudo	pseudo	NOUN
ijassa-2051	3	32	-	-	ADJ
ijassa-2051	3	33	riemannian	riemannian	ADJ
ijassa-2051	3	34	)	)	PUNCT
ijassa-2051	3	35	metrics	metric	NOUN
ijassa-2051	3	36	.	.	PUNCT
ijassa-2051	4	1	keywords	keyword	NOUN
ijassa-2051	4	2	:	:	PUNCT
ijassa-2051	4	3	vector	vector	NOUN
ijassa-2051	4	4	fields	field	NOUN
ijassa-2051	4	5	,	,	PUNCT
ijassa-2051	4	6	singular	singular	ADJ
ijassa-2051	4	7	points	point	NOUN
ijassa-2051	4	8	,	,	PUNCT
ijassa-2051	4	9	center	center	NOUN
ijassa-2051	4	10	manifold	manifold	ADJ
ijassa-2051	4	11	,	,	PUNCT
ijassa-2051	4	12	normal	normal	ADJ
ijassa-2051	4	13	forms	form	NOUN
ijassa-2051	4	14	,	,	PUNCT
ijassa-2051	4	15	resonances	resonance	NOUN
ijassa-2051	4	16	1	1	NUM
ijassa-2051	4	17	.	.	PUNCT
ijassa-2051	5	1	introduction	introduction	NOUN
ijassa-2051	5	2	we	we	PRON
ijassa-2051	5	3	start	start	VERB
ijassa-2051	5	4	with	with	ADP
ijassa-2051	5	5	a	a	DET
ijassa-2051	5	6	general	general	ADJ
ijassa-2051	5	7	construction	construction	NOUN
ijassa-2051	5	8	,	,	PUNCT
ijassa-2051	5	9	which	which	PRON
ijassa-2051	5	10	naturally	naturally	ADV
ijassa-2051	5	11	leads	lead	VERB
ijassa-2051	5	12	us	we	PRON
ijassa-2051	5	13	to	to	ADP
ijassa-2051	5	14	vector	vector	NOUN
ijassa-2051	5	15	field	field	NOUN
ijassa-2051	5	16	with	with	ADP
ijassa-2051	5	17	non	non	ADJ
ijassa-2051	5	18	-	-	ADJ
ijassa-2051	5	19	isplated	isplated	ADJ
ijassa-2051	5	20	singular	singular	ADJ
ijassa-2051	5	21	points	point	NOUN
ijassa-2051	5	22	(	(	PUNCT
ijassa-2051	5	23	more	more	ADV
ijassa-2051	5	24	precisely	precisely	ADV
ijassa-2051	5	25	,	,	PUNCT
ijassa-2051	5	26	singular	singular	ADJ
ijassa-2051	5	27	points	point	NOUN
ijassa-2051	5	28	fill	fill	VERB
ijassa-2051	5	29	a	a	DET
ijassa-2051	5	30	manifols	manifol	NOUN
ijassa-2051	5	31	of	of	ADP
ijassa-2051	5	32	codimension	codimension	NOUN
ijassa-2051	5	33	two	two	NUM
ijassa-2051	5	34	in	in	ADP
ijassa-2051	5	35	the	the	DET
ijassa-2051	5	36	phase	phase	NOUN
ijassa-2051	5	37	space	space	NOUN
ijassa-2051	5	38	)	)	PUNCT
ijassa-2051	5	39	.	.	PUNCT
ijassa-2051	6	1	let	let	VERB
ijassa-2051	6	2	m	m	PRON
ijassa-2051	6	3	be	be	AUX
ijassa-2051	6	4	a	a	DET
ijassa-2051	6	5	real	real	ADJ
ijassa-2051	6	6	smooth	smooth	ADJ
ijassa-2051	6	7	(	(	PUNCT
ijassa-2051	6	8	c∞	c∞	NOUN
ijassa-2051	6	9	)	)	PUNCT
ijassa-2051	6	10	manifold	manifold	NOUN
ijassa-2051	6	11	of	of	ADP
ijassa-2051	6	12	dimension	dimension	NOUN
ijassa-2051	6	13	n+	n+	PUNCT
ijassa-2051	7	1	2	2	X
ijassa-2051	7	2	.	.	PUNCT
ijassa-2051	7	3	here	here	ADV
ijassa-2051	7	4	and	and	CCONJ
ijassa-2051	7	5	further	far	ADV
ijassa-2051	7	6	we	we	PRON
ijassa-2051	7	7	use	use	VERB
ijassa-2051	7	8	the	the	DET
ijassa-2051	7	9	following	following	ADJ
ijassa-2051	7	10	standard	standard	ADJ
ijassa-2051	7	11	notations	notation	NOUN
ijassa-2051	7	12	:	:	PUNCT
ijassa-2051	7	13	•	•	NUM
ijassa-2051	7	14	c∞(m	c∞(m	NOUN
ijassa-2051	7	15	)	)	PUNCT
ijassa-2051	7	16	is	be	AUX
ijassa-2051	7	17	the	the	DET
ijassa-2051	7	18	ring	ring	NOUN
ijassa-2051	7	19	of	of	ADP
ijassa-2051	7	20	smooth	smooth	ADJ
ijassa-2051	7	21	functions	function	NOUN
ijassa-2051	7	22	on	on	ADP
ijassa-2051	7	23	m	m	PROPN
ijassa-2051	7	24	•	•	ADP
ijassa-2051	7	25	γ(tm	γ(tm	NOUN
ijassa-2051	7	26	)	)	PUNCT
ijassa-2051	7	27	is	be	AUX
ijassa-2051	7	28	the	the	DET
ijassa-2051	7	29	module	module	NOUN
ijassa-2051	7	30	of	of	ADP
ijassa-2051	7	31	smooth	smooth	ADJ
ijassa-2051	7	32	vector	vector	NOUN
ijassa-2051	7	33	fields	field	NOUN
ijassa-2051	7	34	on	on	ADP
ijassa-2051	7	35	m	m	PROPN
ijassa-2051	7	36	•	•	ADJ
ijassa-2051	7	37	γ(t	γ(t	NOUN
ijassa-2051	7	38	∗m	∗m	NOUN
ijassa-2051	7	39	)	)	PUNCT
ijassa-2051	7	40	is	be	AUX
ijassa-2051	7	41	the	the	DET
ijassa-2051	7	42	module	module	NOUN
ijassa-2051	7	43	of	of	ADP
ijassa-2051	7	44	smooth	smooth	ADJ
ijassa-2051	7	45	covector	covector	NOUN
ijassa-2051	7	46	fields	field	NOUN
ijassa-2051	7	47	(	(	PUNCT
ijassa-2051	7	48	1	1	NUM
ijassa-2051	7	49	-	-	PUNCT
ijassa-2051	7	50	forms	form	NOUN
ijassa-2051	7	51	)	)	PUNCT
ijassa-2051	7	52	on	on	ADP
ijassa-2051	7	53	m	m	PROPN
ijassa-2051	7	54	consider	consider	VERB
ijassa-2051	7	55	a	a	DET
ijassa-2051	7	56	distribution	distribution	NOUN
ijassa-2051	7	57	on	on	ADP
ijassa-2051	7	58	m	m	VERB
ijassa-2051	7	59	defined	define	VERB
ijassa-2051	7	60	via	via	ADP
ijassa-2051	7	61	n+	n+	NUM
ijassa-2051	7	62	1	1	NUM
ijassa-2051	7	63	differential	differential	NOUN
ijassa-2051	7	64	1	1	NUM
ijassa-2051	7	65	-	-	PUNCT
ijassa-2051	7	66	forms	form	NOUN
ijassa-2051	7	67	:	:	PUNCT
ijassa-2051	7	68	ω1	ω1	PROPN
ijassa-2051	7	69	=	=	SYM
ijassa-2051	7	70	0	0	PROPN
ijassa-2051	7	71	,	,	PUNCT
ijassa-2051	7	72	.	.	PUNCT
ijassa-2051	7	73	.	.	PUNCT
ijassa-2051	8	1	.	.	PUNCT
ijassa-2051	9	1	,	,	PUNCT
ijassa-2051	9	2	ωn+1	ωn+1	NUM
ijassa-2051	9	3	=	=	SYM
ijassa-2051	9	4	0	0	NUM
ijassa-2051	9	5	,	,	PUNCT
ijassa-2051	9	6	ωi	ωi	NUM
ijassa-2051	9	7	∈	∈	PROPN
ijassa-2051	9	8	γ(t	γ(t	PROPN
ijassa-2051	9	9	∗m	∗m	NOUN
ijassa-2051	9	10	)	)	PUNCT
ijassa-2051	9	11	.	.	PUNCT
ijassa-2051	10	1	(	(	PUNCT
ijassa-2051	10	2	1.1	1.1	NUM
ijassa-2051	10	3	)	)	PUNCT
ijassa-2051	10	4	at	at	ADP
ijassa-2051	10	5	points	point	NOUN
ijassa-2051	10	6	of	of	ADP
ijassa-2051	10	7	m	m	PRON
ijassa-2051	10	8	where	where	SCONJ
ijassa-2051	10	9	the	the	DET
ijassa-2051	10	10	1	1	NUM
ijassa-2051	10	11	-	-	PUNCT
ijassa-2051	10	12	forms	form	NOUN
ijassa-2051	10	13	ω1	ω1	NOUN
ijassa-2051	10	14	,	,	PUNCT
ijassa-2051	10	15	.	.	PUNCT
ijassa-2051	10	16	.	.	PUNCT
ijassa-2051	10	17	.	.	PUNCT
ijassa-2051	11	1	,	,	PUNCT
ijassa-2051	11	2	ωn+1	ωn+1	NUM
ijassa-2051	11	3	are	be	AUX
ijassa-2051	11	4	linearly	linearly	ADV
ijassa-2051	11	5	independent	independent	ADJ
ijassa-2051	11	6	,	,	PUNCT
ijassa-2051	11	7	system	system	NOUN
ijassa-2051	11	8	(	(	PUNCT
ijassa-2051	11	9	1.1	1.1	NUM
ijassa-2051	11	10	)	)	PUNCT
ijassa-2051	11	11	defines	define	VERB
ijassa-2051	11	12	a	a	DET
ijassa-2051	11	13	one	one	NUM
ijassa-2051	11	14	-	-	PUNCT
ijassa-2051	11	15	dimensional	dimensional	ADJ
ijassa-2051	11	16	distribution	distribution	NOUN
ijassa-2051	11	17	,	,	PUNCT
ijassa-2051	11	18	that	that	ADV
ijassa-2051	11	19	is	is	ADV
ijassa-2051	11	20	,	,	PUNCT
ijassa-2051	11	21	a	a	DET
ijassa-2051	11	22	direction	direction	NOUN
ijassa-2051	11	23	field	field	NOUN
ijassa-2051	11	24	,	,	PUNCT
ijassa-2051	11	25	which	which	PRON
ijassa-2051	11	26	can	can	AUX
ijassa-2051	11	27	be	be	AUX
ijassa-2051	11	28	a	a	DET
ijassa-2051	11	29	class	class	NOUN
ijassa-2051	11	30	of	of	ADP
ijassa-2051	11	31	collinear	collinear	ADJ
ijassa-2051	11	32	vector	vector	NOUN
ijassa-2051	11	33	fields	field	NOUN
ijassa-2051	11	34	,	,	PUNCT
ijassa-2051	11	35	such	such	ADJ
ijassa-2051	11	36	points	point	NOUN
ijassa-2051	11	37	we	we	PRON
ijassa-2051	11	38	shall	shall	AUX
ijassa-2051	11	39	call	call	VERB
ijassa-2051	11	40	regular	regular	ADV
ijassa-2051	11	41	.	.	PUNCT
ijassa-2051	12	1	at	at	ADP
ijassa-2051	12	2	points	point	NOUN
ijassa-2051	12	3	of	of	ADP
ijassa-2051	12	4	m	m	PRON
ijassa-2051	12	5	where	where	SCONJ
ijassa-2051	12	6	the	the	DET
ijassa-2051	12	7	1	1	NUM
ijassa-2051	12	8	-	-	PUNCT
ijassa-2051	12	9	forms	form	NOUN
ijassa-2051	12	10	ω1	ω1	NOUN
ijassa-2051	12	11	,	,	PUNCT
ijassa-2051	12	12	.	.	PUNCT
ijassa-2051	12	13	.	.	PUNCT
ijassa-2051	12	14	.	.	PUNCT
ijassa-2051	13	1	,	,	PUNCT
ijassa-2051	13	2	ωn+1	ωn+1	NUM
ijassa-2051	13	3	are	be	AUX
ijassa-2051	13	4	nor	nor	CCONJ
ijassa-2051	13	5	linearly	linearly	ADV
ijassa-2051	13	6	independent	independent	ADJ
ijassa-2051	13	7	,	,	PUNCT
ijassa-2051	13	8	the	the	DET
ijassa-2051	13	9	distribution	distribution	NOUN
ijassa-2051	13	10	has	have	AUX
ijassa-2051	13	11	dimension	dimension	VERB
ijassa-2051	13	12	greater	great	ADJ
ijassa-2051	13	13	then	then	ADP
ijassa-2051	13	14	1	1	NUM
ijassa-2051	13	15	,	,	PUNCT
ijassa-2051	13	16	such	such	ADJ
ijassa-2051	13	17	points	point	NOUN
ijassa-2051	13	18	we	we	PRON
ijassa-2051	13	19	shall	shall	AUX
ijassa-2051	13	20	call	call	VERB
ijassa-2051	13	21	singular	singular	NOUN
ijassa-2051	13	22	.	.	PUNCT
ijassa-2051	14	1	in	in	ADP
ijassa-2051	14	2	(	(	PUNCT
ijassa-2051	14	3	local	local	ADJ
ijassa-2051	14	4	)	)	PUNCT
ijassa-2051	14	5	coordinates	coordinate	VERB
ijassa-2051	14	6	u	u	NOUN
ijassa-2051	14	7	=	=	PUNCT
ijassa-2051	14	8	(	(	PUNCT
ijassa-2051	14	9	u1	u1	PROPN
ijassa-2051	14	10	,	,	PUNCT
ijassa-2051	14	11	.	.	PUNCT
ijassa-2051	14	12	.	.	PUNCT
ijassa-2051	14	13	.	.	PUNCT
ijassa-2051	15	1	,	,	PUNCT
ijassa-2051	15	2	un+2	un+2	X
ijassa-2051	15	3	)	)	PUNCT
ijassa-2051	15	4	on	on	ADP
ijassa-2051	15	5	m	m	PROPN
ijassa-2051	15	6	system	system	NOUN
ijassa-2051	15	7	(	(	PUNCT
ijassa-2051	15	8	1.1	1.1	NUM
ijassa-2051	15	9	)	)	PUNCT
ijassa-2051	15	10	yields	yield	VERB
ijassa-2051	15	11	the	the	DET
ijassa-2051	15	12	pfaffian	pfaffian	ADJ
ijassa-2051	15	13	system	system	NOUN
ijassa-2051	15	14	ωi	ωi	NOUN
ijassa-2051	15	15	=	=	SYM
ijassa-2051	15	16	n+2∑	n+2∑	PROPN
ijassa-2051	15	17	j=1	j=1	PROPN
ijassa-2051	15	18	ωij(u	ωij(u	PROPN
ijassa-2051	15	19	)	)	PUNCT
ijassa-2051	15	20	duj	duj	NOUN
ijassa-2051	15	21	=	=	SYM
ijassa-2051	15	22	0	0	NUM
ijassa-2051	15	23	,	,	PUNCT
ijassa-2051	15	24	i	i	PRON
ijassa-2051	15	25	=	=	NOUN
ijassa-2051	15	26	1	1	NUM
ijassa-2051	15	27	,	,	PUNCT
ijassa-2051	15	28	.	.	PUNCT
ijassa-2051	15	29	.	.	PUNCT
ijassa-2051	16	1	.	.	PUNCT
ijassa-2051	17	1	,	,	PUNCT
ijassa-2051	17	2	n+	n+	ADP
ijassa-2051	17	3	1	1	NUM
ijassa-2051	17	4	,	,	PUNCT
ijassa-2051	17	5	(	(	PUNCT
ijassa-2051	17	6	1.2	1.2	NUM
ijassa-2051	17	7	)	)	PUNCT
ijassa-2051	17	8	with	with	ADP
ijassa-2051	17	9	(	(	PUNCT
ijassa-2051	17	10	n+	n+	NUM
ijassa-2051	17	11	1)×	1)×	NUM
ijassa-2051	17	12	(	(	PUNCT
ijassa-2051	17	13	n+	n+	NOUN
ijassa-2051	17	14	2	2	NUM
ijassa-2051	17	15	)	)	PUNCT
ijassa-2051	17	16	matrix	matrix	NOUN
ijassa-2051	17	17	ω	ω	NOUN
ijassa-2051	17	18	=	=	SYM
ijassa-2051	17	19	(	(	PUNCT
ijassa-2051	17	20	ωij	ωij	PROPN
ijassa-2051	17	21	)	)	PUNCT
ijassa-2051	17	22	.	.	PUNCT
ijassa-2051	18	1	∗corresponding	∗corresponde	VERB
ijassa-2051	18	2	author	author	NOUN
ijassa-2051	18	3	:	:	PUNCT
ijassa-2051	18	4	alexey-remizov@yandex.ru	alexey-remizov@yandex.ru	NUM
ijassa-2051	18	5	vector	vector	NOUN
ijassa-2051	18	6	fields	field	NOUN
ijassa-2051	18	7	with	with	ADP
ijassa-2051	18	8	non	non	ADJ
ijassa-2051	18	9	-	-	ADJ
ijassa-2051	18	10	isolated	isolated	ADJ
ijassa-2051	18	11	singular	singular	ADJ
ijassa-2051	18	12	points	point	NOUN
ijassa-2051	18	13	...	...	PUNCT
ijassa-2051	18	14	93	93	NUM
ijassa-2051	18	15	singular	singular	ADJ
ijassa-2051	18	16	points	point	NOUN
ijassa-2051	18	17	fill	fill	VERB
ijassa-2051	18	18	a	a	DET
ijassa-2051	18	19	stratified	stratified	ADJ
ijassa-2051	18	20	manifold	manifold	ADJ
ijassa-2051	18	21	σ	σ	PROPN
ijassa-2051	18	22	⊂	⊂	PROPN
ijassa-2051	18	23	m	m	VERB
ijassa-2051	18	24	that	that	SCONJ
ijassa-2051	18	25	consists	consist	VERB
ijassa-2051	18	26	of	of	ADP
ijassa-2051	18	27	the	the	DET
ijassa-2051	18	28	strata	strata	NOUN
ijassa-2051	18	29	σi	σi	NOUN
ijassa-2051	18	30	=	=	PUNCT
ijassa-2051	18	31	{	{	PUNCT
ijassa-2051	18	32	u	u	NOUN
ijassa-2051	18	33	∈	∈	PROPN
ijassa-2051	18	34	m	m	VERB
ijassa-2051	18	35	:	:	PUNCT
ijassa-2051	18	36	rg	rg	PROPN
ijassa-2051	18	37	ω(u	ω(u	PROPN
ijassa-2051	18	38	)	)	PUNCT
ijassa-2051	18	39	=	=	PUNCT
ijassa-2051	18	40	(	(	PUNCT
ijassa-2051	18	41	n+	n+	NUM
ijassa-2051	18	42	1)−	1)−	NUM
ijassa-2051	18	43	i	i	NOUN
ijassa-2051	18	44	}	}	PUNCT
ijassa-2051	18	45	,	,	PUNCT
ijassa-2051	18	46	i	i	PRON
ijassa-2051	18	47	=	=	NOUN
ijassa-2051	18	48	1	1	NUM
ijassa-2051	18	49	,	,	PUNCT
ijassa-2051	18	50	.	.	PUNCT
ijassa-2051	18	51	.	.	PUNCT
ijassa-2051	18	52	.	.	PUNCT
ijassa-2051	19	1	,	,	PUNCT
ijassa-2051	19	2	n+	n+	PUNCT
ijassa-2051	20	1	1	1	X
ijassa-2051	20	2	.	.	PUNCT
ijassa-2051	20	3	the	the	DET
ijassa-2051	20	4	dimension	dimension	NOUN
ijassa-2051	20	5	of	of	ADP
ijassa-2051	20	6	σi	σi	PROPN
ijassa-2051	20	7	decreases	decrease	VERB
ijassa-2051	20	8	rapidly	rapidly	ADV
ijassa-2051	20	9	with	with	ADP
ijassa-2051	20	10	increasing	increase	VERB
ijassa-2051	20	11	i	i	PRON
ijassa-2051	20	12	,	,	PUNCT
ijassa-2051	20	13	namely	namely	ADV
ijassa-2051	20	14	:	:	PUNCT
ijassa-2051	20	15	codimσi	codimσi	NOUN
ijassa-2051	20	16	=	=	PUNCT
ijassa-2051	20	17	i(i+	i(i+	ADJ
ijassa-2051	20	18	1	1	NUM
ijassa-2051	20	19	)	)	PUNCT
ijassa-2051	20	20	;	;	PUNCT
ijassa-2051	20	21	see	see	VERB
ijassa-2051	20	22	,	,	PUNCT
ijassa-2051	20	23	for	for	ADP
ijassa-2051	20	24	example	example	NOUN
ijassa-2051	20	25	,	,	PUNCT
ijassa-2051	20	26	[	[	X
ijassa-2051	20	27	2	2	NUM
ijassa-2051	20	28	]	]	PUNCT
ijassa-2051	20	29	.	.	PUNCT
ijassa-2051	21	1	the	the	DET
ijassa-2051	21	2	maximal	maximal	ADJ
ijassa-2051	21	3	stratum	stratum	NOUN
ijassa-2051	21	4	σ1	σ1	PROPN
ijassa-2051	21	5	of	of	ADP
ijassa-2051	21	6	codimension	codimension	NOUN
ijassa-2051	21	7	2	2	NUM
ijassa-2051	21	8	is	be	AUX
ijassa-2051	21	9	stable	stable	ADJ
ijassa-2051	21	10	with	with	ADP
ijassa-2051	21	11	respect	respect	NOUN
ijassa-2051	21	12	to	to	ADP
ijassa-2051	21	13	small	small	ADJ
ijassa-2051	21	14	perturbation	perturbation	NOUN
ijassa-2051	21	15	of	of	ADP
ijassa-2051	21	16	ωi	ωi	PROPN
ijassa-2051	21	17	,	,	PUNCT
ijassa-2051	21	18	while	while	SCONJ
ijassa-2051	21	19	the	the	DET
ijassa-2051	21	20	strata	strata	NOUN
ijassa-2051	21	21	of	of	ADP
ijassa-2051	21	22	higher	high	ADJ
ijassa-2051	21	23	codimension	codimension	NOUN
ijassa-2051	21	24	are	be	AUX
ijassa-2051	21	25	,	,	PUNCT
ijassa-2051	21	26	generally	generally	ADV
ijassa-2051	21	27	speaking	speak	VERB
ijassa-2051	21	28	,	,	PUNCT
ijassa-2051	21	29	not	not	PART
ijassa-2051	21	30	.	.	PUNCT
ijassa-2051	22	1	the	the	DET
ijassa-2051	22	2	goal	goal	NOUN
ijassa-2051	22	3	of	of	ADP
ijassa-2051	22	4	the	the	DET
ijassa-2051	22	5	paper	paper	NOUN
ijassa-2051	22	6	is	be	AUX
ijassa-2051	22	7	to	to	PART
ijassa-2051	22	8	study	study	VERB
ijassa-2051	22	9	integral	integral	ADJ
ijassa-2051	22	10	curve	curve	NOUN
ijassa-2051	22	11	of	of	ADP
ijassa-2051	22	12	the	the	DET
ijassa-2051	22	13	distribution	distribution	NOUN
ijassa-2051	22	14	(	(	PUNCT
ijassa-2051	22	15	1.1	1.1	NUM
ijassa-2051	22	16	)	)	PUNCT
ijassa-2051	22	17	entering	enter	VERB
ijassa-2051	22	18	its	its	PRON
ijassa-2051	22	19	singular	singular	ADJ
ijassa-2051	22	20	points	point	NOUN
ijassa-2051	22	21	of	of	ADP
ijassa-2051	22	22	the	the	DET
ijassa-2051	22	23	maximal	maximal	ADJ
ijassa-2051	22	24	stratum	stratum	NOUN
ijassa-2051	22	25	σ1	σ1	PROPN
ijassa-2051	22	26	.	.	PUNCT
ijassa-2051	23	1	we	we	PRON
ijassa-2051	23	2	also	also	ADV
ijassa-2051	23	3	consider	consider	VERB
ijassa-2051	23	4	some	some	DET
ijassa-2051	23	5	application	application	NOUN
ijassa-2051	23	6	of	of	ADP
ijassa-2051	23	7	the	the	DET
ijassa-2051	23	8	obtained	obtain	VERB
ijassa-2051	23	9	results	result	NOUN
ijassa-2051	23	10	for	for	ADP
ijassa-2051	23	11	studying	study	VERB
ijassa-2051	23	12	singularities	singularity	NOUN
ijassa-2051	23	13	of	of	ADP
ijassa-2051	23	14	differential	differential	ADJ
ijassa-2051	23	15	equations	equation	NOUN
ijassa-2051	23	16	of	of	ADP
ijassa-2051	23	17	special	special	ADJ
ijassa-2051	23	18	types	type	NOUN
ijassa-2051	23	19	,	,	PUNCT
ijassa-2051	23	20	which	which	PRON
ijassa-2051	23	21	are	be	AUX
ijassa-2051	23	22	interesting	interesting	ADJ
ijassa-2051	23	23	due	due	ADP
ijassa-2051	23	24	to	to	ADP
ijassa-2051	23	25	various	various	ADJ
ijassa-2051	23	26	applications	application	NOUN
ijassa-2051	23	27	.	.	PUNCT
ijassa-2051	24	1	2	2	X
ijassa-2051	24	2	.	.	X
ijassa-2051	24	3	the	the	DET
ijassa-2051	24	4	main	main	ADJ
ijassa-2051	24	5	results	result	NOUN
ijassa-2051	24	6	the	the	DET
ijassa-2051	24	7	distribution	distribution	NOUN
ijassa-2051	24	8	(	(	PUNCT
ijassa-2051	24	9	1.2	1.2	NUM
ijassa-2051	24	10	)	)	PUNCT
ijassa-2051	24	11	can	can	AUX
ijassa-2051	24	12	be	be	AUX
ijassa-2051	24	13	determined	determine	VERB
ijassa-2051	24	14	(	(	PUNCT
ijassa-2051	24	15	at	at	ADP
ijassa-2051	24	16	least	least	ADJ
ijassa-2051	24	17	locally	locally	ADV
ijassa-2051	24	18	)	)	PUNCT
ijassa-2051	24	19	by	by	ADP
ijassa-2051	24	20	a	a	DET
ijassa-2051	24	21	smooth	smooth	ADJ
ijassa-2051	24	22	vector	vector	NOUN
ijassa-2051	24	23	field	field	NOUN
ijassa-2051	24	24	v̄	v̄	NOUN
ijassa-2051	24	25	∈	∈	PROPN
ijassa-2051	24	26	γ(tm	γ(tm	NOUN
ijassa-2051	24	27	)	)	PUNCT
ijassa-2051	24	28	that	that	PRON
ijassa-2051	24	29	is	be	AUX
ijassa-2051	24	30	zero	zero	NUM
ijassa-2051	24	31	at	at	ADP
ijassa-2051	24	32	points	point	NOUN
ijassa-2051	24	33	of	of	ADP
ijassa-2051	24	34	σ	σ	PROPN
ijassa-2051	24	35	.	.	PUNCT
ijassa-2051	25	1	this	this	DET
ijassa-2051	25	2	field	field	NOUN
ijassa-2051	25	3	is	be	AUX
ijassa-2051	25	4	unique	unique	ADJ
ijassa-2051	25	5	up	up	ADP
ijassa-2051	25	6	to	to	ADP
ijassa-2051	25	7	multiplying	multiply	VERB
ijassa-2051	25	8	by	by	ADP
ijassa-2051	25	9	a	a	DET
ijassa-2051	25	10	scalar	scalar	ADJ
ijassa-2051	25	11	factor	factor	NOUN
ijassa-2051	25	12	:	:	PUNCT
ijassa-2051	25	13	v̄	v̄	PROPN
ijassa-2051	25	14	=	=	SYM
ijassa-2051	25	15	n+2∑	n+2∑	PROPN
ijassa-2051	25	16	j=1	j=1	PROPN
ijassa-2051	25	17	vj(u	vj(u	NUM
ijassa-2051	25	18	)	)	PUNCT
ijassa-2051	25	19	∂	∂	PROPN
ijassa-2051	26	1	∂uj	∂uj	PROPN
ijassa-2051	26	2	,	,	PUNCT
ijassa-2051	26	3	vj	vj	PROPN
ijassa-2051	26	4	=	=	SYM
ijassa-2051	26	5	(	(	PUNCT
ijassa-2051	26	6	−1)j+1∆j	−1)j+1∆j	PROPN
ijassa-2051	26	7	,	,	PUNCT
ijassa-2051	26	8	j	j	PROPN
ijassa-2051	26	9	=	=	SYM
ijassa-2051	26	10	1	1	NUM
ijassa-2051	26	11	,	,	PUNCT
ijassa-2051	26	12	.	.	PUNCT
ijassa-2051	26	13	.	.	PUNCT
ijassa-2051	26	14	.	.	PUNCT
ijassa-2051	27	1	,	,	PUNCT
ijassa-2051	27	2	n+	n+	ADP
ijassa-2051	27	3	2	2	NUM
ijassa-2051	27	4	,	,	PUNCT
ijassa-2051	27	5	(	(	PUNCT
ijassa-2051	27	6	2.3	2.3	NUM
ijassa-2051	27	7	)	)	PUNCT
ijassa-2051	27	8	where	where	SCONJ
ijassa-2051	27	9	∆j	∆j	PROPN
ijassa-2051	27	10	is	be	AUX
ijassa-2051	27	11	the	the	DET
ijassa-2051	27	12	minor	minor	ADJ
ijassa-2051	27	13	of	of	ADP
ijassa-2051	27	14	ω	ω	NUM
ijassa-2051	27	15	obtained	obtain	VERB
ijassa-2051	27	16	by	by	ADP
ijassa-2051	27	17	elimination	elimination	NOUN
ijassa-2051	27	18	of	of	ADP
ijassa-2051	27	19	the	the	DET
ijassa-2051	27	20	j	j	PROPN
ijassa-2051	27	21	-	-	PUNCT
ijassa-2051	27	22	th	th	X
ijassa-2051	27	23	column	column	NOUN
ijassa-2051	27	24	.	.	PUNCT
ijassa-2051	28	1	example	example	NOUN
ijassa-2051	28	2	2.1	2.1	NUM
ijassa-2051	29	1	:	:	PUNCT
ijassa-2051	29	2	consider	consider	VERB
ijassa-2051	29	3	the	the	DET
ijassa-2051	29	4	lowest	low	ADJ
ijassa-2051	29	5	dimension	dimension	NOUN
ijassa-2051	29	6	case	case	NOUN
ijassa-2051	29	7	:	:	PUNCT
ijassa-2051	29	8	n	n	PROPN
ijassa-2051	29	9	=	=	SYM
ijassa-2051	29	10	1	1	X
ijassa-2051	29	11	.	.	PUNCT
ijassa-2051	30	1	then	then	ADV
ijassa-2051	30	2	the	the	DET
ijassa-2051	30	3	distribution	distribution	NOUN
ijassa-2051	30	4	(	(	PUNCT
ijassa-2051	30	5	1.2	1.2	NUM
ijassa-2051	30	6	)	)	PUNCT
ijassa-2051	30	7	in	in	ADP
ijassa-2051	30	8	3	3	NUM
ijassa-2051	30	9	-	-	PUNCT
ijassa-2051	30	10	dimensional	dimensional	ADJ
ijassa-2051	30	11	space	space	NOUN
ijassa-2051	30	12	is	be	AUX
ijassa-2051	30	13	the	the	DET
ijassa-2051	30	14	intersection	intersection	NOUN
ijassa-2051	30	15	of	of	ADP
ijassa-2051	30	16	two	two	NUM
ijassa-2051	30	17	fields	field	NOUN
ijassa-2051	30	18	of	of	ADP
ijassa-2051	30	19	planes	plane	NOUN
ijassa-2051	30	20	:	:	PUNCT
ijassa-2051	30	21	ωi	ωi	PROPN
ijassa-2051	30	22	=	=	PUNCT
ijassa-2051	30	23	ωi1du1	ωi1du1	VERB
ijassa-2051	30	24	+	+	PUNCT
ijassa-2051	30	25	ωi2du2	ωi2du2	ADJ
ijassa-2051	30	26	+	+	CCONJ
ijassa-2051	30	27	ωi3du3	ωi3du3	PUNCT
ijassa-2051	30	28	=	=	SYM
ijassa-2051	30	29	0	0	NUM
ijassa-2051	30	30	,	,	PUNCT
ijassa-2051	30	31	i	i	PRON
ijassa-2051	30	32	=	=	NOUN
ijassa-2051	30	33	1	1	NUM
ijassa-2051	30	34	,	,	PUNCT
ijassa-2051	30	35	2	2	NUM
ijassa-2051	30	36	.	.	X
ijassa-2051	30	37	here	here	ADV
ijassa-2051	30	38	ω	ω	PROPN
ijassa-2051	30	39	is	be	AUX
ijassa-2051	30	40	a	a	DET
ijassa-2051	30	41	2×	2×	NUM
ijassa-2051	30	42	3	3	NUM
ijassa-2051	30	43	matrix	matrix	NOUN
ijassa-2051	30	44	ω	ω	NOUN
ijassa-2051	30	45	=	=	SYM
ijassa-2051	30	46			PROPN
ijassa-2051	30	47	ω11	ω11	NOUN
ijassa-2051	30	48	ω12	ω12	PROPN
ijassa-2051	30	49	ω13	ω13	NUM
ijassa-2051	30	50	ω21	ω21	VERB
ijassa-2051	30	51	ω22	ω22	PROPN
ijassa-2051	30	52	ω23	ω23	PROPN
ijassa-2051	30	53			NOUN
ijassa-2051	30	54	and	and	CCONJ
ijassa-2051	30	55	v̄	v̄	NOUN
ijassa-2051	30	56	is	be	AUX
ijassa-2051	30	57	the	the	DET
ijassa-2051	30	58	vector	vector	NOUN
ijassa-2051	30	59	product	product	NOUN
ijassa-2051	30	60	of	of	ADP
ijassa-2051	30	61	its	its	PRON
ijassa-2051	30	62	columns	column	NOUN
ijassa-2051	30	63	:	:	PUNCT
ijassa-2051	30	64	v1	v1	NOUN
ijassa-2051	30	65	=	=	SYM
ijassa-2051	30	66	∣∣∣∣∣∣ω12	∣∣∣∣∣∣ω12	PRON
ijassa-2051	30	67	ω13	ω13	VERB
ijassa-2051	30	68	ω22	ω22	NOUN
ijassa-2051	30	69	ω23	ω23	PROPN
ijassa-2051	30	70	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ijassa-2051	30	71	,	,	PUNCT
ijassa-2051	30	72	v2	v2	PROPN
ijassa-2051	30	73	=	=	SYM
ijassa-2051	30	74	−	−	PROPN
ijassa-2051	30	75	∣∣∣∣∣∣ω11	∣∣∣∣∣∣ω11	NOUN
ijassa-2051	30	76	ω13	ω13	NOUN
ijassa-2051	30	77	ω21	ω21	VERB
ijassa-2051	30	78	ω23	ω23	PROPN
ijassa-2051	30	79	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ijassa-2051	30	80	,	,	PUNCT
ijassa-2051	30	81	v3	v3	PROPN
ijassa-2051	30	82	=	=	PUNCT
ijassa-2051	30	83	∣∣∣∣∣∣ω11	∣∣∣∣∣∣ω11	PROPN
ijassa-2051	30	84	ω12	ω12	NOUN
ijassa-2051	30	85	ω21	ω21	VERB
ijassa-2051	30	86	ω22	ω22	ADV
ijassa-2051	30	87	∣∣∣∣∣∣	∣∣∣∣∣∣	PROPN
ijassa-2051	30	88	.	.	PUNCT
ijassa-2051	31	1	the	the	DET
ijassa-2051	31	2	maximal	maximal	ADJ
ijassa-2051	31	3	stratum	stratum	NOUN
ijassa-2051	31	4	σ1	σ1	PROPN
ijassa-2051	31	5	is	be	AUX
ijassa-2051	31	6	defined	define	VERB
ijassa-2051	31	7	by	by	ADP
ijassa-2051	31	8	the	the	DET
ijassa-2051	31	9	condition	condition	NOUN
ijassa-2051	31	10	rg	rg	PROPN
ijassa-2051	31	11	ω	ω	PROPN
ijassa-2051	31	12	=	=	PROPN
ijassa-2051	31	13	1	1	NUM
ijassa-2051	31	14	,	,	PUNCT
ijassa-2051	31	15	that	that	ADV
ijassa-2051	31	16	is	is	ADV
ijassa-2051	31	17	,	,	PUNCT
ijassa-2051	31	18	the	the	DET
ijassa-2051	31	19	matrix	matrix	NOUN
ijassa-2051	31	20	ω	ω	NOUN
ijassa-2051	31	21	has	have	VERB
ijassa-2051	31	22	at	at	ADV
ijassa-2051	31	23	least	least	ADV
ijassa-2051	31	24	one	one	NUM
ijassa-2051	31	25	non	non	ADJ
ijassa-2051	31	26	-	-	ADJ
ijassa-2051	31	27	zero	zero	NUM
ijassa-2051	31	28	element	element	NOUN
ijassa-2051	31	29	.	.	PUNCT
ijassa-2051	32	1	without	without	ADP
ijassa-2051	32	2	loss	loss	NOUN
ijassa-2051	32	3	of	of	ADP
ijassa-2051	32	4	generality	generality	NOUN
ijassa-2051	32	5	,	,	PUNCT
ijassa-2051	32	6	assume	assume	VERB
ijassa-2051	32	7	that	that	SCONJ
ijassa-2051	32	8	ωi3	ωi3	ADV
ijassa-2051	32	9	̸=	̸=	PROPN
ijassa-2051	32	10	0	0	NUM
ijassa-2051	32	11	.	.	PUNCT
ijassa-2051	33	1	then	then	ADV
ijassa-2051	33	2	the	the	DET
ijassa-2051	33	3	equality	equality	NOUN
ijassa-2051	33	4	ωi1v1	ωi1v1	PUNCT
ijassa-2051	33	5	+	+	CCONJ
ijassa-2051	33	6	ωi2v2	ωi2v2	PROPN
ijassa-2051	33	7	+	+	SYM
ijassa-2051	33	8	ωi3v3	ωi3v3	SYM
ijassa-2051	33	9	=	=	SYM
ijassa-2051	33	10	0	0	NUM
ijassa-2051	33	11	yields	yield	VERB
ijassa-2051	33	12	the	the	DET
ijassa-2051	33	13	expression	expression	NOUN
ijassa-2051	33	14	v3	v3	PROPN
ijassa-2051	33	15	=	=	SYM
ijassa-2051	33	16	−ωi1	−ωi1	PROPN
ijassa-2051	33	17	ωi3	ωi3	X
ijassa-2051	33	18	v1	v1	PROPN
ijassa-2051	33	19	−	−	PROPN
ijassa-2051	33	20	ωi2	ωi2	NOUN
ijassa-2051	33	21	ωi3	ωi3	CCONJ
ijassa-2051	33	22	v2	v2	PROPN
ijassa-2051	33	23	,	,	PUNCT
ijassa-2051	33	24	(	(	PUNCT
ijassa-2051	33	25	2.4	2.4	NUM
ijassa-2051	33	26	)	)	PUNCT
ijassa-2051	33	27	which	which	PRON
ijassa-2051	33	28	is	be	AUX
ijassa-2051	33	29	valid	valid	ADJ
ijassa-2051	33	30	locally	locally	ADV
ijassa-2051	33	31	,	,	PUNCT
ijassa-2051	33	32	in	in	ADP
ijassa-2051	33	33	a	a	DET
ijassa-2051	33	34	neighborhood	neighborhood	NOUN
ijassa-2051	33	35	of	of	ADP
ijassa-2051	33	36	a	a	DET
ijassa-2051	33	37	point	point	NOUN
ijassa-2051	33	38	where	where	SCONJ
ijassa-2051	33	39	ωi3	ωi3	ADV
ijassa-2051	33	40	̸=	̸=	PROPN
ijassa-2051	33	41	0	0	NUM
ijassa-2051	33	42	.	.	PUNCT
ijassa-2051	34	1	expression	expression	NOUN
ijassa-2051	34	2	(	(	PUNCT
ijassa-2051	34	3	2.4	2.4	NUM
ijassa-2051	34	4	)	)	PUNCT
ijassa-2051	34	5	shows	show	VERB
ijassa-2051	34	6	that	that	SCONJ
ijassa-2051	34	7	the	the	DET
ijassa-2051	34	8	components	component	NOUN
ijassa-2051	34	9	of	of	ADP
ijassa-2051	34	10	the	the	DET
ijassa-2051	34	11	vector	vector	NOUN
ijassa-2051	34	12	field	field	NOUN
ijassa-2051	34	13	v̄	v̄	NOUN
ijassa-2051	34	14	are	be	AUX
ijassa-2051	34	15	connected	connect	VERB
ijassa-2051	34	16	by	by	ADP
ijassa-2051	34	17	functional	functional	ADJ
ijassa-2051	34	18	relations	relation	NOUN
ijassa-2051	34	19	:	:	PUNCT
ijassa-2051	34	20	in	in	ADP
ijassa-2051	34	21	a	a	DET
ijassa-2051	34	22	neighborhood	neighborhood	NOUN
ijassa-2051	34	23	of	of	ADP
ijassa-2051	34	24	a	a	DET
ijassa-2051	34	25	point	point	NOUN
ijassa-2051	34	26	of	of	ADP
ijassa-2051	34	27	σ1	σ1	NOUN
ijassa-2051	34	28	they	they	PRON
ijassa-2051	34	29	belong	belong	VERB
ijassa-2051	34	30	to	to	ADP
ijassa-2051	34	31	the	the	DET
ijassa-2051	34	32	ideal	ideal	NOUN
ijassa-2051	34	33	in	in	ADP
ijassa-2051	34	34	the	the	DET
ijassa-2051	34	35	ring	ring	NOUN
ijassa-2051	34	36	c∞(m	c∞(m	NOUN
ijassa-2051	34	37	)	)	PUNCT
ijassa-2051	34	38	generated	generate	VERB
ijassa-2051	34	39	by	by	ADP
ijassa-2051	34	40	two	two	NUM
ijassa-2051	34	41	of	of	ADP
ijassa-2051	34	42	them	they	PRON
ijassa-2051	34	43	.	.	PUNCT
ijassa-2051	35	1	the	the	DET
ijassa-2051	35	2	letter	letter	NOUN
ijassa-2051	35	3	property	property	NOUN
ijassa-2051	35	4	established	establish	VERB
ijassa-2051	35	5	for	for	ADP
ijassa-2051	35	6	n	n	NOUN
ijassa-2051	35	7	=	=	SYM
ijassa-2051	35	8	1	1	NUM
ijassa-2051	35	9	,	,	PUNCT
ijassa-2051	35	10	is	be	AUX
ijassa-2051	35	11	valid	valid	ADJ
ijassa-2051	35	12	for	for	ADP
ijassa-2051	35	13	arbitrary	arbitrary	ADJ
ijassa-2051	35	14	n	n	CCONJ
ijassa-2051	35	15	:	:	PUNCT
ijassa-2051	35	16	copyright	copyright	NOUN
ijassa-2051	35	17	©	©	PROPN
ijassa-2051	35	18	2025	2025	NUM
ijassa-2051	35	19	assa	assa	NOUN
ijassa-2051	35	20	.	.	PUNCT
ijassa-2051	36	1	adv	adv	PROPN
ijassa-2051	36	2	syst	syst	PROPN
ijassa-2051	36	3	sci	sci	PROPN
ijassa-2051	36	4	appl	appl	PROPN
ijassa-2051	36	5	(	(	PUNCT
ijassa-2051	36	6	2025	2025	NUM
ijassa-2051	36	7	)	)	PUNCT
ijassa-2051	36	8	94	94	NUM
ijassa-2051	36	9	n.	n.	NOUN
ijassa-2051	36	10	g.	g.	PROPN
ijassa-2051	36	11	pavlova	pavlova	PROPN
ijassa-2051	36	12	,	,	PUNCT
ijassa-2051	36	13	a.	a.	PROPN
ijassa-2051	36	14	o.	o.	PROPN
ijassa-2051	36	15	remizov	remizov	PROPN
ijassa-2051	36	16	lemma	lemma	PROPN
ijassa-2051	36	17	2.1	2.1	NUM
ijassa-2051	36	18	:	:	PUNCT
ijassa-2051	36	19	in	in	ADP
ijassa-2051	36	20	a	a	DET
ijassa-2051	36	21	neighborhood	neighborhood	NOUN
ijassa-2051	36	22	of	of	ADP
ijassa-2051	36	23	a	a	DET
ijassa-2051	36	24	point	point	NOUN
ijassa-2051	36	25	of	of	ADP
ijassa-2051	36	26	σ1	σ1	PROPN
ijassa-2051	36	27	,	,	PUNCT
ijassa-2051	36	28	all	all	DET
ijassa-2051	36	29	components	component	NOUN
ijassa-2051	36	30	of	of	ADP
ijassa-2051	36	31	the	the	DET
ijassa-2051	36	32	field	field	NOUN
ijassa-2051	36	33	(	(	PUNCT
ijassa-2051	36	34	2.3	2.3	NUM
ijassa-2051	36	35	)	)	PUNCT
ijassa-2051	36	36	belong	belong	VERB
ijassa-2051	36	37	to	to	ADP
ijassa-2051	36	38	the	the	DET
ijassa-2051	36	39	ideal	ideal	NOUN
ijassa-2051	36	40	(	(	PUNCT
ijassa-2051	36	41	in	in	ADP
ijassa-2051	36	42	c∞(m	c∞(m	NOUN
ijassa-2051	36	43	)	)	PUNCT
ijassa-2051	36	44	)	)	PUNCT
ijassa-2051	36	45	generated	generate	VERB
ijassa-2051	36	46	by	by	ADP
ijassa-2051	36	47	two	two	NUM
ijassa-2051	36	48	of	of	ADP
ijassa-2051	36	49	them	they	PRON
ijassa-2051	36	50	.	.	PUNCT
ijassa-2051	37	1	therefore	therefore	ADV
ijassa-2051	37	2	,	,	PUNCT
ijassa-2051	37	3	one	one	PRON
ijassa-2051	37	4	can	can	AUX
ijassa-2051	37	5	choose	choose	VERB
ijassa-2051	37	6	coordinates	coordinate	NOUN
ijassa-2051	37	7	x	x	SYM
ijassa-2051	37	8	,	,	PUNCT
ijassa-2051	37	9	y	y	PROPN
ijassa-2051	37	10	,	,	PUNCT
ijassa-2051	37	11	z	z	NOUN
ijassa-2051	37	12	=	=	SYM
ijassa-2051	37	13	(	(	PUNCT
ijassa-2051	37	14	z1	z1	PROPN
ijassa-2051	37	15	,	,	PUNCT
ijassa-2051	37	16	.	.	PUNCT
ijassa-2051	37	17	.	.	PUNCT
ijassa-2051	37	18	.	.	PUNCT
ijassa-2051	38	1	,	,	PUNCT
ijassa-2051	38	2	zn	zn	X
ijassa-2051	38	3	)	)	PUNCT
ijassa-2051	38	4	such	such	ADJ
ijassa-2051	38	5	that	that	SCONJ
ijassa-2051	38	6	the	the	DET
ijassa-2051	38	7	germ	germ	NOUN
ijassa-2051	38	8	of	of	ADP
ijassa-2051	38	9	the	the	DET
ijassa-2051	38	10	field	field	NOUN
ijassa-2051	38	11	(	(	PUNCT
ijassa-2051	38	12	2.3	2.3	NUM
ijassa-2051	38	13	)	)	PUNCT
ijassa-2051	38	14	has	have	VERB
ijassa-2051	38	15	the	the	DET
ijassa-2051	38	16	form	form	NOUN
ijassa-2051	38	17	ẋ	ẋ	PUNCT
ijassa-2051	39	1	=	=	SYM
ijassa-2051	39	2	v	v	NOUN
ijassa-2051	39	3	,	,	PUNCT
ijassa-2051	39	4	ẏ	ẏ	PROPN
ijassa-2051	39	5	=	=	SYM
ijassa-2051	39	6	w	w	PROPN
ijassa-2051	39	7	,	,	PUNCT
ijassa-2051	39	8	żi	żi	NOUN
ijassa-2051	39	9	=	=	SYM
ijassa-2051	39	10	aiv	aiv	PROPN
ijassa-2051	39	11	+	+	CCONJ
ijassa-2051	39	12	biw	biw	NOUN
ijassa-2051	39	13	,	,	PUNCT
ijassa-2051	39	14	i	i	PRON
ijassa-2051	39	15	=	=	NOUN
ijassa-2051	39	16	1	1	NUM
ijassa-2051	39	17	,	,	PUNCT
ijassa-2051	39	18	.	.	PUNCT
ijassa-2051	39	19	.	.	PUNCT
ijassa-2051	40	1	.	.	PUNCT
ijassa-2051	41	1	,	,	PUNCT
ijassa-2051	41	2	n	n	CCONJ
ijassa-2051	41	3	,	,	PUNCT
ijassa-2051	41	4	(	(	PUNCT
ijassa-2051	41	5	2.5	2.5	NUM
ijassa-2051	41	6	)	)	PUNCT
ijassa-2051	41	7	where	where	SCONJ
ijassa-2051	41	8	v	v	NOUN
ijassa-2051	41	9	,	,	PUNCT
ijassa-2051	41	10	w	w	PROPN
ijassa-2051	41	11	,	,	PUNCT
ijassa-2051	41	12	ai	ai	VERB
ijassa-2051	41	13	,	,	PUNCT
ijassa-2051	41	14	bi	bi	NOUN
ijassa-2051	41	15	∈	∈	PROPN
ijassa-2051	41	16	c∞(m	c∞(m	NOUN
ijassa-2051	41	17	)	)	PUNCT
ijassa-2051	41	18	.	.	PUNCT
ijassa-2051	42	1	proof	proof	NOUN
ijassa-2051	42	2	the	the	DET
ijassa-2051	42	3	proof	proof	NOUN
ijassa-2051	42	4	of	of	ADP
ijassa-2051	42	5	the	the	DET
ijassa-2051	42	6	first	first	ADJ
ijassa-2051	42	7	statement	statement	NOUN
ijassa-2051	42	8	of	of	ADP
ijassa-2051	42	9	the	the	DET
ijassa-2051	42	10	lemma	lemma	PROPN
ijassa-2051	42	11	is	be	AUX
ijassa-2051	42	12	similar	similar	ADJ
ijassa-2051	42	13	to	to	ADP
ijassa-2051	42	14	those	those	PRON
ijassa-2051	42	15	for	for	ADP
ijassa-2051	42	16	the	the	DET
ijassa-2051	42	17	case	case	NOUN
ijassa-2051	42	18	n	n	NOUN
ijassa-2051	42	19	=	=	SYM
ijassa-2051	42	20	1	1	NUM
ijassa-2051	42	21	considered	consider	VERB
ijassa-2051	42	22	above	above	ADV
ijassa-2051	42	23	.	.	PUNCT
ijassa-2051	43	1	the	the	DET
ijassa-2051	43	2	second	second	ADJ
ijassa-2051	43	3	statement	statement	NOUN
ijassa-2051	43	4	obviously	obviously	ADV
ijassa-2051	43	5	follows	follow	VERB
ijassa-2051	43	6	from	from	ADP
ijassa-2051	43	7	the	the	DET
ijassa-2051	43	8	first	first	ADJ
ijassa-2051	43	9	one	one	NUM
ijassa-2051	43	10	.	.	PUNCT
ijassa-2051	44	1	lemma	lemma	PROPN
ijassa-2051	44	2	2.1	2.1	NUM
ijassa-2051	44	3	establish	establish	VERB
ijassa-2051	44	4	some	some	DET
ijassa-2051	44	5	important	important	ADJ
ijassa-2051	44	6	properties	property	NOUN
ijassa-2051	44	7	of	of	ADP
ijassa-2051	44	8	vector	vector	NOUN
ijassa-2051	44	9	fields	field	NOUN
ijassa-2051	44	10	defined	define	VERB
ijassa-2051	44	11	by	by	ADP
ijassa-2051	44	12	pfaffian	pfaffian	ADJ
ijassa-2051	44	13	systems	system	NOUN
ijassa-2051	44	14	(	(	PUNCT
ijassa-2051	44	15	1.2	1.2	NUM
ijassa-2051	44	16	)	)	PUNCT
ijassa-2051	44	17	.	.	PUNCT
ijassa-2051	45	1	the	the	DET
ijassa-2051	45	2	main	main	ADJ
ijassa-2051	45	3	distinctive	distinctive	ADJ
ijassa-2051	45	4	feature	feature	NOUN
ijassa-2051	45	5	is	be	AUX
ijassa-2051	45	6	that	that	SCONJ
ijassa-2051	45	7	singular	singular	ADJ
ijassa-2051	45	8	points	point	NOUN
ijassa-2051	45	9	of	of	ADP
ijassa-2051	45	10	such	such	ADJ
ijassa-2051	45	11	fields	field	NOUN
ijassa-2051	45	12	are	be	AUX
ijassa-2051	45	13	not	not	PART
ijassa-2051	45	14	isolated	isolate	VERB
ijassa-2051	45	15	,	,	PUNCT
ijassa-2051	45	16	but	but	CCONJ
ijassa-2051	45	17	filled	fill	VERB
ijassa-2051	45	18	a	a	DET
ijassa-2051	45	19	manifold	manifold	NOUN
ijassa-2051	45	20	of	of	ADP
ijassa-2051	45	21	codimension	codimension	NOUN
ijassa-2051	45	22	two	two	NUM
ijassa-2051	45	23	.	.	PUNCT
ijassa-2051	46	1	for	for	ADP
ijassa-2051	46	2	instance	instance	NOUN
ijassa-2051	46	3	,	,	PUNCT
ijassa-2051	46	4	singular	singular	ADJ
ijassa-2051	46	5	points	point	NOUN
ijassa-2051	46	6	of	of	ADP
ijassa-2051	46	7	the	the	DET
ijassa-2051	46	8	field	field	NOUN
ijassa-2051	46	9	(	(	PUNCT
ijassa-2051	46	10	2.5	2.5	NUM
ijassa-2051	46	11	)	)	PUNCT
ijassa-2051	46	12	are	be	AUX
ijassa-2051	46	13	given	give	VERB
ijassa-2051	46	14	by	by	ADP
ijassa-2051	46	15	two	two	NUM
ijassa-2051	46	16	equations	equation	NOUN
ijassa-2051	46	17	v(x	v(x	PROPN
ijassa-2051	46	18	,	,	PUNCT
ijassa-2051	46	19	y	y	PROPN
ijassa-2051	46	20	,	,	PUNCT
ijassa-2051	46	21	z	z	NOUN
ijassa-2051	46	22	)	)	PUNCT
ijassa-2051	46	23	=	=	SYM
ijassa-2051	46	24	0	0	NUM
ijassa-2051	46	25	,	,	PUNCT
ijassa-2051	46	26	w(x	w(x	PROPN
ijassa-2051	46	27	,	,	PUNCT
ijassa-2051	46	28	y	y	PROPN
ijassa-2051	46	29	,	,	PUNCT
ijassa-2051	46	30	z	z	NOUN
ijassa-2051	46	31	)	)	PUNCT
ijassa-2051	46	32	=	=	SYM
ijassa-2051	47	1	0	0	X
ijassa-2051	47	2	.	.	PUNCT
ijassa-2051	48	1	(	(	PUNCT
ijassa-2051	48	2	2.6	2.6	NUM
ijassa-2051	48	3	)	)	PUNCT
ijassa-2051	48	4	therefore	therefore	ADV
ijassa-2051	48	5	,	,	PUNCT
ijassa-2051	48	6	the	the	DET
ijassa-2051	48	7	spectrum	spectrum	NOUN
ijassa-2051	48	8	of	of	ADP
ijassa-2051	48	9	the	the	DET
ijassa-2051	48	10	linear	linear	ADJ
ijassa-2051	48	11	part	part	NOUN
ijassa-2051	48	12	of	of	ADP
ijassa-2051	48	13	field	field	NOUN
ijassa-2051	48	14	(	(	PUNCT
ijassa-2051	48	15	2.5	2.5	NUM
ijassa-2051	48	16	)	)	PUNCT
ijassa-2051	48	17	at	at	ADP
ijassa-2051	48	18	every	every	DET
ijassa-2051	48	19	singular	singular	NOUN
ijassa-2051	48	20	points	point	NOUN
ijassa-2051	48	21	t	t	PROPN
ijassa-2051	48	22	∈	∈	PROPN
ijassa-2051	48	23	σ1	σ1	PROPN
ijassa-2051	48	24	has	have	VERB
ijassa-2051	48	25	the	the	DET
ijassa-2051	48	26	form	form	NOUN
ijassa-2051	48	27	spec	spec	NOUN
ijassa-2051	48	28	(	(	PUNCT
ijassa-2051	48	29	t	t	PROPN
ijassa-2051	48	30	)	)	PUNCT
ijassa-2051	48	31	=	=	PUNCT
ijassa-2051	49	1	(	(	PUNCT
ijassa-2051	49	2	λ1(t	λ1(t	PUNCT
ijassa-2051	49	3	)	)	PUNCT
ijassa-2051	49	4	,	,	PUNCT
ijassa-2051	49	5	λ2(t	λ2(t	PROPN
ijassa-2051	49	6	)	)	PUNCT
ijassa-2051	49	7	,	,	PUNCT
ijassa-2051	49	8	0	0	NUM
ijassa-2051	49	9	,	,	PUNCT
ijassa-2051	49	10	.	.	PUNCT
ijassa-2051	49	11	.	.	PUNCT
ijassa-2051	50	1	.	.	PUNCT
ijassa-2051	51	1	,	,	PUNCT
ijassa-2051	51	2	0	0	NUM
ijassa-2051	51	3	)	)	PUNCT
ijassa-2051	51	4	,	,	PUNCT
ijassa-2051	51	5	#	#	SYM
ijassa-2051	51	6	0	0	NUM
ijassa-2051	51	7	=	=	SYM
ijassa-2051	51	8	n	n	CCONJ
ijassa-2051	51	9	,	,	PUNCT
ijassa-2051	51	10	where	where	SCONJ
ijassa-2051	51	11	the	the	DET
ijassa-2051	51	12	eigenvalues	eigenvalue	NOUN
ijassa-2051	51	13	λ1,2(t	λ1,2(t	PROPN
ijassa-2051	51	14	)	)	PUNCT
ijassa-2051	51	15	continuously	continuously	ADV
ijassa-2051	51	16	depend	depend	VERB
ijassa-2051	51	17	on	on	ADP
ijassa-2051	51	18	t	t	PROPN
ijassa-2051	51	19	∈	∈	PROPN
ijassa-2051	51	20	σ1	σ1	PROPN
ijassa-2051	51	21	.	.	PUNCT
ijassa-2051	52	1	further	far	ADV
ijassa-2051	52	2	we	we	PRON
ijassa-2051	52	3	shall	shall	AUX
ijassa-2051	52	4	use	use	VERB
ijassa-2051	52	5	the	the	DET
ijassa-2051	52	6	notation	notation	NOUN
ijassa-2051	52	7	λ1,2	λ1,2	PROPN
ijassa-2051	52	8	=	=	SYM
ijassa-2051	52	9	λ1,2(t0	λ1,2(t0	PROPN
ijassa-2051	52	10	)	)	PUNCT
ijassa-2051	52	11	.	.	PUNCT
ijassa-2051	53	1	further	far	ADV
ijassa-2051	53	2	we	we	PRON
ijassa-2051	53	3	shall	shall	AUX
ijassa-2051	53	4	consider	consider	VERB
ijassa-2051	53	5	the	the	DET
ijassa-2051	53	6	germ	germ	NOUN
ijassa-2051	53	7	(	(	PUNCT
ijassa-2051	53	8	2.3	2.3	NUM
ijassa-2051	53	9	)	)	PUNCT
ijassa-2051	53	10	at	at	ADP
ijassa-2051	53	11	a	a	DET
ijassa-2051	53	12	generic	generic	ADJ
ijassa-2051	53	13	singular	singular	NOUN
ijassa-2051	53	14	point	point	NOUN
ijassa-2051	53	15	t0	t0	PROPN
ijassa-2051	53	16	∈	∈	PROPN
ijassa-2051	53	17	σ1	σ1	PROPN
ijassa-2051	53	18	,	,	PUNCT
ijassa-2051	53	19	where	where	SCONJ
ijassa-2051	53	20	reλ1,2	reλ1,2	PROPN
ijassa-2051	53	21	̸=	̸=	PROPN
ijassa-2051	53	22	0	0	NUM
ijassa-2051	53	23	.	.	PUNCT
ijassa-2051	54	1	(	(	PUNCT
ijassa-2051	54	2	2.7	2.7	NUM
ijassa-2051	54	3	)	)	PUNCT
ijassa-2051	54	4	in	in	ADP
ijassa-2051	54	5	this	this	DET
ijassa-2051	54	6	case	case	NOUN
ijassa-2051	54	7	,	,	PUNCT
ijassa-2051	54	8	the	the	DET
ijassa-2051	54	9	set	set	NOUN
ijassa-2051	54	10	of	of	ADP
ijassa-2051	54	11	singular	singular	ADJ
ijassa-2051	54	12	points	point	NOUN
ijassa-2051	54	13	σ1	σ1	PROPN
ijassa-2051	54	14	is	be	AUX
ijassa-2051	54	15	the	the	DET
ijassa-2051	54	16	(	(	PUNCT
ijassa-2051	54	17	unique	unique	ADJ
ijassa-2051	54	18	)	)	PUNCT
ijassa-2051	54	19	center	center	NOUN
ijassa-2051	54	20	manifold	manifold	ADJ
ijassa-2051	54	21	w	w	PROPN
ijassa-2051	54	22	c	c	PROPN
ijassa-2051	54	23	of	of	ADP
ijassa-2051	54	24	the	the	DET
ijassa-2051	54	25	field	field	NOUN
ijassa-2051	54	26	(	(	PUNCT
ijassa-2051	54	27	2.5	2.5	NUM
ijassa-2051	54	28	)	)	PUNCT
ijassa-2051	54	29	passing	pass	VERB
ijassa-2051	54	30	through	through	ADP
ijassa-2051	54	31	the	the	DET
ijassa-2051	54	32	point	point	NOUN
ijassa-2051	54	33	t0	t0	PROPN
ijassa-2051	54	34	.	.	PUNCT
ijassa-2051	55	1	this	this	PRON
ijassa-2051	55	2	allows	allow	VERB
ijassa-2051	55	3	us	we	PRON
ijassa-2051	55	4	to	to	PART
ijassa-2051	55	5	apply	apply	VERB
ijassa-2051	55	6	the	the	DET
ijassa-2051	55	7	reduction	reduction	NOUN
ijassa-2051	55	8	principle	principle	NOUN
ijassa-2051	56	1	[	[	X
ijassa-2051	56	2	1	1	NUM
ijassa-2051	56	3	,	,	PUNCT
ijassa-2051	56	4	6	6	NUM
ijassa-2051	56	5	]	]	PUNCT
ijassa-2051	56	6	,	,	PUNCT
ijassa-2051	56	7	which	which	PRON
ijassa-2051	56	8	yields	yield	VERB
ijassa-2051	56	9	the	the	DET
ijassa-2051	56	10	following	follow	VERB
ijassa-2051	56	11	result	result	NOUN
ijassa-2051	56	12	:	:	PUNCT
ijassa-2051	56	13	theorem	theorem	VERB
ijassa-2051	56	14	2.1	2.1	NUM
ijassa-2051	56	15	:	:	PUNCT
ijassa-2051	56	16	the	the	DET
ijassa-2051	56	17	germ	germ	NOUN
ijassa-2051	56	18	of	of	ADP
ijassa-2051	56	19	the	the	DET
ijassa-2051	56	20	field	field	NOUN
ijassa-2051	56	21	(	(	PUNCT
ijassa-2051	56	22	2.5	2.5	NUM
ijassa-2051	56	23	)	)	PUNCT
ijassa-2051	56	24	at	at	ADP
ijassa-2051	56	25	a	a	DET
ijassa-2051	56	26	generic	generic	ADJ
ijassa-2051	56	27	singular	singular	NOUN
ijassa-2051	56	28	point	point	NOUN
ijassa-2051	56	29	t0	t0	NOUN
ijassa-2051	56	30	satisfying	satisfy	VERB
ijassa-2051	56	31	the	the	DET
ijassa-2051	56	32	condition	condition	NOUN
ijassa-2051	56	33	(	(	PUNCT
ijassa-2051	56	34	2.7	2.7	NUM
ijassa-2051	56	35	)	)	PUNCT
ijassa-2051	56	36	is	be	AUX
ijassa-2051	56	37	topologically	topologically	ADV
ijassa-2051	56	38	equivalent	equivalent	ADJ
ijassa-2051	56	39	to	to	ADP
ijassa-2051	56	40	the	the	DET
ijassa-2051	56	41	field	field	NOUN
ijassa-2051	56	42	ξ̇	ξ̇	NOUN
ijassa-2051	56	43	=	=	SYM
ijassa-2051	56	44	a1ξ	a1ξ	PROPN
ijassa-2051	56	45	,	,	PUNCT
ijassa-2051	56	46	η̇	η̇	PROPN
ijassa-2051	56	47	=	=	PUNCT
ijassa-2051	56	48	a2η	a2η	PROPN
ijassa-2051	56	49	,	,	PUNCT
ijassa-2051	56	50	ζ̇i	ζ̇i	PROPN
ijassa-2051	56	51	=	=	SYM
ijassa-2051	56	52	0	0	NUM
ijassa-2051	56	53	,	,	PUNCT
ijassa-2051	56	54	i	i	PRON
ijassa-2051	56	55	=	=	NOUN
ijassa-2051	56	56	1	1	NUM
ijassa-2051	56	57	,	,	PUNCT
ijassa-2051	56	58	.	.	PUNCT
ijassa-2051	56	59	.	.	PUNCT
ijassa-2051	57	1	.	.	PUNCT
ijassa-2051	58	1	,	,	PUNCT
ijassa-2051	58	2	n	n	CCONJ
ijassa-2051	58	3	,	,	PUNCT
ijassa-2051	58	4	(	(	PUNCT
ijassa-2051	58	5	2.8	2.8	NUM
ijassa-2051	58	6	)	)	PUNCT
ijassa-2051	58	7	where	where	SCONJ
ijassa-2051	58	8	aj	aj	PROPN
ijassa-2051	58	9	=	=	PROPN
ijassa-2051	58	10	sgn(reλj	sgn(reλj	X
ijassa-2051	58	11	)	)	PUNCT
ijassa-2051	58	12	.	.	PUNCT
ijassa-2051	59	1	proof	proof	NOUN
ijassa-2051	59	2	this	this	PRON
ijassa-2051	59	3	is	be	AUX
ijassa-2051	59	4	a	a	DET
ijassa-2051	59	5	trivial	trivial	ADJ
ijassa-2051	59	6	corollary	corollary	NOUN
ijassa-2051	59	7	of	of	ADP
ijassa-2051	59	8	the	the	DET
ijassa-2051	59	9	reduction	reduction	NOUN
ijassa-2051	59	10	principle	principle	NOUN
ijassa-2051	59	11	,	,	PUNCT
ijassa-2051	59	12	which	which	PRON
ijassa-2051	59	13	states	state	VERB
ijassa-2051	59	14	that	that	SCONJ
ijassa-2051	59	15	the	the	DET
ijassa-2051	59	16	germ	germ	NOUN
ijassa-2051	59	17	of	of	ADP
ijassa-2051	59	18	the	the	DET
ijassa-2051	59	19	field	field	NOUN
ijassa-2051	59	20	(	(	PUNCT
ijassa-2051	59	21	2.5	2.5	NUM
ijassa-2051	59	22	)	)	PUNCT
ijassa-2051	59	23	at	at	ADP
ijassa-2051	59	24	t0	t0	PROPN
ijassa-2051	59	25	is	be	AUX
ijassa-2051	59	26	topologically	topologically	ADV
ijassa-2051	59	27	equivalent	equivalent	ADJ
ijassa-2051	59	28	to	to	ADP
ijassa-2051	59	29	the	the	DET
ijassa-2051	59	30	product	product	NOUN
ijassa-2051	59	31	of	of	ADP
ijassa-2051	59	32	the	the	DET
ijassa-2051	59	33	field	field	NOUN
ijassa-2051	59	34	ξ̇	ξ̇	NOUN
ijassa-2051	59	35	=	=	SYM
ijassa-2051	59	36	a1ξ	a1ξ	PROPN
ijassa-2051	59	37	,	,	PUNCT
ijassa-2051	59	38	η̇	η̇	PROPN
ijassa-2051	59	39	=	=	PUNCT
ijassa-2051	59	40	a2η	a2η	ADJ
ijassa-2051	59	41	and	and	CCONJ
ijassa-2051	59	42	the	the	DET
ijassa-2051	59	43	restriction	restriction	NOUN
ijassa-2051	59	44	of	of	ADP
ijassa-2051	59	45	(	(	PUNCT
ijassa-2051	59	46	2.5	2.5	NUM
ijassa-2051	59	47	)	)	PUNCT
ijassa-2051	59	48	to	to	ADP
ijassa-2051	59	49	its	its	PRON
ijassa-2051	59	50	center	center	NOUN
ijassa-2051	59	51	manifold	manifold	PROPN
ijassa-2051	59	52	w	w	PROPN
ijassa-2051	59	53	c.	c.	PROPN
ijassa-2051	59	54	since	since	SCONJ
ijassa-2051	59	55	w	w	PROPN
ijassa-2051	59	56	c	c	PROPN
ijassa-2051	59	57	consists	consist	VERB
ijassa-2051	59	58	of	of	ADP
ijassa-2051	59	59	singular	singular	ADJ
ijassa-2051	59	60	points	point	NOUN
ijassa-2051	59	61	of	of	ADP
ijassa-2051	59	62	the	the	DET
ijassa-2051	59	63	field	field	NOUN
ijassa-2051	59	64	(	(	PUNCT
ijassa-2051	59	65	2.5	2.5	NUM
ijassa-2051	59	66	)	)	PUNCT
ijassa-2051	59	67	,	,	PUNCT
ijassa-2051	59	68	this	this	PRON
ijassa-2051	59	69	yields	yield	VERB
ijassa-2051	59	70	normal	normal	ADJ
ijassa-2051	59	71	form	form	NOUN
ijassa-2051	59	72	(	(	PUNCT
ijassa-2051	59	73	2.8	2.8	NUM
ijassa-2051	59	74	)	)	PUNCT
ijassa-2051	59	75	.	.	PUNCT
ijassa-2051	60	1	the	the	DET
ijassa-2051	60	2	next	next	ADJ
ijassa-2051	60	3	step	step	NOUN
ijassa-2051	60	4	in	in	ADP
ijassa-2051	60	5	the	the	DET
ijassa-2051	60	6	study	study	NOUN
ijassa-2051	60	7	of	of	ADP
ijassa-2051	60	8	fields	field	NOUN
ijassa-2051	60	9	(	(	PUNCT
ijassa-2051	60	10	2.5	2.5	NUM
ijassa-2051	60	11	)	)	PUNCT
ijassa-2051	60	12	is	be	AUX
ijassa-2051	60	13	their	their	PRON
ijassa-2051	60	14	smooth	smooth	ADJ
ijassa-2051	60	15	local	local	ADJ
ijassa-2051	60	16	classification	classification	NOUN
ijassa-2051	60	17	.	.	PUNCT
ijassa-2051	61	1	for	for	ADP
ijassa-2051	61	2	this	this	PRON
ijassa-2051	61	3	,	,	PUNCT
ijassa-2051	61	4	we	we	PRON
ijassa-2051	61	5	need	need	VERB
ijassa-2051	61	6	to	to	PART
ijassa-2051	61	7	consider	consider	VERB
ijassa-2051	61	8	two	two	NUM
ijassa-2051	61	9	types	type	NOUN
ijassa-2051	61	10	of	of	ADP
ijassa-2051	61	11	resonances	resonance	NOUN
ijassa-2051	61	12	(	(	PUNCT
ijassa-2051	61	13	integer	integer	NOUN
ijassa-2051	61	14	relations	relation	NOUN
ijassa-2051	61	15	)	)	PUNCT
ijassa-2051	61	16	between	between	ADP
ijassa-2051	61	17	the	the	DET
ijassa-2051	61	18	non	non	ADJ
ijassa-2051	61	19	-	-	ADJ
ijassa-2051	61	20	zero	zero	NUM
ijassa-2051	61	21	eigenvalues	eigenvalue	NOUN
ijassa-2051	61	22	:	:	PUNCT
ijassa-2051	61	23	s1λ1	s1λ1	X
ijassa-2051	61	24	+	+	CCONJ
ijassa-2051	61	25	s2λ2	s2λ2	X
ijassa-2051	61	26	=	=	SYM
ijassa-2051	61	27	0	0	NUM
ijassa-2051	61	28	,	,	PUNCT
ijassa-2051	61	29	si	si	PROPN
ijassa-2051	61	30	∈	∈	PROPN
ijassa-2051	61	31	z+	z+	X
ijassa-2051	61	32	,	,	PUNCT
ijassa-2051	61	33	i	i	PRON
ijassa-2051	61	34	=	=	NOUN
ijassa-2051	61	35	1	1	NUM
ijassa-2051	61	36	,	,	PUNCT
ijassa-2051	61	37	2	2	NUM
ijassa-2051	61	38	,	,	PUNCT
ijassa-2051	61	39	(	(	PUNCT
ijassa-2051	61	40	2.9	2.9	NUM
ijassa-2051	61	41	)	)	PUNCT
ijassa-2051	61	42	s1λ1	s1λ1	NOUN
ijassa-2051	62	1	+	+	CCONJ
ijassa-2051	62	2	s2λ2	s2λ2	X
ijassa-2051	62	3	=	=	SYM
ijassa-2051	62	4	λj	λj	PROPN
ijassa-2051	62	5	,	,	PUNCT
ijassa-2051	62	6	si	si	PROPN
ijassa-2051	62	7	∈	∈	PROPN
ijassa-2051	62	8	z+	z+	X
ijassa-2051	62	9	,	,	PUNCT
ijassa-2051	62	10	i	i	PRON
ijassa-2051	62	11	,	,	PUNCT
ijassa-2051	62	12	j	j	PROPN
ijassa-2051	62	13	=	=	SYM
ijassa-2051	62	14	1	1	NUM
ijassa-2051	62	15	,	,	PUNCT
ijassa-2051	62	16	2	2	NUM
ijassa-2051	62	17	.	.	PUNCT
ijassa-2051	62	18	(	(	PUNCT
ijassa-2051	62	19	2.10	2.10	NUM
ijassa-2051	62	20	)	)	PUNCT
ijassa-2051	62	21	from	from	ADP
ijassa-2051	62	22	them	they	PRON
ijassa-2051	62	23	we	we	PRON
ijassa-2051	62	24	have	have	VERB
ijassa-2051	62	25	to	to	PART
ijassa-2051	62	26	exclude	exclude	VERB
ijassa-2051	62	27	trivial	trivial	ADJ
ijassa-2051	62	28	resonances	resonance	NOUN
ijassa-2051	62	29	,	,	PUNCT
ijassa-2051	62	30	which	which	PRON
ijassa-2051	62	31	always	always	ADV
ijassa-2051	62	32	exist	exist	VERB
ijassa-2051	62	33	:	:	PUNCT
ijassa-2051	62	34	resonance	resonance	NOUN
ijassa-2051	62	35	(	(	PUNCT
ijassa-2051	62	36	2.9	2.9	NUM
ijassa-2051	62	37	)	)	PUNCT
ijassa-2051	62	38	with	with	ADP
ijassa-2051	62	39	s1	s1	PROPN
ijassa-2051	62	40	=	=	SYM
ijassa-2051	62	41	s2	s2	PROPN
ijassa-2051	62	42	=	=	SYM
ijassa-2051	62	43	0	0	NUM
ijassa-2051	62	44	and	and	CCONJ
ijassa-2051	62	45	resonance	resonance	NOUN
ijassa-2051	62	46	(	(	PUNCT
ijassa-2051	62	47	2.10	2.10	NUM
ijassa-2051	62	48	)	)	PUNCT
ijassa-2051	62	49	with	with	ADP
ijassa-2051	62	50	s1	s1	PROPN
ijassa-2051	62	51	=	=	SYM
ijassa-2051	62	52	1	1	NUM
ijassa-2051	62	53	,	,	PUNCT
ijassa-2051	62	54	s2	s2	X
ijassa-2051	62	55	=	=	SYM
ijassa-2051	62	56	0	0	PROPN
ijassa-2051	62	57	,	,	PUNCT
ijassa-2051	62	58	j	j	NOUN
ijassa-2051	63	1	=	=	SYM
ijassa-2051	63	2	1	1	NUM
ijassa-2051	63	3	or	or	CCONJ
ijassa-2051	63	4	s1	s1	NOUN
ijassa-2051	63	5	=	=	SYM
ijassa-2051	63	6	0	0	NUM
ijassa-2051	63	7	,	,	PUNCT
ijassa-2051	63	8	s2	s2	X
ijassa-2051	63	9	=	=	SYM
ijassa-2051	63	10	1	1	NUM
ijassa-2051	63	11	,	,	PUNCT
ijassa-2051	63	12	j	j	NOUN
ijassa-2051	63	13	=	=	SYM
ijassa-2051	63	14	2	2	X
ijassa-2051	63	15	.	.	PUNCT
ijassa-2051	64	1	the	the	DET
ijassa-2051	64	2	number	number	NOUN
ijassa-2051	64	3	|s|	|s|	PROPN
ijassa-2051	64	4	=	=	SYM
ijassa-2051	64	5	s1	s1	PROPN
ijassa-2051	64	6	+	+	CCONJ
ijassa-2051	64	7	s2	s2	PROPN
ijassa-2051	64	8	is	be	AUX
ijassa-2051	64	9	called	call	VERB
ijassa-2051	64	10	the	the	DET
ijassa-2051	64	11	order	order	NOUN
ijassa-2051	64	12	of	of	ADP
ijassa-2051	64	13	resonance	resonance	NOUN
ijassa-2051	64	14	(	(	PUNCT
ijassa-2051	64	15	2.9	2.9	NUM
ijassa-2051	64	16	)	)	PUNCT
ijassa-2051	64	17	or	or	CCONJ
ijassa-2051	64	18	(	(	PUNCT
ijassa-2051	64	19	2.10	2.10	NUM
ijassa-2051	64	20	)	)	PUNCT
ijassa-2051	64	21	.	.	PUNCT
ijassa-2051	65	1	copyright	copyright	NOUN
ijassa-2051	65	2	©	©	PROPN
ijassa-2051	65	3	2025	2025	NUM
ijassa-2051	65	4	assa	assa	NOUN
ijassa-2051	65	5	.	.	PUNCT
ijassa-2051	66	1	adv	adv	PROPN
ijassa-2051	66	2	syst	syst	PROPN
ijassa-2051	66	3	sci	sci	PROPN
ijassa-2051	66	4	appl	appl	PROPN
ijassa-2051	66	5	(	(	PUNCT
ijassa-2051	66	6	2025	2025	NUM
ijassa-2051	66	7	)	)	PUNCT
ijassa-2051	66	8	vector	vector	NOUN
ijassa-2051	66	9	fields	field	NOUN
ijassa-2051	66	10	with	with	ADP
ijassa-2051	66	11	non	non	ADJ
ijassa-2051	66	12	-	-	ADJ
ijassa-2051	66	13	isolated	isolated	ADJ
ijassa-2051	66	14	singular	singular	ADJ
ijassa-2051	66	15	points	point	NOUN
ijassa-2051	66	16	...	...	PUNCT
ijassa-2051	66	17	95	95	NUM
ijassa-2051	66	18	remark	remark	NOUN
ijassa-2051	66	19	2.1	2.1	NUM
ijassa-2051	66	20	:	:	SYM
ijassa-2051	66	21	1	1	NUM
ijassa-2051	66	22	.	.	X
ijassa-2051	67	1	the	the	DET
ijassa-2051	67	2	absence	absence	NOUN
ijassa-2051	67	3	of	of	ADP
ijassa-2051	67	4	resonances	resonance	NOUN
ijassa-2051	67	5	(	(	PUNCT
ijassa-2051	67	6	2.10	2.10	NUM
ijassa-2051	67	7	)	)	PUNCT
ijassa-2051	67	8	implies	imply	VERB
ijassa-2051	67	9	the	the	DET
ijassa-2051	67	10	absence	absence	NOUN
ijassa-2051	67	11	of	of	ADP
ijassa-2051	67	12	the	the	DET
ijassa-2051	67	13	resonances	resonance	NOUN
ijassa-2051	67	14	(	(	PUNCT
ijassa-2051	67	15	2.9	2.9	NUM
ijassa-2051	67	16	):	):	PUNCT
ijassa-2051	67	17	2	2	NUM
ijassa-2051	67	18	.	.	X
ijassa-2051	68	1	in	in	ADP
ijassa-2051	68	2	the	the	DET
ijassa-2051	68	3	absence	absence	NOUN
ijassa-2051	68	4	of	of	ADP
ijassa-2051	68	5	resonances	resonance	NOUN
ijassa-2051	68	6	(	(	PUNCT
ijassa-2051	68	7	2.9	2.9	NUM
ijassa-2051	68	8	)	)	PUNCT
ijassa-2051	68	9	,	,	PUNCT
ijassa-2051	68	10	resonances	resonance	NOUN
ijassa-2051	68	11	(	(	PUNCT
ijassa-2051	68	12	2.10	2.10	NUM
ijassa-2051	68	13	)	)	PUNCT
ijassa-2051	68	14	may	may	AUX
ijassa-2051	68	15	have	have	VERB
ijassa-2051	68	16	only	only	ADV
ijassa-2051	68	17	the	the	DET
ijassa-2051	68	18	simplest	simple	ADJ
ijassa-2051	68	19	form	form	NOUN
ijassa-2051	68	20	λ1	λ1	NOUN
ijassa-2051	68	21	=	=	PUNCT
ijassa-2051	68	22	mλ2	mλ2	NOUN
ijassa-2051	68	23	or	or	CCONJ
ijassa-2051	68	24	λ2	λ2	NOUN
ijassa-2051	68	25	=	=	SYM
ijassa-2051	68	26	mλ1	mλ1	NOUN
ijassa-2051	68	27	(	(	PUNCT
ijassa-2051	68	28	2.11	2.11	NUM
ijassa-2051	68	29	)	)	PUNCT
ijassa-2051	68	30	with	with	ADP
ijassa-2051	68	31	integer	integer	PROPN
ijassa-2051	68	32	m	m	PROPN
ijassa-2051	68	33	≥	≥	NOUN
ijassa-2051	68	34	1	1	NUM
ijassa-2051	68	35	.	.	PUNCT
ijassa-2051	68	36	theorem	theorem	VERB
ijassa-2051	68	37	2.2	2.2	NUM
ijassa-2051	68	38	:	:	PUNCT
ijassa-2051	68	39	if	if	SCONJ
ijassa-2051	68	40	between	between	ADP
ijassa-2051	68	41	the	the	DET
ijassa-2051	68	42	eigenvalues	eigenvalue	NOUN
ijassa-2051	68	43	λ1,2(t	λ1,2(t	PROPN
ijassa-2051	68	44	)	)	PUNCT
ijassa-2051	68	45	there	there	PRON
ijassa-2051	68	46	are	be	VERB
ijassa-2051	68	47	no	no	DET
ijassa-2051	68	48	non	non	ADJ
ijassa-2051	68	49	-	-	ADJ
ijassa-2051	68	50	trivial	trivial	ADJ
ijassa-2051	68	51	resonances	resonance	NOUN
ijassa-2051	68	52	(	(	PUNCT
ijassa-2051	68	53	2.9	2.9	NUM
ijassa-2051	68	54	)	)	PUNCT
ijassa-2051	68	55	of	of	ADP
ijassa-2051	68	56	any	any	DET
ijassa-2051	68	57	order	order	NOUN
ijassa-2051	68	58	|s|	|s|	VERB
ijassa-2051	68	59	≥	≥	NOUN
ijassa-2051	68	60	1	1	NUM
ijassa-2051	68	61	for	for	ADP
ijassa-2051	68	62	all	all	DET
ijassa-2051	68	63	t	t	NOUN
ijassa-2051	68	64	∈	∈	PROPN
ijassa-2051	68	65	w	w	NOUN
ijassa-2051	68	66	c	c	NOUN
ijassa-2051	68	67	sufficiently	sufficiently	ADV
ijassa-2051	68	68	close	close	ADJ
ijassa-2051	68	69	to	to	ADP
ijassa-2051	68	70	t0	t0	NOUN
ijassa-2051	68	71	,	,	PUNCT
ijassa-2051	68	72	then	then	ADV
ijassa-2051	68	73	the	the	DET
ijassa-2051	68	74	germ	germ	NOUN
ijassa-2051	68	75	of	of	ADP
ijassa-2051	68	76	the	the	DET
ijassa-2051	68	77	field	field	NOUN
ijassa-2051	68	78	(	(	PUNCT
ijassa-2051	68	79	2.5	2.5	NUM
ijassa-2051	68	80	)	)	PUNCT
ijassa-2051	68	81	at	at	ADP
ijassa-2051	68	82	t0	t0	PROPN
ijassa-2051	68	83	is	be	AUX
ijassa-2051	68	84	c∞smoothly	c∞smoothly	ADV
ijassa-2051	68	85	equivalent	equivalent	ADJ
ijassa-2051	68	86	to	to	ADP
ijassa-2051	68	87	ξ̇	ξ̇	NOUN
ijassa-2051	68	88	=	=	SYM
ijassa-2051	68	89	x(ξ	x(ξ	PROPN
ijassa-2051	68	90	,	,	PUNCT
ijassa-2051	68	91	η	η	PROPN
ijassa-2051	68	92	,	,	PUNCT
ijassa-2051	68	93	ζ	ζ	NOUN
ijassa-2051	68	94	)	)	PUNCT
ijassa-2051	68	95	,	,	PUNCT
ijassa-2051	68	96	η̇	η̇	PROPN
ijassa-2051	68	97	=	=	SYM
ijassa-2051	68	98	y	y	PROPN
ijassa-2051	68	99	(	(	PUNCT
ijassa-2051	68	100	ξ	ξ	PROPN
ijassa-2051	68	101	,	,	PUNCT
ijassa-2051	68	102	η	η	NOUN
ijassa-2051	68	103	,	,	PUNCT
ijassa-2051	68	104	ζ	ζ	NOUN
ijassa-2051	68	105	)	)	PUNCT
ijassa-2051	68	106	,	,	PUNCT
ijassa-2051	68	107	ζ̇j	ζ̇j	NOUN
ijassa-2051	68	108	=	=	SYM
ijassa-2051	68	109	0	0	NUM
ijassa-2051	68	110	,	,	PUNCT
ijassa-2051	68	111	j	j	PROPN
ijassa-2051	68	112	=	=	SYM
ijassa-2051	68	113	1	1	NUM
ijassa-2051	68	114	,	,	PUNCT
ijassa-2051	68	115	.	.	PUNCT
ijassa-2051	68	116	.	.	PUNCT
ijassa-2051	69	1	.	.	PUNCT
ijassa-2051	70	1	,	,	PUNCT
ijassa-2051	70	2	n	n	CCONJ
ijassa-2051	70	3	,	,	PUNCT
ijassa-2051	70	4	(	(	PUNCT
ijassa-2051	70	5	2.12	2.12	NUM
ijassa-2051	70	6	)	)	PUNCT
ijassa-2051	70	7	where	where	SCONJ
ijassa-2051	70	8	x	x	PRON
ijassa-2051	70	9	and	and	CCONJ
ijassa-2051	70	10	y	y	PROPN
ijassa-2051	70	11	are	be	AUX
ijassa-2051	70	12	smooth	smooth	ADJ
ijassa-2051	70	13	functions	function	NOUN
ijassa-2051	70	14	vanishing	vanish	VERB
ijassa-2051	70	15	on	on	ADP
ijassa-2051	70	16	the	the	DET
ijassa-2051	70	17	center	center	NOUN
ijassa-2051	70	18	manifold	manifold	ADJ
ijassa-2051	70	19	.	.	PUNCT
ijassa-2051	71	1	if	if	SCONJ
ijassa-2051	71	2	,	,	PUNCT
ijassa-2051	71	3	in	in	ADP
ijassa-2051	71	4	addition	addition	NOUN
ijassa-2051	71	5	,	,	PUNCT
ijassa-2051	71	6	|λ1|	|λ1|	ADP
ijassa-2051	71	7	>	>	PUNCT
ijassa-2051	71	8	|λ2|	|λ2|	NOUN
ijassa-2051	71	9	at	at	ADP
ijassa-2051	71	10	t0	t0	NOUN
ijassa-2051	71	11	,	,	PUNCT
ijassa-2051	71	12	then	then	ADV
ijassa-2051	71	13	x	x	X
ijassa-2051	71	14	=	=	PUNCT
ijassa-2051	71	15	λ1(ζ)ξ	λ1(ζ)ξ	PUNCT
ijassa-2051	71	16	+	+	NUM
ijassa-2051	71	17	φ(ζ)ηm	φ(ζ)ηm	PROPN
ijassa-2051	71	18	,	,	PUNCT
ijassa-2051	71	19	y	y	NOUN
ijassa-2051	71	20	=	=	PUNCT
ijassa-2051	71	21	λ2(ζ)η	λ2(ζ)η	PROPN
ijassa-2051	71	22	,	,	PUNCT
ijassa-2051	71	23	(	(	PUNCT
ijassa-2051	71	24	2.13	2.13	NUM
ijassa-2051	71	25	)	)	PUNCT
ijassa-2051	71	26	where	where	SCONJ
ijassa-2051	71	27	φ(ζ	φ(ζ	NOUN
ijassa-2051	71	28	)	)	PUNCT
ijassa-2051	71	29	̸≡	̸≡	X
ijassa-2051	71	30	0	0	PUNCT
ijassa-2051	72	1	only	only	ADV
ijassa-2051	72	2	if	if	SCONJ
ijassa-2051	72	3	λ1	λ1	ADJ
ijassa-2051	72	4	=	=	PUNCT
ijassa-2051	72	5	mλ2	mλ2	NOUN
ijassa-2051	72	6	with	with	ADP
ijassa-2051	72	7	some	some	DET
ijassa-2051	72	8	integer	integer	NOUN
ijassa-2051	72	9	m	m	VERB
ijassa-2051	72	10	>	>	X
ijassa-2051	72	11	1	1	NUM
ijassa-2051	72	12	.	.	PUNCT
ijassa-2051	73	1	the	the	DET
ijassa-2051	73	2	condition	condition	NOUN
ijassa-2051	73	3	that	that	SCONJ
ijassa-2051	73	4	between	between	ADP
ijassa-2051	73	5	λ1,2(t	λ1,2(t	PROPN
ijassa-2051	73	6	)	)	PUNCT
ijassa-2051	73	7	there	there	PRON
ijassa-2051	73	8	are	be	VERB
ijassa-2051	73	9	no	no	DET
ijassa-2051	73	10	non	non	ADJ
ijassa-2051	73	11	-	-	ADJ
ijassa-2051	73	12	trivial	trivial	ADJ
ijassa-2051	73	13	resonances	resonance	NOUN
ijassa-2051	73	14	(	(	PUNCT
ijassa-2051	73	15	2.9	2.9	NUM
ijassa-2051	73	16	)	)	PUNCT
ijassa-2051	73	17	of	of	ADP
ijassa-2051	73	18	any	any	DET
ijassa-2051	73	19	order	order	NOUN
ijassa-2051	73	20	|s|	|s|	VERB
ijassa-2051	73	21	≥	≥	NOUN
ijassa-2051	73	22	1	1	NUM
ijassa-2051	73	23	for	for	ADP
ijassa-2051	73	24	all	all	DET
ijassa-2051	73	25	t	t	NOUN
ijassa-2051	73	26	∈	∈	PROPN
ijassa-2051	73	27	w	w	PROPN
ijassa-2051	73	28	c	c	NOUN
ijassa-2051	73	29	appears	appear	VERB
ijassa-2051	73	30	when	when	SCONJ
ijassa-2051	73	31	we	we	PRON
ijassa-2051	73	32	consider	consider	VERB
ijassa-2051	73	33	infinitely	infinitely	ADV
ijassa-2051	73	34	smooth	smooth	ADJ
ijassa-2051	73	35	classification	classification	NOUN
ijassa-2051	73	36	of	of	ADP
ijassa-2051	73	37	vector	vector	NOUN
ijassa-2051	73	38	fields	field	NOUN
ijassa-2051	73	39	with	with	ADP
ijassa-2051	73	40	non	non	ADJ
ijassa-2051	73	41	-	-	ADJ
ijassa-2051	73	42	isolated	isolated	ADJ
ijassa-2051	73	43	singular	singular	ADJ
ijassa-2051	73	44	points	point	NOUN
ijassa-2051	73	45	.	.	PUNCT
ijassa-2051	74	1	first	first	ADV
ijassa-2051	74	2	it	it	PRON
ijassa-2051	74	3	was	be	AUX
ijassa-2051	74	4	formulated	formulate	VERB
ijassa-2051	74	5	in	in	ADP
ijassa-2051	74	6	the	the	DET
ijassa-2051	74	7	paper	paper	NOUN
ijassa-2051	74	8	[	[	X
ijassa-2051	74	9	17	17	NUM
ijassa-2051	74	10	]	]	PUNCT
ijassa-2051	74	11	and	and	CCONJ
ijassa-2051	74	12	then	then	ADV
ijassa-2051	74	13	it	it	PRON
ijassa-2051	74	14	is	be	AUX
ijassa-2051	74	15	often	often	ADV
ijassa-2051	74	16	named	name	VERB
ijassa-2051	74	17	after	after	ADP
ijassa-2051	74	18	him	he	PRON
ijassa-2051	74	19	.	.	PUNCT
ijassa-2051	75	1	remark	remark	VERB
ijassa-2051	75	2	2.2	2.2	NUM
ijassa-2051	75	3	:	:	SYM
ijassa-2051	75	4	1	1	NUM
ijassa-2051	75	5	.	.	X
ijassa-2051	76	1	if	if	SCONJ
ijassa-2051	76	2	the	the	DET
ijassa-2051	76	3	pair	pair	NOUN
ijassa-2051	76	4	λ1,2	λ1,2	X
ijassa-2051	76	5	=	=	SYM
ijassa-2051	76	6	λ1,2(t0	λ1,2(t0	PROPN
ijassa-2051	76	7	)	)	PUNCT
ijassa-2051	76	8	belongs	belong	VERB
ijassa-2051	76	9	to	to	ADP
ijassa-2051	76	10	the	the	DET
ijassa-2051	76	11	poincaré	poincaré	ADJ
ijassa-2051	76	12	domain	domain	NOUN
ijassa-2051	76	13	,	,	PUNCT
ijassa-2051	76	14	that	that	ADV
ijassa-2051	76	15	is	is	ADV
ijassa-2051	76	16	,	,	PUNCT
ijassa-2051	76	17	λ1,2	λ1,2	PROPN
ijassa-2051	76	18	are	be	AUX
ijassa-2051	76	19	real	real	ADJ
ijassa-2051	76	20	and	and	CCONJ
ijassa-2051	76	21	of	of	ADP
ijassa-2051	76	22	the	the	DET
ijassa-2051	76	23	same	same	ADJ
ijassa-2051	76	24	sign	sign	NOUN
ijassa-2051	76	25	or	or	CCONJ
ijassa-2051	76	26	complex	complex	ADJ
ijassa-2051	76	27	conjugate	conjugate	NOUN
ijassa-2051	76	28	with	with	ADP
ijassa-2051	76	29	the	the	DET
ijassa-2051	76	30	condition	condition	NOUN
ijassa-2051	76	31	(	(	PUNCT
ijassa-2051	76	32	2.7	2.7	NUM
ijassa-2051	76	33	)	)	PUNCT
ijassa-2051	76	34	,	,	PUNCT
ijassa-2051	76	35	then	then	ADV
ijassa-2051	76	36	the	the	DET
ijassa-2051	76	37	roussarie	roussarie	ADJ
ijassa-2051	76	38	condition	condition	NOUN
ijassa-2051	76	39	holds	hold	VERB
ijassa-2051	76	40	true	true	ADJ
ijassa-2051	76	41	,	,	PUNCT
ijassa-2051	76	42	whence	whence	NOUN
ijassa-2051	76	43	theorem	theorem	NOUN
ijassa-2051	76	44	2.2	2.2	NUM
ijassa-2051	76	45	is	be	AUX
ijassa-2051	76	46	valid	valid	ADJ
ijassa-2051	76	47	.	.	PUNCT
ijassa-2051	77	1	2	2	X
ijassa-2051	77	2	.	.	X
ijassa-2051	77	3	if	if	SCONJ
ijassa-2051	77	4	the	the	DET
ijassa-2051	77	5	pair	pair	NOUN
ijassa-2051	77	6	λ1,2	λ1,2	X
ijassa-2051	77	7	=	=	SYM
ijassa-2051	77	8	λ1,2(t0	λ1,2(t0	PROPN
ijassa-2051	77	9	)	)	PUNCT
ijassa-2051	77	10	belongs	belong	VERB
ijassa-2051	77	11	to	to	ADP
ijassa-2051	77	12	the	the	DET
ijassa-2051	77	13	siegel	siegel	NOUN
ijassa-2051	77	14	domain	domain	NOUN
ijassa-2051	77	15	,	,	PUNCT
ijassa-2051	77	16	that	that	ADV
ijassa-2051	77	17	is	is	ADV
ijassa-2051	77	18	,	,	PUNCT
ijassa-2051	77	19	λ1,2	λ1,2	PROPN
ijassa-2051	77	20	are	be	AUX
ijassa-2051	77	21	real	real	ADJ
ijassa-2051	77	22	and	and	CCONJ
ijassa-2051	77	23	of	of	ADP
ijassa-2051	77	24	different	different	ADJ
ijassa-2051	77	25	signs	sign	NOUN
ijassa-2051	77	26	,	,	PUNCT
ijassa-2051	77	27	the	the	DET
ijassa-2051	77	28	roussarie	roussarie	NOUN
ijassa-2051	77	29	condition	condition	NOUN
ijassa-2051	77	30	holds	hold	VERB
ijassa-2051	77	31	true	true	ADJ
ijassa-2051	77	32	if	if	SCONJ
ijassa-2051	77	33	and	and	CCONJ
ijassa-2051	77	34	only	only	ADV
ijassa-2051	77	35	if	if	SCONJ
ijassa-2051	77	36	λ1(t	λ1(t	PUNCT
ijassa-2051	77	37	)	)	PUNCT
ijassa-2051	77	38	:	:	PUNCT
ijassa-2051	77	39	λ2(t	λ2(t	X
ijassa-2051	77	40	)	)	PUNCT
ijassa-2051	77	41	≡	≡	PROPN
ijassa-2051	77	42	const	const	X
ijassa-2051	77	43	/∈	/∈	PUNCT
ijassa-2051	78	1	q	q	ADJ
ijassa-2051	78	2	,	,	PUNCT
ijassa-2051	78	3	∀t	∀t	PROPN
ijassa-2051	78	4	∈	∈	PROPN
ijassa-2051	78	5	w	w	PROPN
ijassa-2051	78	6	c.	c.	PROPN
ijassa-2051	78	7	if	if	SCONJ
ijassa-2051	78	8	we	we	PRON
ijassa-2051	78	9	consider	consider	VERB
ijassa-2051	78	10	ck	ck	ADJ
ijassa-2051	78	11	-	-	PUNCT
ijassa-2051	78	12	smooth	smooth	ADJ
ijassa-2051	78	13	equivalence	equivalence	NOUN
ijassa-2051	78	14	with	with	ADP
ijassa-2051	78	15	k	k	PROPN
ijassa-2051	78	16	<	<	X
ijassa-2051	78	17	∞	∞	PROPN
ijassa-2051	78	18	,	,	PUNCT
ijassa-2051	78	19	the	the	DET
ijassa-2051	78	20	absence	absence	NOUN
ijassa-2051	78	21	of	of	ADP
ijassa-2051	78	22	resonances	resonance	NOUN
ijassa-2051	78	23	of	of	ADP
ijassa-2051	78	24	all	all	DET
ijassa-2051	78	25	orders	order	NOUN
ijassa-2051	78	26	|s|	|s|	NOUN
ijassa-2051	78	27	at	at	ADP
ijassa-2051	78	28	all	all	DET
ijassa-2051	78	29	points	point	NOUN
ijassa-2051	78	30	t	t	PROPN
ijassa-2051	78	31	∈	∈	PROPN
ijassa-2051	78	32	w	w	PROPN
ijassa-2051	78	33	c	c	NOUN
ijassa-2051	78	34	can	can	AUX
ijassa-2051	78	35	be	be	AUX
ijassa-2051	78	36	replaced	replace	VERB
ijassa-2051	78	37	with	with	ADP
ijassa-2051	78	38	the	the	DET
ijassa-2051	78	39	absence	absence	NOUN
ijassa-2051	78	40	of	of	ADP
ijassa-2051	78	41	resonances	resonance	NOUN
ijassa-2051	78	42	of	of	ADP
ijassa-2051	78	43	the	the	DET
ijassa-2051	78	44	orders	order	NOUN
ijassa-2051	78	45	|s|	|s|	VERB
ijassa-2051	78	46	≤	≤	NOUN
ijassa-2051	78	47	n(k	n(k	PROPN
ijassa-2051	78	48	)	)	PUNCT
ijassa-2051	78	49	at	at	ADP
ijassa-2051	78	50	t0	t0	NOUN
ijassa-2051	78	51	,	,	PUNCT
ijassa-2051	78	52	where	where	SCONJ
ijassa-2051	78	53	n(k	n(k	NOUN
ijassa-2051	78	54	)	)	PUNCT
ijassa-2051	79	1	=	=	SYM
ijassa-2051	79	2	2	2	NUM
ijassa-2051	79	3	[	[	PUNCT
ijassa-2051	79	4	(	(	PUNCT
ijassa-2051	79	5	2k	2k	NOUN
ijassa-2051	79	6	+	+	CCONJ
ijassa-2051	79	7	1	1	X
ijassa-2051	79	8	)	)	PUNCT
ijassa-2051	79	9	max	max	PROPN
ijassa-2051	79	10	|reλ1,2|	|reλ1,2|	PROPN
ijassa-2051	79	11	min	min	PROPN
ijassa-2051	79	12	|reλ1,2|	|reλ1,2|	NOUN
ijassa-2051	79	13	]	]	PUNCT
ijassa-2051	79	14	+	+	CCONJ
ijassa-2051	79	15	2	2	NUM
ijassa-2051	79	16	,	,	PUNCT
ijassa-2051	79	17	(	(	PUNCT
ijassa-2051	79	18	2.14	2.14	NUM
ijassa-2051	79	19	)	)	PUNCT
ijassa-2051	79	20	the	the	DET
ijassa-2051	79	21	square	square	ADJ
ijassa-2051	79	22	brackets	bracket	NOUN
ijassa-2051	79	23	denote	denote	VERB
ijassa-2051	79	24	the	the	DET
ijassa-2051	79	25	integer	integer	NOUN
ijassa-2051	79	26	part	part	NOUN
ijassa-2051	79	27	of	of	ADP
ijassa-2051	79	28	a	a	DET
ijassa-2051	79	29	number	number	NOUN
ijassa-2051	79	30	.	.	PUNCT
ijassa-2051	80	1	the	the	DET
ijassa-2051	80	2	estimation	estimation	NOUN
ijassa-2051	80	3	(	(	PUNCT
ijassa-2051	80	4	2.14	2.14	NUM
ijassa-2051	80	5	)	)	PUNCT
ijassa-2051	80	6	is	be	AUX
ijassa-2051	80	7	taken	take	VERB
ijassa-2051	80	8	from	from	ADP
ijassa-2051	80	9	[	[	X
ijassa-2051	80	10	18	18	NUM
ijassa-2051	80	11	]	]	PUNCT
ijassa-2051	80	12	.	.	PUNCT
ijassa-2051	81	1	theorem	theorem	VERB
ijassa-2051	81	2	2.3	2.3	NUM
ijassa-2051	81	3	:	:	PUNCT
ijassa-2051	81	4	if	if	SCONJ
ijassa-2051	81	5	between	between	ADP
ijassa-2051	81	6	the	the	DET
ijassa-2051	81	7	eigenvalues	eigenvalues	PROPN
ijassa-2051	81	8	λ1,2	λ1,2	PROPN
ijassa-2051	81	9	=	=	SYM
ijassa-2051	81	10	λ1,2(t0	λ1,2(t0	NOUN
ijassa-2051	81	11	)	)	PUNCT
ijassa-2051	81	12	there	there	PRON
ijassa-2051	81	13	are	be	VERB
ijassa-2051	81	14	no	no	DET
ijassa-2051	81	15	non	non	ADJ
ijassa-2051	81	16	-	-	ADJ
ijassa-2051	81	17	trivial	trivial	ADJ
ijassa-2051	81	18	resonances	resonance	NOUN
ijassa-2051	81	19	(	(	PUNCT
ijassa-2051	81	20	2.9	2.9	NUM
ijassa-2051	81	21	)	)	PUNCT
ijassa-2051	81	22	of	of	ADP
ijassa-2051	81	23	any	any	DET
ijassa-2051	81	24	order	order	NOUN
ijassa-2051	81	25	1	1	NUM
ijassa-2051	81	26	≤	≤	NUM
ijassa-2051	81	27	|s|	|s|	NOUN
ijassa-2051	81	28	≤	≤	NOUN
ijassa-2051	81	29	n(k	n(k	PROPN
ijassa-2051	81	30	)	)	PUNCT
ijassa-2051	81	31	,	,	PUNCT
ijassa-2051	81	32	then	then	ADV
ijassa-2051	81	33	the	the	DET
ijassa-2051	81	34	germ	germ	NOUN
ijassa-2051	81	35	of	of	ADP
ijassa-2051	81	36	the	the	DET
ijassa-2051	81	37	field	field	NOUN
ijassa-2051	81	38	(	(	PUNCT
ijassa-2051	81	39	2.5	2.5	NUM
ijassa-2051	81	40	)	)	PUNCT
ijassa-2051	81	41	at	at	ADP
ijassa-2051	81	42	t0	t0	PROPN
ijassa-2051	81	43	is	be	AUX
ijassa-2051	81	44	ck	ck	ADV
ijassa-2051	81	45	-	-	PUNCT
ijassa-2051	81	46	smoothly	smoothly	ADV
ijassa-2051	81	47	equivalent	equivalent	ADJ
ijassa-2051	81	48	to	to	ADP
ijassa-2051	81	49	ξ̇	ξ̇	NOUN
ijassa-2051	81	50	=	=	SYM
ijassa-2051	81	51	x(ξ	x(ξ	PROPN
ijassa-2051	81	52	,	,	PUNCT
ijassa-2051	81	53	η	η	PROPN
ijassa-2051	81	54	,	,	PUNCT
ijassa-2051	81	55	ζ	ζ	NOUN
ijassa-2051	81	56	)	)	PUNCT
ijassa-2051	81	57	,	,	PUNCT
ijassa-2051	81	58	η̇	η̇	PROPN
ijassa-2051	81	59	=	=	SYM
ijassa-2051	81	60	y	y	PROPN
ijassa-2051	81	61	(	(	PUNCT
ijassa-2051	81	62	ξ	ξ	PROPN
ijassa-2051	81	63	,	,	PUNCT
ijassa-2051	81	64	η	η	NOUN
ijassa-2051	81	65	,	,	PUNCT
ijassa-2051	81	66	ζ	ζ	NOUN
ijassa-2051	81	67	)	)	PUNCT
ijassa-2051	81	68	,	,	PUNCT
ijassa-2051	81	69	ζ̇j	ζ̇j	NOUN
ijassa-2051	81	70	=	=	SYM
ijassa-2051	81	71	0	0	NUM
ijassa-2051	81	72	,	,	PUNCT
ijassa-2051	81	73	j	j	PROPN
ijassa-2051	81	74	=	=	SYM
ijassa-2051	81	75	1	1	NUM
ijassa-2051	81	76	,	,	PUNCT
ijassa-2051	81	77	.	.	PUNCT
ijassa-2051	81	78	.	.	PUNCT
ijassa-2051	82	1	.	.	PUNCT
ijassa-2051	83	1	,	,	PUNCT
ijassa-2051	83	2	n	n	CCONJ
ijassa-2051	83	3	,	,	PUNCT
ijassa-2051	83	4	where	where	SCONJ
ijassa-2051	83	5	x	x	PUNCT
ijassa-2051	83	6	and	and	CCONJ
ijassa-2051	83	7	y	y	PROPN
ijassa-2051	83	8	are	be	AUX
ijassa-2051	83	9	smooth	smooth	ADJ
ijassa-2051	83	10	functions	function	NOUN
ijassa-2051	83	11	vanishing	vanish	VERB
ijassa-2051	83	12	on	on	ADP
ijassa-2051	83	13	the	the	DET
ijassa-2051	83	14	center	center	NOUN
ijassa-2051	83	15	manifold	manifold	ADJ
ijassa-2051	83	16	.	.	PUNCT
ijassa-2051	84	1	if	if	SCONJ
ijassa-2051	84	2	,	,	PUNCT
ijassa-2051	84	3	in	in	ADP
ijassa-2051	84	4	addition	addition	NOUN
ijassa-2051	84	5	,	,	PUNCT
ijassa-2051	84	6	|λ1|	|λ1|	ADP
ijassa-2051	84	7	>	>	PUNCT
ijassa-2051	84	8	|λ2|	|λ2|	NOUN
ijassa-2051	84	9	at	at	ADP
ijassa-2051	84	10	t0	t0	NOUN
ijassa-2051	84	11	,	,	PUNCT
ijassa-2051	84	12	then	then	ADV
ijassa-2051	84	13	x	x	X
ijassa-2051	84	14	=	=	PUNCT
ijassa-2051	84	15	λ1(ζ)ξ	λ1(ζ)ξ	PUNCT
ijassa-2051	84	16	+	+	NUM
ijassa-2051	84	17	φ(ζ)ηm	φ(ζ)ηm	PROPN
ijassa-2051	84	18	,	,	PUNCT
ijassa-2051	84	19	y	y	NOUN
ijassa-2051	84	20	=	=	PUNCT
ijassa-2051	84	21	λ2(ζ)η	λ2(ζ)η	PROPN
ijassa-2051	84	22	,	,	PUNCT
ijassa-2051	84	23	where	where	SCONJ
ijassa-2051	84	24	φ(ζ	φ(ζ	NOUN
ijassa-2051	84	25	)	)	PUNCT
ijassa-2051	84	26	̸≡	̸≡	X
ijassa-2051	84	27	0	0	PUNCT
ijassa-2051	85	1	only	only	ADV
ijassa-2051	85	2	if	if	SCONJ
ijassa-2051	85	3	λ1	λ1	ADJ
ijassa-2051	85	4	=	=	SYM
ijassa-2051	85	5	mλ2	mλ2	NOUN
ijassa-2051	85	6	with	with	ADP
ijassa-2051	85	7	positive	positive	ADJ
ijassa-2051	85	8	integer	integer	NOUN
ijassa-2051	85	9	m	m	NOUN
ijassa-2051	85	10	≤	≤	NOUN
ijassa-2051	85	11	n(k	n(k	PROPN
ijassa-2051	85	12	)	)	PUNCT
ijassa-2051	85	13	.	.	PUNCT
ijassa-2051	86	1	copyright	copyright	NOUN
ijassa-2051	86	2	©	©	PROPN
ijassa-2051	86	3	2025	2025	NUM
ijassa-2051	86	4	assa	assa	NOUN
ijassa-2051	86	5	.	.	PUNCT
ijassa-2051	87	1	adv	adv	PROPN
ijassa-2051	87	2	syst	syst	PROPN
ijassa-2051	87	3	sci	sci	PROPN
ijassa-2051	87	4	appl	appl	PROPN
ijassa-2051	87	5	(	(	PUNCT
ijassa-2051	87	6	2025	2025	NUM
ijassa-2051	87	7	)	)	PUNCT
ijassa-2051	87	8	96	96	NUM
ijassa-2051	87	9	n.	n.	NOUN
ijassa-2051	87	10	g.	g.	PROPN
ijassa-2051	87	11	pavlova	pavlova	PROPN
ijassa-2051	87	12	,	,	PUNCT
ijassa-2051	87	13	a.	a.	PROPN
ijassa-2051	87	14	o.	o.	PROPN
ijassa-2051	87	15	remizov	remizov	PROPN
ijassa-2051	87	16	for	for	ADP
ijassa-2051	87	17	the	the	DET
ijassa-2051	87	18	proofs	proof	NOUN
ijassa-2051	87	19	of	of	ADP
ijassa-2051	87	20	theorems	theorem	NOUN
ijassa-2051	87	21	2.2	2.2	NUM
ijassa-2051	87	22	,	,	PUNCT
ijassa-2051	87	23	2.3	2.3	NUM
ijassa-2051	87	24	,	,	PUNCT
ijassa-2051	87	25	see	see	VERB
ijassa-2051	87	26	[	[	X
ijassa-2051	87	27	5	5	NUM
ijassa-2051	87	28	,	,	PUNCT
ijassa-2051	87	29	13	13	NUM
ijassa-2051	87	30	]	]	PUNCT
ijassa-2051	87	31	.	.	PUNCT
ijassa-2051	88	1	remark	remark	VERB
ijassa-2051	88	2	2.3	2.3	NUM
ijassa-2051	88	3	:	:	PUNCT
ijassa-2051	88	4	geometrically	geometrically	ADV
ijassa-2051	88	5	,	,	PUNCT
ijassa-2051	88	6	theorems	theorem	VERB
ijassa-2051	88	7	2.2	2.2	NUM
ijassa-2051	88	8	,	,	PUNCT
ijassa-2051	88	9	2.3	2.3	NUM
ijassa-2051	88	10	state	state	NOUN
ijassa-2051	88	11	that	that	SCONJ
ijassa-2051	88	12	the	the	DET
ijassa-2051	88	13	vector	vector	NOUN
ijassa-2051	88	14	field	field	NOUN
ijassa-2051	88	15	(	(	PUNCT
ijassa-2051	88	16	2.5	2.5	NUM
ijassa-2051	88	17	)	)	PUNCT
ijassa-2051	88	18	has	have	VERB
ijassa-2051	88	19	2	2	NUM
ijassa-2051	88	20	-	-	PUNCT
ijassa-2051	88	21	dimensional	dimensional	ADJ
ijassa-2051	88	22	invariant	invariant	ADJ
ijassa-2051	88	23	foliation	foliation	NOUN
ijassa-2051	88	24	such	such	ADJ
ijassa-2051	88	25	that	that	SCONJ
ijassa-2051	88	26	the	the	DET
ijassa-2051	88	27	restriction	restriction	NOUN
ijassa-2051	88	28	of	of	ADP
ijassa-2051	88	29	the	the	DET
ijassa-2051	88	30	field	field	NOUN
ijassa-2051	88	31	to	to	ADP
ijassa-2051	88	32	its	its	PRON
ijassa-2051	88	33	leaves	leave	NOUN
ijassa-2051	88	34	has	have	VERB
ijassa-2051	88	35	the	the	DET
ijassa-2051	88	36	spectrum	spectrum	NOUN
ijassa-2051	88	37	λ1,2(t	λ1,2(t	PROPN
ijassa-2051	88	38	)	)	PUNCT
ijassa-2051	88	39	,	,	PUNCT
ijassa-2051	88	40	that	that	ADV
ijassa-2051	88	41	is	is	ADV
ijassa-2051	88	42	,	,	PUNCT
ijassa-2051	88	43	it	it	PRON
ijassa-2051	88	44	is	be	AUX
ijassa-2051	88	45	a	a	DET
ijassa-2051	88	46	node	node	NOUN
ijassa-2051	88	47	or	or	CCONJ
ijassa-2051	88	48	a	a	DET
ijassa-2051	88	49	saddle	saddle	NOUN
ijassa-2051	88	50	od	od	ADP
ijassa-2051	88	51	a	a	DET
ijassa-2051	88	52	focus	focus	NOUN
ijassa-2051	88	53	.	.	PUNCT
ijassa-2051	89	1	see	see	VERB
ijassa-2051	89	2	,	,	PUNCT
ijassa-2051	89	3	for	for	ADP
ijassa-2051	89	4	example	example	NOUN
ijassa-2051	89	5	,	,	PUNCT
ijassa-2051	89	6	fig	fig	NOUN
ijassa-2051	89	7	.	.	PUNCT
ijassa-2051	90	1	2.1	2.1	NUM
ijassa-2051	90	2	.	.	PUNCT
ijassa-2051	91	1	from	from	ADP
ijassa-2051	91	2	the	the	DET
ijassa-2051	91	3	analytical	analytical	ADJ
ijassa-2051	91	4	viewpoint	viewpoint	NOUN
ijassa-2051	91	5	,	,	PUNCT
ijassa-2051	91	6	theorems	theorem	VERB
ijassa-2051	91	7	2.2	2.2	NUM
ijassa-2051	91	8	,	,	PUNCT
ijassa-2051	91	9	2.3	2.3	NUM
ijassa-2051	91	10	are	be	AUX
ijassa-2051	91	11	generalization	generalization	NOUN
ijassa-2051	91	12	of	of	ADP
ijassa-2051	91	13	the	the	DET
ijassa-2051	91	14	poincare	poincare	PROPN
ijassa-2051	91	15	–	–	PUNCT
ijassa-2051	91	16	dulac	dulac	PROPN
ijassa-2051	91	17	normal	normal	ADJ
ijassa-2051	91	18	form	form	NOUN
ijassa-2051	91	19	for	for	ADP
ijassa-2051	91	20	vector	vector	NOUN
ijassa-2051	91	21	fields	field	NOUN
ijassa-2051	91	22	that	that	PRON
ijassa-2051	91	23	have	have	VERB
ijassa-2051	91	24	zero	zero	NUM
ijassa-2051	91	25	eigenvalues	eigenvalue	NOUN
ijassa-2051	91	26	.	.	PUNCT
ijassa-2051	92	1	fig	fig	NOUN
ijassa-2051	92	2	.	.	PUNCT
ijassa-2051	93	1	2.1	2.1	NUM
ijassa-2051	93	2	.	.	PUNCT
ijassa-2051	93	3	illustration	illustration	NOUN
ijassa-2051	93	4	of	of	ADP
ijassa-2051	93	5	theorems	theorem	NOUN
ijassa-2051	93	6	2.1	2.1	NUM
ijassa-2051	93	7	–	–	PUNCT
ijassa-2051	93	8	2.3	2.3	NUM
ijassa-2051	93	9	:	:	PUNCT
ijassa-2051	93	10	local	local	ADJ
ijassa-2051	93	11	phase	phase	NOUN
ijassa-2051	93	12	portraits	portrait	NOUN
ijassa-2051	93	13	of	of	ADP
ijassa-2051	93	14	the	the	DET
ijassa-2051	93	15	vector	vector	NOUN
ijassa-2051	93	16	field	field	NOUN
ijassa-2051	93	17	(	(	PUNCT
ijassa-2051	93	18	2.5	2.5	NUM
ijassa-2051	93	19	)	)	PUNCT
ijassa-2051	93	20	.	.	PUNCT
ijassa-2051	94	1	here	here	ADV
ijassa-2051	94	2	n	n	NOUN
ijassa-2051	94	3	=	=	SYM
ijassa-2051	94	4	1	1	NUM
ijassa-2051	94	5	and	and	CCONJ
ijassa-2051	94	6	w	w	PROPN
ijassa-2051	94	7	c	c	PROPN
ijassa-2051	94	8	coincides	coincide	VERB
ijassa-2051	94	9	with	with	ADP
ijassa-2051	94	10	the	the	DET
ijassa-2051	94	11	z	z	NOUN
ijassa-2051	94	12	-	-	PUNCT
ijassa-2051	94	13	axis	axis	NOUN
ijassa-2051	94	14	.	.	PUNCT
ijassa-2051	95	1	3	3	X
ijassa-2051	95	2	.	.	X
ijassa-2051	95	3	roussarie	roussarie	PROPN
ijassa-2051	95	4	vector	vector	NOUN
ijassa-2051	95	5	fields	field	NOUN
ijassa-2051	95	6	now	now	ADV
ijassa-2051	95	7	we	we	PRON
ijassa-2051	95	8	consider	consider	VERB
ijassa-2051	95	9	vector	vector	NOUN
ijassa-2051	95	10	fields	field	NOUN
ijassa-2051	95	11	of	of	ADP
ijassa-2051	95	12	the	the	DET
ijassa-2051	95	13	form	form	NOUN
ijassa-2051	95	14	(	(	PUNCT
ijassa-2051	95	15	2.5	2.5	NUM
ijassa-2051	95	16	)	)	PUNCT
ijassa-2051	95	17	satisfying	satisfy	VERB
ijassa-2051	95	18	the	the	DET
ijassa-2051	95	19	additional	additional	ADJ
ijassa-2051	95	20	condition	condition	NOUN
ijassa-2051	95	21	:	:	PUNCT
ijassa-2051	95	22	spec	spec	PROPN
ijassa-2051	95	23	(	(	PUNCT
ijassa-2051	95	24	t	t	PROPN
ijassa-2051	95	25	)	)	PUNCT
ijassa-2051	95	26	≡	≡	PROPN
ijassa-2051	95	27	(	(	PUNCT
ijassa-2051	95	28	λ1(t	λ1(t	PROPN
ijassa-2051	95	29	)	)	PUNCT
ijassa-2051	95	30	,	,	PUNCT
ijassa-2051	95	31	λ2(t	λ2(t	PROPN
ijassa-2051	95	32	)	)	PUNCT
ijassa-2051	95	33	,	,	PUNCT
ijassa-2051	95	34	0	0	NUM
ijassa-2051	95	35	,	,	PUNCT
ijassa-2051	95	36	.	.	PUNCT
ijassa-2051	95	37	.	.	PUNCT
ijassa-2051	96	1	.	.	PUNCT
ijassa-2051	97	1	,	,	PUNCT
ijassa-2051	97	2	0	0	NUM
ijassa-2051	97	3	)	)	PUNCT
ijassa-2051	97	4	,	,	PUNCT
ijassa-2051	97	5	∀t	∀t	PROPN
ijassa-2051	97	6	∈	∈	PROPN
ijassa-2051	97	7	w	w	NOUN
ijassa-2051	97	8	c	c	NOUN
ijassa-2051	97	9	,	,	PUNCT
ijassa-2051	97	10	where	where	SCONJ
ijassa-2051	97	11	λ1,2(t	λ1,2(t	PROPN
ijassa-2051	97	12	)	)	PUNCT
ijassa-2051	97	13	are	be	AUX
ijassa-2051	97	14	non	non	ADJ
ijassa-2051	97	15	-	-	ADJ
ijassa-2051	97	16	zero	zero	ADJ
ijassa-2051	97	17	real	real	ADJ
ijassa-2051	97	18	numbers	number	NOUN
ijassa-2051	97	19	such	such	ADJ
ijassa-2051	97	20	that	that	PRON
ijassa-2051	97	21	qλ1(t	qλ1(t	PROPN
ijassa-2051	97	22	)	)	PUNCT
ijassa-2051	98	1	+	+	CCONJ
ijassa-2051	98	2	pλ2(t	pλ2(t	PROPN
ijassa-2051	98	3	)	)	PUNCT
ijassa-2051	99	1	=	=	PUNCT
ijassa-2051	99	2	0	0	NUM
ijassa-2051	99	3	,	,	PUNCT
ijassa-2051	99	4	p	p	X
ijassa-2051	99	5	,	,	PUNCT
ijassa-2051	99	6	q	q	PROPN
ijassa-2051	99	7	∈	∈	PROPN
ijassa-2051	99	8	z+	z+	NUM
ijassa-2051	99	9	,	,	PUNCT
ijassa-2051	99	10	gcd	gcd	NOUN
ijassa-2051	99	11	(	(	PUNCT
ijassa-2051	99	12	p	p	X
ijassa-2051	99	13	,	,	PUNCT
ijassa-2051	99	14	q	q	NOUN
ijassa-2051	99	15	)	)	PUNCT
ijassa-2051	99	16	=	=	SYM
ijassa-2051	99	17	1	1	NUM
ijassa-2051	99	18	,	,	PUNCT
ijassa-2051	99	19	∀t	∀t	PROPN
ijassa-2051	99	20	∈	∈	PROPN
ijassa-2051	99	21	w	w	PROPN
ijassa-2051	99	22	c.	c.	PROPN
ijassa-2051	99	23	(	(	PUNCT
ijassa-2051	99	24	3.15	3.15	NUM
ijassa-2051	99	25	)	)	PUNCT
ijassa-2051	99	26	such	such	ADJ
ijassa-2051	99	27	vector	vector	NOUN
ijassa-2051	99	28	fields	field	NOUN
ijassa-2051	99	29	are	be	AUX
ijassa-2051	99	30	named	name	VERB
ijassa-2051	99	31	after	after	ADP
ijassa-2051	99	32	robert	robert	PROPN
ijassa-2051	99	33	roussarie	roussarie	PROPN
ijassa-2051	99	34	,	,	PUNCT
ijassa-2051	99	35	who	who	PRON
ijassa-2051	99	36	studied	study	VERB
ijassa-2051	99	37	the	the	DET
ijassa-2051	99	38	partial	partial	ADJ
ijassa-2051	99	39	case	case	NOUN
ijassa-2051	100	1	p	p	X
ijassa-2051	100	2	=	=	X
ijassa-2051	100	3	q	q	NOUN
ijassa-2051	100	4	=	=	SYM
ijassa-2051	100	5	1	1	NUM
ijassa-2051	100	6	(	(	PUNCT
ijassa-2051	100	7	3.16	3.16	NUM
ijassa-2051	100	8	)	)	PUNCT
ijassa-2051	100	9	in	in	ADP
ijassa-2051	100	10	his	his	PRON
ijassa-2051	100	11	[	[	X
ijassa-2051	100	12	17	17	NUM
ijassa-2051	100	13	]	]	PUNCT
ijassa-2051	100	14	.	.	PUNCT
ijassa-2051	101	1	this	this	DET
ijassa-2051	101	2	study	study	NOUN
ijassa-2051	101	3	was	be	AUX
ijassa-2051	101	4	motivated	motivate	VERB
ijassa-2051	101	5	by	by	ADP
ijassa-2051	101	6	the	the	DET
ijassa-2051	101	7	degeneracy	degeneracy	NOUN
ijassa-2051	101	8	of	of	ADP
ijassa-2051	101	9	closed	close	VERB
ijassa-2051	101	10	differential	differential	ADJ
ijassa-2051	101	11	2	2	NUM
ijassa-2051	101	12	-	-	PUNCT
ijassa-2051	101	13	forms	form	NOUN
ijassa-2051	101	14	.	.	PUNCT
ijassa-2051	102	1	a	a	DET
ijassa-2051	102	2	generic	generic	ADJ
ijassa-2051	102	3	closed	closed	ADJ
ijassa-2051	102	4	2	2	NUM
ijassa-2051	102	5	-	-	PUNCT
ijassa-2051	102	6	form	form	NOUN
ijassa-2051	102	7	ω	ω	NOUN
ijassa-2051	102	8	on	on	ADP
ijassa-2051	102	9	the	the	DET
ijassa-2051	102	10	4	4	NUM
ijassa-2051	102	11	-	-	PUNCT
ijassa-2051	102	12	dimensional	dimensional	ADJ
ijassa-2051	102	13	real	real	ADJ
ijassa-2051	102	14	space	space	NOUN
ijassa-2051	102	15	degenerates	degenerate	NOUN
ijassa-2051	102	16	on	on	ADP
ijassa-2051	102	17	a	a	DET
ijassa-2051	102	18	smooth	smooth	ADJ
ijassa-2051	102	19	3dimensional	3dimensional	PROPN
ijassa-2051	102	20	manifold	manifold	ADJ
ijassa-2051	102	21	σ	σ	NOUN
ijassa-2051	102	22	.	.	PUNCT
ijassa-2051	103	1	at	at	ADP
ijassa-2051	103	2	a	a	DET
ijassa-2051	103	3	generic	generic	ADJ
ijassa-2051	103	4	point	point	NOUN
ijassa-2051	103	5	of	of	ADP
ijassa-2051	103	6	σ	σ	PROPN
ijassa-2051	103	7	,	,	PUNCT
ijassa-2051	103	8	the	the	DET
ijassa-2051	103	9	2	2	NUM
ijassa-2051	103	10	-	-	PUNCT
ijassa-2051	103	11	dimensional	dimensional	ADJ
ijassa-2051	103	12	kernel	kernel	NOUN
ijassa-2051	103	13	of	of	ADP
ijassa-2051	103	14	the	the	DET
ijassa-2051	103	15	form	form	NOUN
ijassa-2051	103	16	ω	ω	NOUN
ijassa-2051	103	17	is	be	AUX
ijassa-2051	103	18	transversal	transversal	ADJ
ijassa-2051	103	19	to	to	ADP
ijassa-2051	103	20	σ	σ	PROPN
ijassa-2051	103	21	,	,	PUNCT
ijassa-2051	103	22	and	and	CCONJ
ijassa-2051	103	23	the	the	DET
ijassa-2051	103	24	germ	germ	NOUN
ijassa-2051	103	25	of	of	ADP
ijassa-2051	103	26	ω	ω	PROPN
ijassa-2051	103	27	can	can	AUX
ijassa-2051	103	28	be	be	AUX
ijassa-2051	103	29	reduced	reduce	VERB
ijassa-2051	103	30	to	to	ADP
ijassa-2051	103	31	p1dp1	p1dp1	VERB
ijassa-2051	103	32	∧	∧	NOUN
ijassa-2051	103	33	dq1	dq1	NOUN
ijassa-2051	103	34	+	+	CCONJ
ijassa-2051	103	35	dp2	dp2	PROPN
ijassa-2051	103	36	∧	∧	PROPN
ijassa-2051	103	37	dq2	dq2	PROPN
ijassa-2051	103	38	.	.	PUNCT
ijassa-2051	104	1	however	however	ADV
ijassa-2051	104	2	,	,	PUNCT
ijassa-2051	104	3	the	the	DET
ijassa-2051	104	4	kernel	kernel	NOUN
ijassa-2051	104	5	of	of	ADP
ijassa-2051	104	6	ω	ω	PROPN
ijassa-2051	104	7	is	be	AUX
ijassa-2051	104	8	tangent	tangent	NOUN
ijassa-2051	104	9	to	to	ADP
ijassa-2051	104	10	σ	σ	PROPN
ijassa-2051	104	11	at	at	ADP
ijassa-2051	104	12	some	some	DET
ijassa-2051	104	13	points	point	NOUN
ijassa-2051	104	14	,	,	PUNCT
ijassa-2051	104	15	which	which	PRON
ijassa-2051	104	16	generically	generically	ADV
ijassa-2051	104	17	fill	fill	VERB
ijassa-2051	104	18	a	a	DET
ijassa-2051	104	19	curve	curve	NOUN
ijassa-2051	104	20	s	s	PROPN
ijassa-2051	104	21	⊂	⊂	PROPN
ijassa-2051	104	22	σ	σ	PROPN
ijassa-2051	104	23	,	,	PUNCT
ijassa-2051	104	24	the	the	DET
ijassa-2051	104	25	normal	normal	ADJ
ijassa-2051	104	26	form	form	NOUN
ijassa-2051	104	27	of	of	ADP
ijassa-2051	104	28	ω	ω	NUM
ijassa-2051	104	29	at	at	ADP
ijassa-2051	104	30	points	point	NOUN
ijassa-2051	104	31	of	of	ADP
ijassa-2051	104	32	s	s	NOUN
ijassa-2051	104	33	is	be	AUX
ijassa-2051	104	34	more	more	ADV
ijassa-2051	104	35	complicated	complicated	ADJ
ijassa-2051	104	36	.	.	PUNCT
ijassa-2051	105	1	the	the	DET
ijassa-2051	105	2	kernel	kernel	NOUN
ijassa-2051	105	3	of	of	ADP
ijassa-2051	105	4	ω	ω	PROPN
ijassa-2051	105	5	cuts	cut	VERB
ijassa-2051	105	6	out	out	ADP
ijassa-2051	105	7	a	a	DET
ijassa-2051	105	8	direction	direction	NOUN
ijassa-2051	105	9	field	field	NOUN
ijassa-2051	105	10	on	on	ADP
ijassa-2051	105	11	σ	σ	PROPN
ijassa-2051	105	12	,	,	PUNCT
ijassa-2051	105	13	which	which	PRON
ijassa-2051	105	14	can	can	AUX
ijassa-2051	105	15	be	be	AUX
ijassa-2051	105	16	given	give	VERB
ijassa-2051	105	17	(	(	PUNCT
ijassa-2051	105	18	uniquely	uniquely	ADV
ijassa-2051	105	19	up	up	ADP
ijassa-2051	105	20	to	to	ADP
ijassa-2051	105	21	a	a	DET
ijassa-2051	105	22	scalar	scalar	ADJ
ijassa-2051	105	23	factor	factor	NOUN
ijassa-2051	105	24	)	)	PUNCT
ijassa-2051	105	25	by	by	ADP
ijassa-2051	105	26	a	a	DET
ijassa-2051	105	27	vector	vector	NOUN
ijassa-2051	105	28	field	field	NOUN
ijassa-2051	105	29	of	of	ADP
ijassa-2051	105	30	the	the	DET
ijassa-2051	105	31	form	form	NOUN
ijassa-2051	105	32	(	(	PUNCT
ijassa-2051	105	33	2.5	2.5	NUM
ijassa-2051	105	34	)	)	PUNCT
ijassa-2051	105	35	,	,	PUNCT
ijassa-2051	105	36	whose	whose	DET
ijassa-2051	105	37	singular	singular	ADJ
ijassa-2051	105	38	points	point	NOUN
ijassa-2051	105	39	fill	fill	VERB
ijassa-2051	105	40	the	the	DET
ijassa-2051	105	41	curve	curve	NOUN
ijassa-2051	105	42	s.	s.	PROPN
ijassa-2051	106	1	the	the	DET
ijassa-2051	106	2	condition	condition	NOUN
ijassa-2051	106	3	that	that	SCONJ
ijassa-2051	106	4	ω	ω	PROPN
ijassa-2051	106	5	is	be	AUX
ijassa-2051	106	6	closed	closed	ADJ
ijassa-2051	106	7	implies	imply	VERB
ijassa-2051	106	8	that	that	SCONJ
ijassa-2051	106	9	the	the	DET
ijassa-2051	106	10	trace	trace	NOUN
ijassa-2051	106	11	of	of	ADP
ijassa-2051	106	12	the	the	DET
ijassa-2051	106	13	linear	linear	ADJ
ijassa-2051	106	14	part	part	NOUN
ijassa-2051	106	15	of	of	ADP
ijassa-2051	106	16	the	the	DET
ijassa-2051	106	17	vector	vector	NOUN
ijassa-2051	106	18	field	field	NOUN
ijassa-2051	106	19	at	at	ADP
ijassa-2051	106	20	every	every	DET
ijassa-2051	106	21	its	its	PRON
ijassa-2051	106	22	singular	singular	ADJ
ijassa-2051	106	23	point	point	NOUN
ijassa-2051	106	24	is	be	AUX
ijassa-2051	106	25	zero	zero	NUM
ijassa-2051	106	26	,	,	PUNCT
ijassa-2051	106	27	that	that	ADV
ijassa-2051	106	28	is	is	ADV
ijassa-2051	106	29	,	,	PUNCT
ijassa-2051	106	30	the	the	DET
ijassa-2051	106	31	non	non	ADJ
ijassa-2051	106	32	-	-	ADJ
ijassa-2051	106	33	zero	zero	NUM
ijassa-2051	106	34	eigenvalues	eigenvalue	VERB
ijassa-2051	106	35	λ1,2	λ1,2	PRON
ijassa-2051	106	36	satisfy	satisfy	VERB
ijassa-2051	106	37	the	the	DET
ijassa-2051	106	38	resonance	resonance	NOUN
ijassa-2051	106	39	(	(	PUNCT
ijassa-2051	106	40	3.15	3.15	NUM
ijassa-2051	106	41	)	)	PUNCT
ijassa-2051	106	42	with	with	ADP
ijassa-2051	106	43	p	p	NOUN
ijassa-2051	107	1	=	=	NOUN
ijassa-2051	107	2	q	q	NOUN
ijassa-2051	107	3	=	=	NOUN
ijassa-2051	107	4	1	1	X
ijassa-2051	107	5	.	.	PUNCT
ijassa-2051	107	6	copyright	copyright	NOUN
ijassa-2051	107	7	©	©	PROPN
ijassa-2051	107	8	2025	2025	NUM
ijassa-2051	107	9	assa	assa	NOUN
ijassa-2051	107	10	.	.	PUNCT
ijassa-2051	108	1	adv	adv	PROPN
ijassa-2051	108	2	syst	syst	PROPN
ijassa-2051	108	3	sci	sci	PROPN
ijassa-2051	108	4	appl	appl	PROPN
ijassa-2051	108	5	(	(	PUNCT
ijassa-2051	108	6	2025	2025	NUM
ijassa-2051	108	7	)	)	PUNCT
ijassa-2051	108	8	vector	vector	NOUN
ijassa-2051	108	9	fields	field	NOUN
ijassa-2051	108	10	with	with	ADP
ijassa-2051	108	11	non	non	ADJ
ijassa-2051	108	12	-	-	ADJ
ijassa-2051	108	13	isolated	isolated	ADJ
ijassa-2051	108	14	singular	singular	ADJ
ijassa-2051	108	15	points	point	NOUN
ijassa-2051	108	16	...	...	PUNCT
ijassa-2051	108	17	97	97	NUM
ijassa-2051	108	18	actually	actually	ADV
ijassa-2051	108	19	,	,	PUNCT
ijassa-2051	108	20	in	in	ADP
ijassa-2051	108	21	many	many	ADJ
ijassa-2051	108	22	problems	problem	NOUN
ijassa-2051	108	23	we	we	PRON
ijassa-2051	108	24	are	be	AUX
ijassa-2051	108	25	interested	interested	ADJ
ijassa-2051	108	26	not	not	PART
ijassa-2051	108	27	in	in	ADP
ijassa-2051	108	28	vector	vector	NOUN
ijassa-2051	108	29	fields	field	NOUN
ijassa-2051	108	30	themselves	themselves	PRON
ijassa-2051	108	31	,	,	PUNCT
ijassa-2051	108	32	but	but	CCONJ
ijassa-2051	108	33	in	in	ADP
ijassa-2051	108	34	the	the	DET
ijassa-2051	108	35	corresponding	corresponding	ADJ
ijassa-2051	108	36	direction	direction	NOUN
ijassa-2051	108	37	fields	field	NOUN
ijassa-2051	108	38	.	.	PUNCT
ijassa-2051	109	1	therefore	therefore	ADV
ijassa-2051	109	2	,	,	PUNCT
ijassa-2051	109	3	when	when	SCONJ
ijassa-2051	109	4	bringing	bring	VERB
ijassa-2051	109	5	a	a	DET
ijassa-2051	109	6	vector	vector	NOUN
ijassa-2051	109	7	field	field	NOUN
ijassa-2051	109	8	to	to	ADP
ijassa-2051	109	9	its	its	PRON
ijassa-2051	109	10	normal	normal	ADJ
ijassa-2051	109	11	forms	form	NOUN
ijassa-2051	109	12	,	,	PUNCT
ijassa-2051	109	13	one	one	PRON
ijassa-2051	109	14	can	can	AUX
ijassa-2051	109	15	multiply	multiply	VERB
ijassa-2051	109	16	it	it	PRON
ijassa-2051	109	17	by	by	ADP
ijassa-2051	109	18	a	a	DET
ijassa-2051	109	19	non	non	ADJ
ijassa-2051	109	20	-	-	ADJ
ijassa-2051	109	21	vanishing	vanishing	ADJ
ijassa-2051	109	22	scalar	scalar	ADJ
ijassa-2051	109	23	function	function	NOUN
ijassa-2051	109	24	in	in	ADP
ijassa-2051	109	25	addition	addition	NOUN
ijassa-2051	109	26	to	to	ADP
ijassa-2051	109	27	changes	change	NOUN
ijassa-2051	109	28	of	of	ADP
ijassa-2051	109	29	the	the	DET
ijassa-2051	109	30	phase	phase	NOUN
ijassa-2051	109	31	variables	variable	NOUN
ijassa-2051	109	32	.	.	PUNCT
ijassa-2051	110	1	normal	normal	ADJ
ijassa-2051	110	2	forms	form	NOUN
ijassa-2051	110	3	thus	thus	ADV
ijassa-2051	110	4	obtained	obtain	VERB
ijassa-2051	110	5	are	be	AUX
ijassa-2051	110	6	called	call	VERB
ijassa-2051	110	7	orbital	orbital	ADJ
ijassa-2051	110	8	.	.	PUNCT
ijassa-2051	111	1	orbital	orbital	ADJ
ijassa-2051	111	2	normal	normal	ADJ
ijassa-2051	111	3	forms	form	NOUN
ijassa-2051	111	4	allow	allow	VERB
ijassa-2051	111	5	us	we	PRON
ijassa-2051	111	6	to	to	PART
ijassa-2051	111	7	get	get	AUX
ijassa-2051	111	8	rid	rid	VERB
ijassa-2051	111	9	of	of	ADP
ijassa-2051	111	10	a	a	DET
ijassa-2051	111	11	redundant	redundant	ADJ
ijassa-2051	111	12	module	module	NOUN
ijassa-2051	111	13	,	,	PUNCT
ijassa-2051	111	14	and	and	CCONJ
ijassa-2051	111	15	therefore	therefore	ADV
ijassa-2051	111	16	,	,	PUNCT
ijassa-2051	111	17	to	to	PART
ijassa-2051	111	18	simplify	simplify	VERB
ijassa-2051	111	19	the	the	DET
ijassa-2051	111	20	classification	classification	NOUN
ijassa-2051	111	21	.	.	PUNCT
ijassa-2051	112	1	theorem	theorem	VERB
ijassa-2051	112	2	3.1	3.1	NUM
ijassa-2051	112	3	:	:	PUNCT
ijassa-2051	112	4	the	the	DET
ijassa-2051	112	5	germ	germ	NOUN
ijassa-2051	112	6	of	of	ADP
ijassa-2051	112	7	every	every	DET
ijassa-2051	112	8	roussarie	roussarie	ADJ
ijassa-2051	112	9	vector	vector	NOUN
ijassa-2051	112	10	field	field	NOUN
ijassa-2051	112	11	is	be	AUX
ijassa-2051	112	12	c∞-smoothly	c∞-smoothly	ADV
ijassa-2051	112	13	orbitally	orbitally	ADV
ijassa-2051	112	14	equivalent	equivalent	ADJ
ijassa-2051	112	15	to	to	ADP
ijassa-2051	112	16	ẋ	ẋ	PROPN
ijassa-2051	113	1	=	=	PUNCT
ijassa-2051	114	1	px(1	px(1	PROPN
ijassa-2051	114	2	+	+	CCONJ
ijassa-2051	114	3	φ1(r	φ1(r	ADJ
ijassa-2051	114	4	,	,	PUNCT
ijassa-2051	114	5	z	z	NOUN
ijassa-2051	114	6	)	)	PUNCT
ijassa-2051	114	7	)	)	PUNCT
ijassa-2051	114	8	,	,	PUNCT
ijassa-2051	114	9	ẏ	ẏ	PROPN
ijassa-2051	114	10	=	=	PUNCT
ijassa-2051	114	11	qy(−1	qy(−1	PROPN
ijassa-2051	115	1	+	+	CCONJ
ijassa-2051	115	2	φ2(r	φ2(r	PROPN
ijassa-2051	115	3	,	,	PUNCT
ijassa-2051	115	4	z	z	NOUN
ijassa-2051	115	5	)	)	PUNCT
ijassa-2051	115	6	)	)	PUNCT
ijassa-2051	116	1	,	,	PUNCT
ijassa-2051	116	2	żi	żi	NOUN
ijassa-2051	116	3	=	=	SYM
ijassa-2051	116	4	rψi(r	rψi(r	PROPN
ijassa-2051	116	5	,	,	PUNCT
ijassa-2051	116	6	z	z	NOUN
ijassa-2051	116	7	)	)	PUNCT
ijassa-2051	116	8	,	,	PUNCT
ijassa-2051	116	9	i	i	PRON
ijassa-2051	116	10	=	=	NOUN
ijassa-2051	116	11	1	1	NUM
ijassa-2051	116	12	,	,	PUNCT
ijassa-2051	116	13	.	.	PUNCT
ijassa-2051	116	14	.	.	PUNCT
ijassa-2051	117	1	.	.	PUNCT
ijassa-2051	118	1	,	,	PUNCT
ijassa-2051	118	2	n	n	CCONJ
ijassa-2051	118	3	,	,	PUNCT
ijassa-2051	118	4	(	(	PUNCT
ijassa-2051	118	5	3.17	3.17	NUM
ijassa-2051	118	6	)	)	PUNCT
ijassa-2051	118	7	where	where	SCONJ
ijassa-2051	118	8	r	r	NOUN
ijassa-2051	118	9	=	=	SYM
ijassa-2051	118	10	xqyp	xqyp	PROPN
ijassa-2051	118	11	is	be	AUX
ijassa-2051	118	12	the	the	DET
ijassa-2051	118	13	resonant	resonant	ADJ
ijassa-2051	118	14	monomial	monomial	NOUN
ijassa-2051	118	15	of	of	ADP
ijassa-2051	118	16	the	the	DET
ijassa-2051	118	17	resonance	resonance	NOUN
ijassa-2051	118	18	(	(	PUNCT
ijassa-2051	118	19	3.15	3.15	NUM
ijassa-2051	118	20	)	)	PUNCT
ijassa-2051	118	21	,	,	PUNCT
ijassa-2051	118	22	φ1,2,ψi	φ1,2,ψi	NOUN
ijassa-2051	118	23	∈	∈	NOUN
ijassa-2051	118	24	c∞(m	c∞(m	NOUN
ijassa-2051	118	25	)	)	PUNCT
ijassa-2051	118	26	and	and	CCONJ
ijassa-2051	118	27	φ1(0	φ1(0	PROPN
ijassa-2051	118	28	,	,	PUNCT
ijassa-2051	118	29	0	0	NUM
ijassa-2051	118	30	)	)	PUNCT
ijassa-2051	118	31	=	=	SYM
ijassa-2051	118	32	φ2(0	φ2(0	PROPN
ijassa-2051	118	33	,	,	PUNCT
ijassa-2051	118	34	0	0	NUM
ijassa-2051	118	35	)	)	PUNCT
ijassa-2051	118	36	=	=	SYM
ijassa-2051	118	37	0	0	X
ijassa-2051	118	38	.	.	PUNCT
ijassa-2051	118	39	theorem	theorem	VERB
ijassa-2051	118	40	3.1	3.1	NUM
ijassa-2051	118	41	establishes	establish	VERB
ijassa-2051	118	42	a	a	DET
ijassa-2051	118	43	generalization	generalization	NOUN
ijassa-2051	118	44	of	of	ADP
ijassa-2051	118	45	the	the	DET
ijassa-2051	118	46	poincare	poincare	PROPN
ijassa-2051	118	47	–	–	PUNCT
ijassa-2051	118	48	dulac	dulac	PROPN
ijassa-2051	118	49	normal	normal	ADJ
ijassa-2051	118	50	form	form	NOUN
ijassa-2051	118	51	for	for	ADP
ijassa-2051	118	52	roussarie	roussarie	ADJ
ijassa-2051	118	53	vector	vector	NOUN
ijassa-2051	118	54	fields	field	NOUN
ijassa-2051	118	55	:	:	PUNCT
ijassa-2051	118	56	the	the	DET
ijassa-2051	118	57	functions	function	NOUN
ijassa-2051	118	58	φ1,2	φ1,2	ADJ
ijassa-2051	118	59	and	and	CCONJ
ijassa-2051	118	60	ψi	ψi	ADV
ijassa-2051	118	61	contain	contain	VERB
ijassa-2051	118	62	all	all	DET
ijassa-2051	118	63	resonant	resonant	ADJ
ijassa-2051	118	64	terms	term	NOUN
ijassa-2051	118	65	.	.	PUNCT
ijassa-2051	119	1	it	it	PRON
ijassa-2051	119	2	is	be	AUX
ijassa-2051	119	3	wellknown	wellknown	ADJ
ijassa-2051	119	4	that	that	SCONJ
ijassa-2051	119	5	the	the	DET
ijassa-2051	119	6	poincare	poincare	PROPN
ijassa-2051	119	7	–	–	PUNCT
ijassa-2051	119	8	dulac	dulac	PROPN
ijassa-2051	119	9	normal	normal	ADJ
ijassa-2051	119	10	form	form	NOUN
ijassa-2051	119	11	allows	allow	VERB
ijassa-2051	119	12	further	further	ADJ
ijassa-2051	119	13	simplification	simplification	NOUN
ijassa-2051	119	14	.	.	PUNCT
ijassa-2051	120	1	to	to	PART
ijassa-2051	120	2	obtain	obtain	VERB
ijassa-2051	120	3	such	such	ADJ
ijassa-2051	120	4	simplification	simplification	NOUN
ijassa-2051	120	5	for	for	ADP
ijassa-2051	120	6	(	(	PUNCT
ijassa-2051	120	7	3.17	3.17	NUM
ijassa-2051	120	8	)	)	PUNCT
ijassa-2051	120	9	,	,	PUNCT
ijassa-2051	120	10	we	we	PRON
ijassa-2051	120	11	shall	shall	AUX
ijassa-2051	120	12	use	use	VERB
ijassa-2051	120	13	the	the	DET
ijassa-2051	120	14	notion	notion	NOUN
ijassa-2051	120	15	of	of	ADP
ijassa-2051	120	16	the	the	DET
ijassa-2051	120	17	quotient	quotient	NOUN
ijassa-2051	120	18	vector	vector	NOUN
ijassa-2051	120	19	field	field	NOUN
ijassa-2051	120	20	.	.	PUNCT
ijassa-2051	121	1	the	the	DET
ijassa-2051	121	2	field	field	NOUN
ijassa-2051	121	3	(	(	PUNCT
ijassa-2051	121	4	3.17	3.17	NUM
ijassa-2051	121	5	)	)	PUNCT
ijassa-2051	121	6	generates	generate	VERB
ijassa-2051	121	7	the	the	DET
ijassa-2051	121	8	field	field	NOUN
ijassa-2051	121	9	in	in	ADP
ijassa-2051	121	10	the	the	DET
ijassa-2051	121	11	(	(	PUNCT
ijassa-2051	121	12	r	r	NOUN
ijassa-2051	121	13	,	,	PUNCT
ijassa-2051	121	14	z)-space	z)-space	NOUN
ijassa-2051	121	15	:	:	PUNCT
ijassa-2051	121	16	ṙ	ṙ	NOUN
ijassa-2051	121	17	=	=	PUNCT
ijassa-2051	121	18	˙(xqyp	˙(xqyp	PUNCT
ijassa-2051	121	19	)	)	PUNCT
ijassa-2051	122	1	=	=	VERB
ijassa-2051	123	1	qxq−1ypẋ+	qxq−1ypẋ+	PROPN
ijassa-2051	123	2	pxqyp−1ẏ	pxqyp−1ẏ	NOUN
ijassa-2051	123	3	=	=	PUNCT
ijassa-2051	123	4	qxq−1yppx(1	qxq−1yppx(1	PROPN
ijassa-2051	123	5	+	+	CCONJ
ijassa-2051	123	6	φ1	φ1	PROPN
ijassa-2051	123	7	)	)	PUNCT
ijassa-2051	124	1	+	+	NUM
ijassa-2051	124	2	pxqyp−1qy(−1	pxqyp−1qy(−1	NOUN
ijassa-2051	124	3	+	+	CCONJ
ijassa-2051	124	4	φ2	φ2	ADJ
ijassa-2051	124	5	)	)	PUNCT
ijassa-2051	125	1	=	=	SYM
ijassa-2051	125	2	pqr(φ1	pqr(φ1	PROPN
ijassa-2051	125	3	+	+	CCONJ
ijassa-2051	125	4	φ2	φ2	PROPN
ijassa-2051	125	5	)	)	PUNCT
ijassa-2051	125	6	,	,	PUNCT
ijassa-2051	125	7	żi	żi	NOUN
ijassa-2051	125	8	=	=	SYM
ijassa-2051	125	9	rψi(r	rψi(r	PROPN
ijassa-2051	125	10	,	,	PUNCT
ijassa-2051	125	11	z	z	NOUN
ijassa-2051	125	12	)	)	PUNCT
ijassa-2051	125	13	,	,	PUNCT
ijassa-2051	125	14	i	i	PRON
ijassa-2051	125	15	=	=	NOUN
ijassa-2051	125	16	1	1	NUM
ijassa-2051	125	17	,	,	PUNCT
ijassa-2051	125	18	.	.	PUNCT
ijassa-2051	125	19	.	.	PUNCT
ijassa-2051	126	1	.	.	PUNCT
ijassa-2051	127	1	,	,	PUNCT
ijassa-2051	127	2	n.	n.	NOUN
ijassa-2051	127	3	reducing	reduce	VERB
ijassa-2051	127	4	the	the	DET
ijassa-2051	127	5	common	common	ADJ
ijassa-2051	127	6	factor	factor	NOUN
ijassa-2051	127	7	r	r	NOUN
ijassa-2051	127	8	,	,	PUNCT
ijassa-2051	127	9	we	we	PRON
ijassa-2051	127	10	get	get	VERB
ijassa-2051	127	11	the	the	DET
ijassa-2051	127	12	quotient	quotient	NOUN
ijassa-2051	127	13	vector	vector	NOUN
ijassa-2051	127	14	field	field	NOUN
ijassa-2051	127	15	for	for	ADP
ijassa-2051	127	16	(	(	PUNCT
ijassa-2051	127	17	3.17	3.17	NUM
ijassa-2051	127	18	):	):	PUNCT
ijassa-2051	127	19	ṙ	ṙ	NOUN
ijassa-2051	127	20	=	=	SYM
ijassa-2051	127	21	pqφ(r	pqφ(r	PROPN
ijassa-2051	127	22	,	,	PUNCT
ijassa-2051	127	23	z	z	NOUN
ijassa-2051	127	24	)	)	PUNCT
ijassa-2051	127	25	,	,	PUNCT
ijassa-2051	127	26	żi	żi	NOUN
ijassa-2051	127	27	=	=	SYM
ijassa-2051	127	28	ψi(r	ψi(r	NOUN
ijassa-2051	127	29	,	,	PUNCT
ijassa-2051	127	30	z	z	NOUN
ijassa-2051	127	31	)	)	PUNCT
ijassa-2051	127	32	,	,	PUNCT
ijassa-2051	127	33	i	i	PRON
ijassa-2051	127	34	=	=	NOUN
ijassa-2051	127	35	1	1	NUM
ijassa-2051	127	36	,	,	PUNCT
ijassa-2051	127	37	.	.	PUNCT
ijassa-2051	127	38	.	.	PUNCT
ijassa-2051	128	1	.	.	PUNCT
ijassa-2051	129	1	,	,	PUNCT
ijassa-2051	129	2	n	n	CCONJ
ijassa-2051	129	3	,	,	PUNCT
ijassa-2051	129	4	(	(	PUNCT
ijassa-2051	129	5	3.18	3.18	NUM
ijassa-2051	129	6	)	)	PUNCT
ijassa-2051	130	1	where	where	SCONJ
ijassa-2051	130	2	φ(r	φ(r	ADJ
ijassa-2051	130	3	,	,	PUNCT
ijassa-2051	130	4	z	z	NOUN
ijassa-2051	130	5	)	)	PUNCT
ijassa-2051	130	6	=	=	SYM
ijassa-2051	131	1	φ1(r	φ1(r	PROPN
ijassa-2051	131	2	,	,	PUNCT
ijassa-2051	131	3	z	z	NOUN
ijassa-2051	131	4	)	)	PUNCT
ijassa-2051	132	1	+	+	CCONJ
ijassa-2051	132	2	φ2(r	φ2(r	PROPN
ijassa-2051	132	3	,	,	PUNCT
ijassa-2051	132	4	z	z	NOUN
ijassa-2051	132	5	)	)	PUNCT
ijassa-2051	132	6	.	.	PUNCT
ijassa-2051	133	1	remark	remark	PROPN
ijassa-2051	133	2	3.1	3.1	NUM
ijassa-2051	133	3	:	:	PUNCT
ijassa-2051	133	4	from	from	ADP
ijassa-2051	133	5	the	the	DET
ijassa-2051	133	6	resonant	resonant	ADJ
ijassa-2051	133	7	relation	relation	NOUN
ijassa-2051	133	8	(	(	PUNCT
ijassa-2051	133	9	3.15	3.15	NUM
ijassa-2051	133	10	)	)	PUNCT
ijassa-2051	133	11	it	it	PRON
ijassa-2051	133	12	follows	follow	VERB
ijassa-2051	133	13	that	that	SCONJ
ijassa-2051	133	14	φ(0	φ(0	ADJ
ijassa-2051	133	15	,	,	PUNCT
ijassa-2051	133	16	z	z	NOUN
ijassa-2051	133	17	)	)	PUNCT
ijassa-2051	133	18	≡	≡	PROPN
ijassa-2051	133	19	0	0	PUNCT
ijassa-2051	133	20	for	for	ADP
ijassa-2051	133	21	all	all	DET
ijassa-2051	133	22	z	z	PROPN
ijassa-2051	133	23	,	,	PUNCT
ijassa-2051	133	24	i.e.	i.e.	X
ijassa-2051	133	25	,	,	PUNCT
ijassa-2051	133	26	the	the	DET
ijassa-2051	133	27	restriction	restriction	NOUN
ijassa-2051	133	28	of	of	ADP
ijassa-2051	133	29	φ(r	φ(r	PROPN
ijassa-2051	133	30	,	,	PUNCT
ijassa-2051	133	31	z	z	NOUN
ijassa-2051	133	32	)	)	PUNCT
ijassa-2051	133	33	to	to	ADP
ijassa-2051	133	34	the	the	DET
ijassa-2051	133	35	center	center	NOUN
ijassa-2051	133	36	manifold	manifold	NOUN
ijassa-2051	133	37	is	be	AUX
ijassa-2051	133	38	identically	identically	ADV
ijassa-2051	133	39	zero	zero	NUM
ijassa-2051	133	40	.	.	PUNCT
ijassa-2051	134	1	generically	generically	ADV
ijassa-2051	134	2	,	,	PUNCT
ijassa-2051	134	3	for	for	ADP
ijassa-2051	134	4	almost	almost	ADV
ijassa-2051	134	5	all	all	PRON
ijassa-2051	134	6	points	point	NOUN
ijassa-2051	134	7	t0	t0	PROPN
ijassa-2051	134	8	∈	∈	PROPN
ijassa-2051	134	9	w	w	PROPN
ijassa-2051	134	10	c	c	PROPN
ijassa-2051	134	11	the	the	DET
ijassa-2051	134	12	field	field	NOUN
ijassa-2051	134	13	(	(	PUNCT
ijassa-2051	134	14	3.17	3.17	NUM
ijassa-2051	134	15	)	)	PUNCT
ijassa-2051	134	16	satisfies	satisfy	VERB
ijassa-2051	134	17	the	the	DET
ijassa-2051	134	18	following	follow	VERB
ijassa-2051	134	19	condition	condition	NOUN
ijassa-2051	134	20	:	:	PUNCT
ijassa-2051	134	21	∃i	∃i	PROPN
ijassa-2051	134	22	∈	∈	PROPN
ijassa-2051	134	23	{	{	PUNCT
ijassa-2051	134	24	1	1	NUM
ijassa-2051	134	25	,	,	PUNCT
ijassa-2051	134	26	.	.	PUNCT
ijassa-2051	134	27	.	.	PUNCT
ijassa-2051	135	1	.	.	PUNCT
ijassa-2051	136	1	,	,	PUNCT
ijassa-2051	136	2	n	n	CCONJ
ijassa-2051	136	3	}	}	PUNCT
ijassa-2051	136	4	:	:	PUNCT
ijassa-2051	137	1	ψi(0	ψi(0	PROPN
ijassa-2051	137	2	,	,	PUNCT
ijassa-2051	137	3	0	0	NUM
ijassa-2051	137	4	)	)	PUNCT
ijassa-2051	137	5	̸=	̸=	PROPN
ijassa-2051	137	6	0	0	NUM
ijassa-2051	137	7	.	.	PUNCT
ijassa-2051	138	1	(	(	PUNCT
ijassa-2051	138	2	3.19	3.19	NUM
ijassa-2051	138	3	)	)	PUNCT
ijassa-2051	138	4	equivalently	equivalently	ADV
ijassa-2051	138	5	,	,	PUNCT
ijassa-2051	138	6	0	0	NUM
ijassa-2051	138	7	is	be	AUX
ijassa-2051	138	8	not	not	PART
ijassa-2051	138	9	a	a	DET
ijassa-2051	138	10	singular	singular	ADJ
ijassa-2051	138	11	point	point	NOUN
ijassa-2051	138	12	of	of	ADP
ijassa-2051	138	13	its	its	PRON
ijassa-2051	138	14	quotient	quotient	NOUN
ijassa-2051	138	15	field	field	NOUN
ijassa-2051	138	16	(	(	PUNCT
ijassa-2051	138	17	3.18	3.18	NUM
ijassa-2051	138	18	)	)	PUNCT
ijassa-2051	138	19	.	.	PUNCT
ijassa-2051	139	1	this	this	PRON
ijassa-2051	139	2	allows	allow	VERB
ijassa-2051	139	3	us	we	PRON
ijassa-2051	139	4	to	to	PART
ijassa-2051	139	5	establish	establish	VERB
ijassa-2051	139	6	the	the	DET
ijassa-2051	139	7	existence	existence	NOUN
ijassa-2051	139	8	of	of	ADP
ijassa-2051	139	9	n	n	CCONJ
ijassa-2051	139	10	independent	independent	ADJ
ijassa-2051	139	11	first	first	ADJ
ijassa-2051	139	12	integrals	integral	NOUN
ijassa-2051	139	13	of	of	ADP
ijassa-2051	139	14	the	the	DET
ijassa-2051	139	15	field	field	NOUN
ijassa-2051	139	16	(	(	PUNCT
ijassa-2051	139	17	3.18	3.18	NUM
ijassa-2051	139	18	)	)	PUNCT
ijassa-2051	139	19	,	,	PUNCT
ijassa-2051	139	20	which	which	PRON
ijassa-2051	139	21	are	be	AUX
ijassa-2051	139	22	obviously	obviously	ADV
ijassa-2051	139	23	first	first	ADJ
ijassa-2051	139	24	integrals	integral	NOUN
ijassa-2051	139	25	of	of	ADP
ijassa-2051	139	26	the	the	DET
ijassa-2051	139	27	field	field	NOUN
ijassa-2051	139	28	(	(	PUNCT
ijassa-2051	139	29	3.17	3.17	NUM
ijassa-2051	139	30	)	)	PUNCT
ijassa-2051	139	31	.	.	PUNCT
ijassa-2051	140	1	for	for	ADP
ijassa-2051	140	2	details	detail	NOUN
ijassa-2051	140	3	,	,	PUNCT
ijassa-2051	140	4	see	see	VERB
ijassa-2051	140	5	[	[	X
ijassa-2051	140	6	5	5	NUM
ijassa-2051	140	7	,	,	PUNCT
ijassa-2051	140	8	13	13	NUM
ijassa-2051	140	9	]	]	PUNCT
ijassa-2051	140	10	.	.	PUNCT
ijassa-2051	141	1	using	use	VERB
ijassa-2051	141	2	these	these	DET
ijassa-2051	141	3	first	first	ADJ
ijassa-2051	141	4	integrals	integral	NOUN
ijassa-2051	141	5	,	,	PUNCT
ijassa-2051	141	6	one	one	PRON
ijassa-2051	141	7	can	can	AUX
ijassa-2051	141	8	prove	prove	VERB
ijassa-2051	141	9	the	the	DET
ijassa-2051	141	10	following	follow	VERB
ijassa-2051	141	11	theorem	theorem	NOUN
ijassa-2051	141	12	:	:	PUNCT
ijassa-2051	141	13	theorem	theorem	NOUN
ijassa-2051	141	14	3.2	3.2	NUM
ijassa-2051	141	15	:	:	PUNCT
ijassa-2051	141	16	if	if	SCONJ
ijassa-2051	141	17	the	the	DET
ijassa-2051	141	18	condition	condition	NOUN
ijassa-2051	141	19	(	(	PUNCT
ijassa-2051	141	20	3.19	3.19	NUM
ijassa-2051	141	21	)	)	PUNCT
ijassa-2051	141	22	for	for	ADP
ijassa-2051	141	23	(	(	PUNCT
ijassa-2051	141	24	3.17	3.17	NUM
ijassa-2051	141	25	)	)	PUNCT
ijassa-2051	141	26	holds	hold	VERB
ijassa-2051	141	27	true	true	ADJ
ijassa-2051	141	28	,	,	PUNCT
ijassa-2051	141	29	the	the	DET
ijassa-2051	141	30	germ	germ	NOUN
ijassa-2051	141	31	of	of	ADP
ijassa-2051	141	32	the	the	DET
ijassa-2051	141	33	roussarie	roussarie	ADJ
ijassa-2051	141	34	vector	vector	NOUN
ijassa-2051	141	35	field	field	NOUN
ijassa-2051	141	36	is	be	AUX
ijassa-2051	141	37	c∞smoothly	c∞smoothly	ADV
ijassa-2051	141	38	orbitally	orbitally	ADV
ijassa-2051	141	39	equivalent	equivalent	ADJ
ijassa-2051	141	40	to	to	ADP
ijassa-2051	141	41	ẋ	ẋ	PROPN
ijassa-2051	142	1	=	=	SYM
ijassa-2051	142	2	px	px	PROPN
ijassa-2051	142	3	,	,	PUNCT
ijassa-2051	142	4	ẏ	ẏ	PROPN
ijassa-2051	142	5	=	=	SYM
ijassa-2051	142	6	−qy	−qy	PROPN
ijassa-2051	142	7	,	,	PUNCT
ijassa-2051	142	8	ż1	ż1	PROPN
ijassa-2051	142	9	=	=	SYM
ijassa-2051	142	10	xqyp	xqyp	PROPN
ijassa-2051	142	11	,	,	PUNCT
ijassa-2051	142	12	żi	żi	NOUN
ijassa-2051	142	13	=	=	SYM
ijassa-2051	142	14	0	0	NUM
ijassa-2051	142	15	,	,	PUNCT
ijassa-2051	142	16	i	i	PRON
ijassa-2051	142	17	=	=	NOUN
ijassa-2051	142	18	2	2	NUM
ijassa-2051	142	19	,	,	PUNCT
ijassa-2051	142	20	.	.	PUNCT
ijassa-2051	142	21	.	.	PUNCT
ijassa-2051	142	22	.	.	PUNCT
ijassa-2051	143	1	,	,	PUNCT
ijassa-2051	143	2	n.	n.	NOUN
ijassa-2051	143	3	(	(	PUNCT
ijassa-2051	143	4	3.20	3.20	NUM
ijassa-2051	143	5	)	)	PUNCT
ijassa-2051	143	6	moreover	moreover	ADV
ijassa-2051	143	7	,	,	PUNCT
ijassa-2051	143	8	it	it	PRON
ijassa-2051	143	9	is	be	AUX
ijassa-2051	143	10	ck−1	ck−1	NOUN
ijassa-2051	143	11	-	-	PUNCT
ijassa-2051	143	12	smoothly	smoothly	ADV
ijassa-2051	143	13	orbitally	orbitally	ADV
ijassa-2051	143	14	equivalent	equivalent	ADJ
ijassa-2051	143	15	to	to	ADP
ijassa-2051	143	16	ẋ	ẋ	PROPN
ijassa-2051	144	1	=	=	SYM
ijassa-2051	144	2	px	px	PROPN
ijassa-2051	144	3	,	,	PUNCT
ijassa-2051	144	4	ẏ	ẏ	PROPN
ijassa-2051	144	5	=	=	SYM
ijassa-2051	144	6	−qy	−qy	PROPN
ijassa-2051	144	7	,	,	PUNCT
ijassa-2051	144	8	żi	żi	NOUN
ijassa-2051	144	9	=	=	SYM
ijassa-2051	144	10	0	0	NUM
ijassa-2051	144	11	,	,	PUNCT
ijassa-2051	144	12	i	i	PRON
ijassa-2051	144	13	=	=	NOUN
ijassa-2051	144	14	1	1	NUM
ijassa-2051	144	15	,	,	PUNCT
ijassa-2051	144	16	.	.	PUNCT
ijassa-2051	144	17	.	.	PUNCT
ijassa-2051	145	1	.	.	PUNCT
ijassa-2051	146	1	,	,	PUNCT
ijassa-2051	146	2	n	n	CCONJ
ijassa-2051	146	3	,	,	PUNCT
ijassa-2051	146	4	(	(	PUNCT
ijassa-2051	146	5	3.21	3.21	NUM
ijassa-2051	146	6	)	)	PUNCT
ijassa-2051	146	7	where	where	SCONJ
ijassa-2051	146	8	k	k	NOUN
ijassa-2051	146	9	=	=	SYM
ijassa-2051	146	10	max{p	max{p	NOUN
ijassa-2051	146	11	,	,	PUNCT
ijassa-2051	146	12	q	q	NOUN
ijassa-2051	146	13	}	}	PUNCT
ijassa-2051	146	14	,	,	PUNCT
ijassa-2051	146	15	but	but	CCONJ
ijassa-2051	146	16	in	in	ADP
ijassa-2051	146	17	general	general	ADJ
ijassa-2051	146	18	it	it	PRON
ijassa-2051	146	19	is	be	AUX
ijassa-2051	146	20	not	not	PART
ijassa-2051	146	21	ck	ck	ADV
ijassa-2051	146	22	-	-	PUNCT
ijassa-2051	146	23	smoothly	smoothly	ADV
ijassa-2051	146	24	equivalent	equivalent	ADJ
ijassa-2051	146	25	.	.	PUNCT
ijassa-2051	147	1	copyright	copyright	NOUN
ijassa-2051	147	2	©	©	PROPN
ijassa-2051	147	3	2025	2025	NUM
ijassa-2051	147	4	assa	assa	NOUN
ijassa-2051	147	5	.	.	PUNCT
ijassa-2051	148	1	adv	adv	PROPN
ijassa-2051	148	2	syst	syst	PROPN
ijassa-2051	148	3	sci	sci	PROPN
ijassa-2051	148	4	appl	appl	PROPN
ijassa-2051	148	5	(	(	PUNCT
ijassa-2051	148	6	2025	2025	NUM
ijassa-2051	148	7	)	)	PUNCT
ijassa-2051	148	8	98	98	NUM
ijassa-2051	148	9	n.	n.	NOUN
ijassa-2051	148	10	g.	g.	PROPN
ijassa-2051	148	11	pavlova	pavlova	PROPN
ijassa-2051	148	12	,	,	PUNCT
ijassa-2051	148	13	a.	a.	PROPN
ijassa-2051	148	14	o.	o.	PROPN
ijassa-2051	148	15	remizov	remizov	PROPN
ijassa-2051	148	16	fig	fig	PROPN
ijassa-2051	148	17	.	.	PUNCT
ijassa-2051	149	1	3.2	3.2	NUM
ijassa-2051	149	2	.	.	PUNCT
ijassa-2051	150	1	two	two	NUM
ijassa-2051	150	2	examples	example	NOUN
ijassa-2051	150	3	of	of	ADP
ijassa-2051	150	4	c0	c0	PROPN
ijassa-2051	150	5	saddle	saddle	NOUN
ijassa-2051	150	6	surfaces	surface	NOUN
ijassa-2051	150	7	of	of	ADP
ijassa-2051	150	8	the	the	DET
ijassa-2051	150	9	vector	vector	NOUN
ijassa-2051	150	10	field	field	NOUN
ijassa-2051	150	11	ẋ	ẋ	PUNCT
ijassa-2051	151	1	=	=	SYM
ijassa-2051	151	2	x	x	X
ijassa-2051	151	3	,	,	PUNCT
ijassa-2051	151	4	ẏ	ẏ	PROPN
ijassa-2051	151	5	=	=	SYM
ijassa-2051	151	6	−y	−y	PROPN
ijassa-2051	151	7	,	,	PUNCT
ijassa-2051	151	8	ż	ż	NOUN
ijassa-2051	151	9	=	=	PUNCT
ijassa-2051	151	10	xy	xy	PROPN
ijassa-2051	151	11	:	:	PUNCT
ijassa-2051	151	12	z	z	NOUN
ijassa-2051	151	13	=	=	SYM
ijassa-2051	151	14	−	−	PROPN
ijassa-2051	151	15	1	1	NUM
ijassa-2051	151	16	2xy	2xy	ADJ
ijassa-2051	151	17	ln	ln	ADJ
ijassa-2051	151	18	|y	|y	NOUN
ijassa-2051	151	19	/	/	SYM
ijassa-2051	151	20	x|	x|	PROPN
ijassa-2051	151	21	(	(	PUNCT
ijassa-2051	151	22	left	leave	VERB
ijassa-2051	151	23	)	)	PUNCT
ijassa-2051	151	24	and	and	CCONJ
ijassa-2051	151	25	z	z	NOUN
ijassa-2051	151	26	=	=	SYM
ijassa-2051	151	27	−xy	−xy	PROPN
ijassa-2051	151	28	ln	ln	ADJ
ijassa-2051	151	29	|y|	|y|	PROPN
ijassa-2051	151	30	(	(	PUNCT
ijassa-2051	151	31	right	right	ADJ
ijassa-2051	151	32	)	)	PUNCT
ijassa-2051	151	33	.	.	PUNCT
ijassa-2051	152	1	proof	proof	NOUN
ijassa-2051	152	2	the	the	DET
ijassa-2051	152	3	first	first	ADJ
ijassa-2051	152	4	statement	statement	NOUN
ijassa-2051	152	5	of	of	ADP
ijassa-2051	152	6	the	the	DET
ijassa-2051	152	7	theorem	theorem	NOUN
ijassa-2051	152	8	is	be	AUX
ijassa-2051	152	9	proved	prove	VERB
ijassa-2051	152	10	in	in	ADP
ijassa-2051	152	11	the	the	DET
ijassa-2051	152	12	case	case	NOUN
ijassa-2051	153	1	p	p	X
ijassa-2051	153	2	=	=	X
ijassa-2051	153	3	q	q	NOUN
ijassa-2051	153	4	=	=	SYM
ijassa-2051	153	5	1	1	NUM
ijassa-2051	153	6	by	by	ADP
ijassa-2051	153	7	roussarie	roussarie	NOUN
ijassa-2051	153	8	in	in	ADP
ijassa-2051	153	9	1975	1975	NUM
ijassa-2051	153	10	.	.	PUNCT
ijassa-2051	154	1	other	other	ADJ
ijassa-2051	154	2	statements	statement	NOUN
ijassa-2051	154	3	are	be	AUX
ijassa-2051	154	4	proved	prove	VERB
ijassa-2051	154	5	in	in	ADP
ijassa-2051	154	6	[	[	X
ijassa-2051	154	7	10	10	NUM
ijassa-2051	154	8	]	]	PUNCT
ijassa-2051	154	9	.	.	PUNCT
ijassa-2051	155	1	example	example	NOUN
ijassa-2051	155	2	3.1	3.1	NUM
ijassa-2051	155	3	:	:	PUNCT
ijassa-2051	155	4	consider	consider	VERB
ijassa-2051	155	5	the	the	DET
ijassa-2051	155	6	vector	vector	NOUN
ijassa-2051	155	7	field	field	NOUN
ijassa-2051	155	8	ẋ	ẋ	PUNCT
ijassa-2051	156	1	=	=	SYM
ijassa-2051	156	2	x	x	X
ijassa-2051	156	3	,	,	PUNCT
ijassa-2051	156	4	ẏ	ẏ	PROPN
ijassa-2051	156	5	=	=	SYM
ijassa-2051	156	6	−y	−y	PROPN
ijassa-2051	156	7	,	,	PUNCT
ijassa-2051	156	8	ż	ż	NOUN
ijassa-2051	156	9	=	=	PUNCT
ijassa-2051	156	10	xy	xy	PROPN
ijassa-2051	156	11	,	,	PUNCT
ijassa-2051	156	12	(	(	PUNCT
ijassa-2051	156	13	x	x	X
ijassa-2051	156	14	,	,	PUNCT
ijassa-2051	156	15	y	y	PROPN
ijassa-2051	156	16	,	,	PUNCT
ijassa-2051	156	17	z	z	NOUN
ijassa-2051	156	18	)	)	PUNCT
ijassa-2051	156	19	∈	∈	PROPN
ijassa-2051	156	20	r3	r3	PROPN
ijassa-2051	156	21	.	.	PUNCT
ijassa-2051	157	1	any	any	DET
ijassa-2051	157	2	saddle	saddle	NOUN
ijassa-2051	157	3	surface	surface	NOUN
ijassa-2051	157	4	of	of	ADP
ijassa-2051	157	5	this	this	DET
ijassa-2051	157	6	field	field	NOUN
ijassa-2051	157	7	has	have	VERB
ijassa-2051	157	8	the	the	DET
ijassa-2051	157	9	form	form	NOUN
ijassa-2051	157	10	z	z	NOUN
ijassa-2051	157	11	=	=	SYM
ijassa-2051	157	12	−1	−1	NOUN
ijassa-2051	157	13	2	2	NUM
ijassa-2051	157	14	f	f	NOUN
ijassa-2051	157	15	(	(	PUNCT
ijassa-2051	157	16	x	x	PROPN
ijassa-2051	157	17	,	,	PUNCT
ijassa-2051	157	18	y	y	PROPN
ijassa-2051	157	19	)	)	PUNCT
ijassa-2051	157	20	,	,	PUNCT
ijassa-2051	157	21	where	where	SCONJ
ijassa-2051	157	22	f	f	PROPN
ijassa-2051	157	23	(	(	PUNCT
ijassa-2051	157	24	x	x	PROPN
ijassa-2051	157	25	,	,	PUNCT
ijassa-2051	157	26	y	y	NOUN
ijassa-2051	157	27	)	)	PUNCT
ijassa-2051	157	28	=	=	SYM
ijassa-2051	157	29	f(xy	f(xy	NOUN
ijassa-2051	157	30	)	)	PUNCT
ijassa-2051	157	31	+	+	CCONJ
ijassa-2051	157	32	xy	xy	PROPN
ijassa-2051	157	33	ln	ln	ADJ
ijassa-2051	157	34	∣∣∣y	∣∣∣y	NOUN
ijassa-2051	157	35	x	x	X
ijassa-2051	157	36	∣∣∣	∣∣∣	ADJ
ijassa-2051	157	37	,	,	PUNCT
ijassa-2051	157	38	if	if	SCONJ
ijassa-2051	157	39	xy	xy	PROPN
ijassa-2051	157	40	̸=	̸=	PROPN
ijassa-2051	157	41	0	0	NUM
ijassa-2051	157	42	,	,	PUNCT
ijassa-2051	157	43	and	and	CCONJ
ijassa-2051	157	44	f	f	PROPN
ijassa-2051	157	45	(	(	PUNCT
ijassa-2051	157	46	x	x	X
ijassa-2051	157	47	,	,	PUNCT
ijassa-2051	157	48	y	y	NOUN
ijassa-2051	157	49	)	)	PUNCT
ijassa-2051	157	50	=	=	SYM
ijassa-2051	158	1	0	0	NUM
ijassa-2051	158	2	,	,	PUNCT
ijassa-2051	158	3	if	if	SCONJ
ijassa-2051	158	4	xy	xy	PROPN
ijassa-2051	158	5	=	=	NOUN
ijassa-2051	158	6	0	0	PROPN
ijassa-2051	158	7	.	.	PUNCT
ijassa-2051	159	1	here	here	ADV
ijassa-2051	159	2	f	f	PROPN
ijassa-2051	159	3	is	be	AUX
ijassa-2051	159	4	an	an	DET
ijassa-2051	159	5	arbitrary	arbitrary	ADJ
ijassa-2051	159	6	continuous	continuous	ADJ
ijassa-2051	159	7	function	function	NOUN
ijassa-2051	159	8	.	.	PUNCT
ijassa-2051	160	1	the	the	DET
ijassa-2051	160	2	obtained	obtain	VERB
ijassa-2051	160	3	formula	formula	NOUN
ijassa-2051	160	4	shows	show	VERB
ijassa-2051	160	5	that	that	SCONJ
ijassa-2051	160	6	f	f	PROPN
ijassa-2051	160	7	is	be	AUX
ijassa-2051	160	8	continuous	continuous	ADJ
ijassa-2051	160	9	(	(	PUNCT
ijassa-2051	160	10	for	for	ADP
ijassa-2051	160	11	continuous	continuous	ADJ
ijassa-2051	160	12	f	f	PROPN
ijassa-2051	160	13	)	)	PUNCT
ijassa-2051	160	14	,	,	PUNCT
ijassa-2051	160	15	but	but	CCONJ
ijassa-2051	160	16	it	it	PRON
ijassa-2051	160	17	is	be	AUX
ijassa-2051	160	18	never	never	ADV
ijassa-2051	160	19	c1	c1	PROPN
ijassa-2051	160	20	.	.	PUNCT
ijassa-2051	161	1	see	see	VERB
ijassa-2051	161	2	examples	example	NOUN
ijassa-2051	161	3	in	in	ADP
ijassa-2051	161	4	fig	fig	NOUN
ijassa-2051	161	5	.	.	PUNCT
ijassa-2051	162	1	3.2	3.2	NUM
ijassa-2051	162	2	.	.	X
ijassa-2051	163	1	4	4	NUM
ijassa-2051	163	2	.	.	X
ijassa-2051	163	3	applications	application	NOUN
ijassa-2051	163	4	:	:	PUNCT
ijassa-2051	163	5	quasi	quasi	ADJ
ijassa-2051	163	6	-	-	ADJ
ijassa-2051	163	7	linear	linear	ADJ
ijassa-2051	163	8	odes	ode	NOUN
ijassa-2051	163	9	of	of	ADP
ijassa-2051	163	10	the	the	DET
ijassa-2051	163	11	second	second	ADJ
ijassa-2051	163	12	order	order	NOUN
ijassa-2051	163	13	consider	consider	VERB
ijassa-2051	163	14	the	the	DET
ijassa-2051	163	15	differential	differential	ADJ
ijassa-2051	163	16	equation	equation	NOUN
ijassa-2051	163	17	∆(x	∆(x	PROPN
ijassa-2051	163	18	,	,	PUNCT
ijassa-2051	163	19	y	y	NOUN
ijassa-2051	163	20	)	)	PUNCT
ijassa-2051	163	21	dp	dp	NOUN
ijassa-2051	163	22	dx	dx	PROPN
ijassa-2051	163	23	=	=	SYM
ijassa-2051	163	24	m(x	m(x	PROPN
ijassa-2051	163	25	,	,	PUNCT
ijassa-2051	163	26	y	y	PROPN
ijassa-2051	163	27	,	,	PUNCT
ijassa-2051	163	28	p	p	NOUN
ijassa-2051	163	29	)	)	PUNCT
ijassa-2051	163	30	,	,	PUNCT
ijassa-2051	163	31	p	p	NOUN
ijassa-2051	163	32	=	=	PUNCT
ijassa-2051	163	33	dy	dy	X
ijassa-2051	163	34	/	/	SYM
ijassa-2051	163	35	dx	dx	PROPN
ijassa-2051	163	36	,	,	PUNCT
ijassa-2051	163	37	(	(	PUNCT
ijassa-2051	163	38	4.22	4.22	NUM
ijassa-2051	163	39	)	)	PUNCT
ijassa-2051	163	40	where	where	SCONJ
ijassa-2051	163	41	∆(x	∆(x	PROPN
ijassa-2051	163	42	,	,	PUNCT
ijassa-2051	163	43	y	y	NOUN
ijassa-2051	163	44	)	)	PUNCT
ijassa-2051	163	45	,	,	PUNCT
ijassa-2051	163	46	m(x	m(x	PROPN
ijassa-2051	163	47	,	,	PUNCT
ijassa-2051	163	48	y	y	PROPN
ijassa-2051	163	49	,	,	PUNCT
ijassa-2051	163	50	p	p	NOUN
ijassa-2051	163	51	)	)	PUNCT
ijassa-2051	163	52	are	be	AUX
ijassa-2051	163	53	smooth	smooth	ADJ
ijassa-2051	163	54	functions	function	NOUN
ijassa-2051	163	55	,	,	PUNCT
ijassa-2051	163	56	m	m	VERB
ijassa-2051	163	57	is	be	AUX
ijassa-2051	163	58	analytic	analytic	ADJ
ijassa-2051	163	59	in	in	ADP
ijassa-2051	163	60	p.	p.	PROPN
ijassa-2051	163	61	generically	generically	ADV
ijassa-2051	163	62	,	,	PUNCT
ijassa-2051	163	63	the	the	DET
ijassa-2051	163	64	set	set	NOUN
ijassa-2051	163	65	of	of	ADP
ijassa-2051	163	66	singular	singular	ADJ
ijassa-2051	163	67	points	point	NOUN
ijassa-2051	163	68	of	of	ADP
ijassa-2051	163	69	equation	equation	NOUN
ijassa-2051	163	70	(	(	PUNCT
ijassa-2051	163	71	4.22	4.22	NUM
ijassa-2051	163	72	)	)	PUNCT
ijassa-2051	163	73	is	be	AUX
ijassa-2051	163	74	a	a	DET
ijassa-2051	163	75	regular	regular	ADJ
ijassa-2051	163	76	curve	curve	NOUN
ijassa-2051	163	77	γ	γ	X
ijassa-2051	163	78	=	=	SYM
ijassa-2051	163	79	{	{	PUNCT
ijassa-2051	163	80	(	(	PUNCT
ijassa-2051	163	81	x	x	NOUN
ijassa-2051	163	82	,	,	PUNCT
ijassa-2051	163	83	y	y	PROPN
ijassa-2051	163	84	)	)	PUNCT
ijassa-2051	163	85	:	:	PUNCT
ijassa-2051	164	1	∆(x	∆(x	INTJ
ijassa-2051	164	2	,	,	PUNCT
ijassa-2051	164	3	y	y	NOUN
ijassa-2051	164	4	)	)	PUNCT
ijassa-2051	164	5	=	=	PUNCT
ijassa-2051	164	6	0	0	NUM
ijassa-2051	164	7	}	}	PUNCT
ijassa-2051	164	8	.	.	PUNCT
ijassa-2051	165	1	if	if	SCONJ
ijassa-2051	165	2	the	the	DET
ijassa-2051	165	3	point	point	NOUN
ijassa-2051	165	4	q0	q0	NOUN
ijassa-2051	165	5	=	=	PUNCT
ijassa-2051	165	6	(	(	PUNCT
ijassa-2051	165	7	x0	x0	PROPN
ijassa-2051	165	8	,	,	PUNCT
ijassa-2051	165	9	y0	y0	PROPN
ijassa-2051	165	10	)	)	PUNCT
ijassa-2051	165	11	/∈	/∈	PUNCT
ijassa-2051	166	1	γ	γ	X
ijassa-2051	166	2	,	,	PUNCT
ijassa-2051	166	3	then	then	ADV
ijassa-2051	166	4	for	for	ADP
ijassa-2051	166	5	every	every	DET
ijassa-2051	166	6	direction	direction	NOUN
ijassa-2051	166	7	p0	p0	NOUN
ijassa-2051	166	8	equation	equation	NOUN
ijassa-2051	166	9	(	(	PUNCT
ijassa-2051	166	10	4.22	4.22	NUM
ijassa-2051	166	11	)	)	PUNCT
ijassa-2051	166	12	has	have	VERB
ijassa-2051	166	13	a	a	DET
ijassa-2051	166	14	unique	unique	ADJ
ijassa-2051	166	15	solution	solution	NOUN
ijassa-2051	166	16	satisfying	satisfy	VERB
ijassa-2051	166	17	the	the	DET
ijassa-2051	166	18	initial	initial	ADJ
ijassa-2051	166	19	condition	condition	NOUN
ijassa-2051	166	20	y(x0	y(x0	NOUN
ijassa-2051	166	21	)	)	PUNCT
ijassa-2051	166	22	=	=	SYM
ijassa-2051	166	23	y0	y0	NOUN
ijassa-2051	166	24	,	,	PUNCT
ijassa-2051	166	25	p(x0	p(x0	NOUN
ijassa-2051	166	26	)	)	PUNCT
ijassa-2051	167	1	=	=	SYM
ijassa-2051	167	2	p0	p0	NOUN
ijassa-2051	167	3	.	.	PUNCT
ijassa-2051	168	1	the	the	DET
ijassa-2051	168	2	situation	situation	NOUN
ijassa-2051	168	3	is	be	AUX
ijassa-2051	168	4	more	more	ADV
ijassa-2051	168	5	complicated	complicated	ADJ
ijassa-2051	168	6	if	if	SCONJ
ijassa-2051	168	7	q0	q0	PROPN
ijassa-2051	168	8	=	=	SYM
ijassa-2051	168	9	(	(	PUNCT
ijassa-2051	168	10	x0	x0	PROPN
ijassa-2051	168	11	,	,	PUNCT
ijassa-2051	168	12	y0	y0	PROPN
ijassa-2051	168	13	)	)	PUNCT
ijassa-2051	168	14	∈	∈	PROPN
ijassa-2051	168	15	γ	γ	PROPN
ijassa-2051	168	16	.	.	PROPN
ijassa-2051	168	17	for	for	ADP
ijassa-2051	168	18	example	example	NOUN
ijassa-2051	168	19	,	,	PUNCT
ijassa-2051	168	20	there	there	PRON
ijassa-2051	168	21	may	may	AUX
ijassa-2051	168	22	be	be	AUX
ijassa-2051	168	23	solutions	solution	NOUN
ijassa-2051	168	24	whose	whose	DET
ijassa-2051	168	25	oscillations	oscillation	NOUN
ijassa-2051	168	26	accumulate	accumulate	VERB
ijassa-2051	168	27	near	near	ADP
ijassa-2051	168	28	a	a	DET
ijassa-2051	168	29	singular	singular	ADJ
ijassa-2051	168	30	point	point	NOUN
ijassa-2051	168	31	.	.	PUNCT
ijassa-2051	169	1	copyright	copyright	NOUN
ijassa-2051	169	2	©	©	PROPN
ijassa-2051	169	3	2025	2025	NUM
ijassa-2051	169	4	assa	assa	NOUN
ijassa-2051	169	5	.	.	PUNCT
ijassa-2051	170	1	adv	adv	PROPN
ijassa-2051	170	2	syst	syst	PROPN
ijassa-2051	170	3	sci	sci	PROPN
ijassa-2051	170	4	appl	appl	PROPN
ijassa-2051	170	5	(	(	PUNCT
ijassa-2051	170	6	2025	2025	NUM
ijassa-2051	170	7	)	)	PUNCT
ijassa-2051	170	8	vector	vector	NOUN
ijassa-2051	170	9	fields	field	NOUN
ijassa-2051	170	10	with	with	ADP
ijassa-2051	170	11	non	non	ADJ
ijassa-2051	170	12	-	-	ADJ
ijassa-2051	170	13	isolated	isolated	ADJ
ijassa-2051	170	14	singular	singular	ADJ
ijassa-2051	170	15	points	point	NOUN
ijassa-2051	170	16	...	...	PUNCT
ijassa-2051	170	17	99	99	NUM
ijassa-2051	170	18	example	example	NOUN
ijassa-2051	170	19	4.1	4.1	NUM
ijassa-2051	170	20	:	:	PUNCT
ijassa-2051	170	21	the	the	DET
ijassa-2051	170	22	equation	equation	NOUN
ijassa-2051	170	23	x4dp	x4dp	PUNCT
ijassa-2051	170	24	/	/	SYM
ijassa-2051	170	25	dx	dx	PROPN
ijassa-2051	170	26	=	=	SYM
ijassa-2051	170	27	2x3p−	2x3p−	NUM
ijassa-2051	170	28	(	(	PUNCT
ijassa-2051	170	29	2x2	2x2	NUM
ijassa-2051	170	30	+	+	NUM
ijassa-2051	170	31	1)y	1)y	NUM
ijassa-2051	170	32	has	have	VERB
ijassa-2051	170	33	a	a	DET
ijassa-2051	170	34	family	family	NOUN
ijassa-2051	170	35	of	of	ADP
ijassa-2051	170	36	solutions	solution	NOUN
ijassa-2051	170	37	y(x	y(x	NOUN
ijassa-2051	170	38	)	)	PUNCT
ijassa-2051	170	39	=	=	PUNCT
ijassa-2051	170	40	x2(α	x2(α	PUNCT
ijassa-2051	170	41	cosx−1	cosx−1	NOUN
ijassa-2051	170	42	+	+	NUM
ijassa-2051	170	43	β	β	X
ijassa-2051	170	44	sinx−1	sinx−1	NOUN
ijassa-2051	170	45	)	)	PUNCT
ijassa-2051	170	46	,	,	PUNCT
ijassa-2051	170	47	α	α	X
ijassa-2051	170	48	,	,	PUNCT
ijassa-2051	170	49	β	β	X
ijassa-2051	170	50	=	=	SYM
ijassa-2051	170	51	const	const	NOUN
ijassa-2051	170	52	,	,	PUNCT
ijassa-2051	170	53	except	except	SCONJ
ijassa-2051	170	54	for	for	ADP
ijassa-2051	170	55	α	α	NOUN
ijassa-2051	170	56	=	=	SYM
ijassa-2051	170	57	β	β	X
ijassa-2051	170	58	=	=	SYM
ijassa-2051	170	59	0	0	NUM
ijassa-2051	170	60	,	,	PUNCT
ijassa-2051	170	61	all	all	DET
ijassa-2051	170	62	solutions	solution	NOUN
ijassa-2051	170	63	are	be	AUX
ijassa-2051	170	64	oscillating	oscillate	VERB
ijassa-2051	170	65	at	at	ADP
ijassa-2051	170	66	x	x	X
ijassa-2051	170	67	=	=	SYM
ijassa-2051	170	68	0	0	NUM
ijassa-2051	170	69	:	:	PUNCT
ijassa-2051	170	70	∃	∃	PROPN
ijassa-2051	170	71	lim	lim	PROPN
ijassa-2051	170	72	x→0	x→0	PROPN
ijassa-2051	170	73	y(x	y(x	PROPN
ijassa-2051	170	74	)	)	PUNCT
ijassa-2051	170	75	=	=	SYM
ijassa-2051	170	76	0	0	NUM
ijassa-2051	170	77	,	,	PUNCT
ijassa-2051	170	78	̸	̸	PUNCT
ijassa-2051	170	79	∃	∃	PROPN
ijassa-2051	170	80	lim	lim	PROPN
ijassa-2051	170	81	x→x0	x→x0	PROPN
ijassa-2051	170	82	y′(x	y′(x	PROPN
ijassa-2051	170	83	)	)	PUNCT
ijassa-2051	170	84	(	(	PUNCT
ijassa-2051	170	85	but	but	CCONJ
ijassa-2051	170	86	y′(0	y′(0	NOUN
ijassa-2051	170	87	)	)	PUNCT
ijassa-2051	170	88	=	=	SYM
ijassa-2051	170	89	0	0	NUM
ijassa-2051	170	90	)	)	PUNCT
ijassa-2051	170	91	.	.	PUNCT
ijassa-2051	171	1	example	example	NOUN
ijassa-2051	171	2	4.2	4.2	NUM
ijassa-2051	171	3	:	:	PUNCT
ijassa-2051	172	1	the	the	DET
ijassa-2051	172	2	equation	equation	NOUN
ijassa-2051	172	3	x2dp	x2dp	PUNCT
ijassa-2051	172	4	/	/	SYM
ijassa-2051	172	5	dx	dx	PROPN
ijassa-2051	172	6	=	=	PUNCT
ijassa-2051	172	7	xp−	xp−	PUNCT
ijassa-2051	172	8	2y	2y	PROPN
ijassa-2051	172	9	has	have	VERB
ijassa-2051	172	10	a	a	DET
ijassa-2051	172	11	family	family	NOUN
ijassa-2051	172	12	of	of	ADP
ijassa-2051	172	13	solutions	solution	NOUN
ijassa-2051	173	1	y	y	PROPN
ijassa-2051	173	2	=	=	PUNCT
ijassa-2051	173	3	x(α	x(α	PROPN
ijassa-2051	173	4	cos	cos	PROPN
ijassa-2051	173	5	ln	ln	PROPN
ijassa-2051	173	6	|x|+	|x|+	PROPN
ijassa-2051	173	7	β	β	X
ijassa-2051	173	8	sin	sin	NOUN
ijassa-2051	173	9	ln	ln	ADJ
ijassa-2051	173	10	|x|	|x|	PROPN
ijassa-2051	173	11	)	)	PUNCT
ijassa-2051	173	12	,	,	PUNCT
ijassa-2051	173	13	α	α	X
ijassa-2051	173	14	,	,	PUNCT
ijassa-2051	173	15	β	β	X
ijassa-2051	173	16	=	=	SYM
ijassa-2051	173	17	const	const	NOUN
ijassa-2051	173	18	,	,	PUNCT
ijassa-2051	173	19	except	except	SCONJ
ijassa-2051	173	20	for	for	ADP
ijassa-2051	173	21	α	α	NOUN
ijassa-2051	173	22	=	=	SYM
ijassa-2051	173	23	β	β	X
ijassa-2051	173	24	=	=	SYM
ijassa-2051	173	25	0	0	NUM
ijassa-2051	173	26	,	,	PUNCT
ijassa-2051	173	27	all	all	DET
ijassa-2051	173	28	solutions	solution	NOUN
ijassa-2051	173	29	are	be	AUX
ijassa-2051	173	30	oscillating	oscillate	VERB
ijassa-2051	173	31	at	at	ADP
ijassa-2051	173	32	x	x	X
ijassa-2051	173	33	=	=	SYM
ijassa-2051	173	34	0	0	NUM
ijassa-2051	173	35	:	:	PUNCT
ijassa-2051	173	36	∃	∃	PROPN
ijassa-2051	173	37	lim	lim	PROPN
ijassa-2051	173	38	x→0	x→0	PROPN
ijassa-2051	173	39	y(x	y(x	PROPN
ijassa-2051	173	40	)	)	PUNCT
ijassa-2051	173	41	=	=	SYM
ijassa-2051	173	42	0	0	NUM
ijassa-2051	173	43	,	,	PUNCT
ijassa-2051	173	44	̸	̸	PUNCT
ijassa-2051	173	45	∃	∃	PROPN
ijassa-2051	173	46	lim	lim	PROPN
ijassa-2051	173	47	x→x0	x→x0	PROPN
ijassa-2051	173	48	y′(x	y′(x	PROPN
ijassa-2051	173	49	)	)	PUNCT
ijassa-2051	173	50	(	(	PUNCT
ijassa-2051	173	51	and	and	CCONJ
ijassa-2051	173	52	̸	̸	NUM
ijassa-2051	173	53	∃	∃	PROPN
ijassa-2051	173	54	y′(0	y′(0	PROPN
ijassa-2051	173	55	)	)	PUNCT
ijassa-2051	173	56	)	)	PUNCT
ijassa-2051	173	57	.	.	PUNCT
ijassa-2051	174	1	the	the	DET
ijassa-2051	174	2	above	above	ADJ
ijassa-2051	174	3	examples	example	NOUN
ijassa-2051	174	4	motivate	motivate	VERB
ijassa-2051	174	5	the	the	DET
ijassa-2051	174	6	following	follow	VERB
ijassa-2051	174	7	formal	formal	ADJ
ijassa-2051	174	8	definition	definition	NOUN
ijassa-2051	174	9	:	:	PUNCT
ijassa-2051	174	10	definition	definition	NOUN
ijassa-2051	174	11	4.1	4.1	NUM
ijassa-2051	174	12	:	:	PUNCT
ijassa-2051	174	13	oscillating	oscillate	VERB
ijassa-2051	174	14	solutions	solution	NOUN
ijassa-2051	174	15	entering	enter	VERB
ijassa-2051	174	16	q0	q0	PROPN
ijassa-2051	174	17	are	be	AUX
ijassa-2051	174	18	solutions	solution	NOUN
ijassa-2051	174	19	such	such	ADJ
ijassa-2051	174	20	that	that	SCONJ
ijassa-2051	174	21	∃	∃	PROPN
ijassa-2051	174	22	lim	lim	PROPN
ijassa-2051	174	23	x→x0	x→x0	PROPN
ijassa-2051	174	24	y(x	y(x	PROPN
ijassa-2051	174	25	)	)	PUNCT
ijassa-2051	174	26	=	=	SYM
ijassa-2051	174	27	y0	y0	NOUN
ijassa-2051	174	28	,	,	PUNCT
ijassa-2051	174	29	̸	̸	PUNCT
ijassa-2051	174	30	∃	∃	PROPN
ijassa-2051	174	31	lim	lim	PROPN
ijassa-2051	174	32	x→x0	x→x0	PROPN
ijassa-2051	174	33	p(x	p(x	PROPN
ijassa-2051	174	34	)	)	PUNCT
ijassa-2051	174	35	.	.	PUNCT
ijassa-2051	175	1	here	here	ADV
ijassa-2051	175	2	x	x	X
ijassa-2051	175	3	→	→	X
ijassa-2051	175	4	x0	x0	PROPN
ijassa-2051	175	5	may	may	AUX
ijassa-2051	175	6	be	be	AUX
ijassa-2051	175	7	either	either	CCONJ
ijassa-2051	175	8	two	two	NUM
ijassa-2051	175	9	-	-	PUNCT
ijassa-2051	175	10	sided	sided	ADJ
ijassa-2051	175	11	or	or	CCONJ
ijassa-2051	175	12	one	one	NUM
ijassa-2051	175	13	-	-	PUNCT
ijassa-2051	175	14	sided	sided	ADJ
ijassa-2051	175	15	limit	limit	NOUN
ijassa-2051	175	16	.	.	PUNCT
ijassa-2051	176	1	the	the	DET
ijassa-2051	176	2	above	above	ADJ
ijassa-2051	176	3	examples	example	NOUN
ijassa-2051	176	4	show	show	VERB
ijassa-2051	176	5	that	that	SCONJ
ijassa-2051	176	6	oscillating	oscillate	VERB
ijassa-2051	176	7	solutions	solution	NOUN
ijassa-2051	176	8	exist	exist	VERB
ijassa-2051	176	9	.	.	PUNCT
ijassa-2051	177	1	however	however	ADV
ijassa-2051	177	2	,	,	PUNCT
ijassa-2051	177	3	the	the	DET
ijassa-2051	177	4	following	follow	VERB
ijassa-2051	177	5	theorem	theorem	ADJ
ijassa-2051	177	6	states	state	NOUN
ijassa-2051	177	7	that	that	SCONJ
ijassa-2051	177	8	oscillating	oscillate	VERB
ijassa-2051	177	9	solutions	solution	NOUN
ijassa-2051	177	10	do	do	AUX
ijassa-2051	177	11	not	not	PART
ijassa-2051	177	12	exist	exist	VERB
ijassa-2051	177	13	generically	generically	ADV
ijassa-2051	177	14	.	.	PUNCT
ijassa-2051	178	1	theorem	theorem	VERB
ijassa-2051	178	2	4.1	4.1	NUM
ijassa-2051	178	3	:	:	PUNCT
ijassa-2051	178	4	let	let	VERB
ijassa-2051	178	5	q0	q0	PROPN
ijassa-2051	178	6	∈	∈	PROPN
ijassa-2051	178	7	γ	γ	NOUN
ijassa-2051	178	8	and	and	CCONJ
ijassa-2051	178	9	m(q0	m(q0	NOUN
ijassa-2051	178	10	,	,	PUNCT
ijassa-2051	178	11	p	p	NOUN
ijassa-2051	178	12	)	)	PUNCT
ijassa-2051	178	13	is	be	AUX
ijassa-2051	178	14	an	an	DET
ijassa-2051	178	15	analytic	analytic	ADJ
ijassa-2051	178	16	function	function	NOUN
ijassa-2051	178	17	not	not	PART
ijassa-2051	178	18	identically	identically	ADV
ijassa-2051	178	19	zero	zero	NUM
ijassa-2051	178	20	.	.	PUNCT
ijassa-2051	179	1	then	then	ADV
ijassa-2051	179	2	equation	equation	NOUN
ijassa-2051	179	3	(	(	PUNCT
ijassa-2051	179	4	4.22	4.22	NUM
ijassa-2051	179	5	)	)	PUNCT
ijassa-2051	179	6	has	have	VERB
ijassa-2051	179	7	no	no	DET
ijassa-2051	179	8	oscillating	oscillate	VERB
ijassa-2051	179	9	solutions	solution	NOUN
ijassa-2051	179	10	entering	enter	VERB
ijassa-2051	179	11	the	the	DET
ijassa-2051	179	12	point	point	NOUN
ijassa-2051	179	13	q0	q0	NOUN
ijassa-2051	179	14	.	.	PUNCT
ijassa-2051	180	1	moreover	moreover	ADV
ijassa-2051	180	2	,	,	PUNCT
ijassa-2051	180	3	solutions	solution	NOUN
ijassa-2051	180	4	can	can	AUX
ijassa-2051	180	5	enter	enter	VERB
ijassa-2051	180	6	q0	q0	NOUN
ijassa-2051	180	7	at	at	ADP
ijassa-2051	180	8	so	so	ADV
ijassa-2051	180	9	-	-	PUNCT
ijassa-2051	180	10	called	call	VERB
ijassa-2051	180	11	admissible	admissible	ADJ
ijassa-2051	180	12	directions	direction	NOUN
ijassa-2051	180	13	p	p	NOUN
ijassa-2051	180	14	that	that	PRON
ijassa-2051	180	15	correspond	correspond	VERB
ijassa-2051	180	16	to	to	ADP
ijassa-2051	180	17	real	real	ADJ
ijassa-2051	180	18	roots	root	NOUN
ijassa-2051	180	19	of	of	ADP
ijassa-2051	180	20	m(q0	m(q0	NOUN
ijassa-2051	180	21	,	,	PUNCT
ijassa-2051	180	22	p	p	NOUN
ijassa-2051	180	23	)	)	PUNCT
ijassa-2051	180	24	only	only	ADV
ijassa-2051	180	25	.	.	PUNCT
ijassa-2051	181	1	the	the	DET
ijassa-2051	181	2	proof	proof	NOUN
ijassa-2051	181	3	of	of	ADP
ijassa-2051	181	4	theorem	theorem	ADJ
ijassa-2051	181	5	4.1	4.1	NUM
ijassa-2051	181	6	is	be	AUX
ijassa-2051	181	7	based	base	VERB
ijassa-2051	181	8	on	on	ADP
ijassa-2051	181	9	the	the	DET
ijassa-2051	181	10	analysis	analysis	NOUN
ijassa-2051	181	11	of	of	ADP
ijassa-2051	181	12	the	the	DET
ijassa-2051	181	13	distribution	distribution	NOUN
ijassa-2051	181	14	defined	define	VERB
ijassa-2051	181	15	by	by	ADP
ijassa-2051	181	16	equation	equation	NOUN
ijassa-2051	181	17	(	(	PUNCT
ijassa-2051	181	18	4.22	4.22	NUM
ijassa-2051	181	19	)	)	PUNCT
ijassa-2051	181	20	in	in	ADP
ijassa-2051	181	21	the	the	DET
ijassa-2051	181	22	(	(	PUNCT
ijassa-2051	181	23	x	x	PROPN
ijassa-2051	181	24	,	,	PUNCT
ijassa-2051	181	25	y	y	PROPN
ijassa-2051	181	26	,	,	PUNCT
ijassa-2051	181	27	p)-space	p)-space	ADV
ijassa-2051	181	28	:	:	PUNCT
ijassa-2051	181	29	ω1	ω1	PROPN
ijassa-2051	181	30	=	=	SYM
ijassa-2051	181	31	∆dp−mdx	∆dp−mdx	PROPN
ijassa-2051	181	32	=	=	SYM
ijassa-2051	181	33	0	0	NUM
ijassa-2051	181	34	,	,	PUNCT
ijassa-2051	181	35	ω2	ω2	NOUN
ijassa-2051	181	36	=	=	PUNCT
ijassa-2051	181	37	dy	dy	NOUN
ijassa-2051	181	38	−	−	NOUN
ijassa-2051	181	39	pdx	pdx	PROPN
ijassa-2051	181	40	=	=	SYM
ijassa-2051	181	41	0	0	PROPN
ijassa-2051	181	42	,	,	PUNCT
ijassa-2051	181	43	which	which	PRON
ijassa-2051	181	44	generates	generate	VERB
ijassa-2051	181	45	the	the	DET
ijassa-2051	181	46	vector	vector	NOUN
ijassa-2051	181	47	field	field	NOUN
ijassa-2051	181	48	ẋ	ẋ	PUNCT
ijassa-2051	182	1	=	=	SYM
ijassa-2051	182	2	∆(x	∆(x	PROPN
ijassa-2051	182	3	,	,	PUNCT
ijassa-2051	182	4	y	y	PROPN
ijassa-2051	182	5	)	)	PUNCT
ijassa-2051	182	6	,	,	PUNCT
ijassa-2051	182	7	ẏ	ẏ	PRON
ijassa-2051	182	8	=	=	SYM
ijassa-2051	182	9	p∆(x	p∆(x	PROPN
ijassa-2051	182	10	,	,	PUNCT
ijassa-2051	182	11	y	y	NOUN
ijassa-2051	182	12	)	)	PUNCT
ijassa-2051	182	13	,	,	PUNCT
ijassa-2051	182	14	ṗ	ṗ	ADJ
ijassa-2051	182	15	=	=	SYM
ijassa-2051	182	16	m(x	m(x	PROPN
ijassa-2051	182	17	,	,	PUNCT
ijassa-2051	182	18	y	y	PROPN
ijassa-2051	182	19	,	,	PUNCT
ijassa-2051	182	20	p	p	NOUN
ijassa-2051	182	21	)	)	PUNCT
ijassa-2051	182	22	.	.	PUNCT
ijassa-2051	183	1	(	(	PUNCT
ijassa-2051	183	2	4.23	4.23	NUM
ijassa-2051	183	3	)	)	PUNCT
ijassa-2051	183	4	all	all	DET
ijassa-2051	183	5	components	component	NOUN
ijassa-2051	183	6	of	of	ADP
ijassa-2051	183	7	the	the	DET
ijassa-2051	183	8	field	field	NOUN
ijassa-2051	183	9	(	(	PUNCT
ijassa-2051	183	10	4.23	4.23	NUM
ijassa-2051	183	11	)	)	PUNCT
ijassa-2051	183	12	belong	belong	VERB
ijassa-2051	183	13	to	to	ADP
ijassa-2051	183	14	the	the	DET
ijassa-2051	183	15	ideal	ideal	NOUN
ijassa-2051	183	16	generated	generate	VERB
ijassa-2051	183	17	by	by	ADP
ijassa-2051	183	18	∆	∆	PROPN
ijassa-2051	183	19	and	and	CCONJ
ijassa-2051	183	20	m	m	PROPN
ijassa-2051	183	21	.	.	PUNCT
ijassa-2051	184	1	given	give	VERB
ijassa-2051	184	2	q0	q0	PROPN
ijassa-2051	184	3	∈	∈	PROPN
ijassa-2051	184	4	γ	γ	NOUN
ijassa-2051	184	5	,	,	PUNCT
ijassa-2051	184	6	the	the	DET
ijassa-2051	184	7	admissible	admissible	ADJ
ijassa-2051	184	8	directions	direction	NOUN
ijassa-2051	184	9	p	p	NOUN
ijassa-2051	184	10	correspond	correspond	VERB
ijassa-2051	184	11	to	to	ADP
ijassa-2051	184	12	singular	singular	ADJ
ijassa-2051	184	13	points	point	NOUN
ijassa-2051	184	14	(	(	PUNCT
ijassa-2051	184	15	q0	q0	PROPN
ijassa-2051	184	16	,	,	PUNCT
ijassa-2051	184	17	p	p	NOUN
ijassa-2051	184	18	)	)	PUNCT
ijassa-2051	184	19	of	of	ADP
ijassa-2051	184	20	the	the	DET
ijassa-2051	184	21	vector	vector	NOUN
ijassa-2051	184	22	field	field	NOUN
ijassa-2051	184	23	(	(	PUNCT
ijassa-2051	184	24	4.23	4.23	NUM
ijassa-2051	184	25	)	)	PUNCT
ijassa-2051	184	26	given	give	VERB
ijassa-2051	184	27	by	by	ADP
ijassa-2051	184	28	two	two	NUM
ijassa-2051	184	29	equations	equation	NOUN
ijassa-2051	184	30	:	:	PUNCT
ijassa-2051	184	31	∆(q0	∆(q0	NUM
ijassa-2051	184	32	)	)	PUNCT
ijassa-2051	184	33	=	=	SYM
ijassa-2051	184	34	0	0	NUM
ijassa-2051	184	35	,	,	PUNCT
ijassa-2051	184	36	m(q0	m(q0	NOUN
ijassa-2051	184	37	,	,	PUNCT
ijassa-2051	184	38	p	p	NOUN
ijassa-2051	184	39	)	)	PUNCT
ijassa-2051	184	40	=	=	SYM
ijassa-2051	184	41	0	0	X
ijassa-2051	184	42	.	.	PUNCT
ijassa-2051	185	1	for	for	ADP
ijassa-2051	185	2	more	more	ADJ
ijassa-2051	185	3	details	detail	NOUN
ijassa-2051	185	4	about	about	ADP
ijassa-2051	185	5	oscillating	oscillate	VERB
ijassa-2051	185	6	solutions	solution	NOUN
ijassa-2051	185	7	see	see	VERB
ijassa-2051	185	8	[	[	X
ijassa-2051	185	9	11	11	NUM
ijassa-2051	185	10	]	]	PUNCT
ijassa-2051	185	11	.	.	PUNCT
ijassa-2051	186	1	further	far	ADV
ijassa-2051	186	2	,	,	PUNCT
ijassa-2051	186	3	we	we	PRON
ijassa-2051	186	4	shall	shall	AUX
ijassa-2051	186	5	analyse	analyse	VERB
ijassa-2051	186	6	vector	vector	NOUN
ijassa-2051	186	7	filed	file	VERB
ijassa-2051	186	8	(	(	PUNCT
ijassa-2051	186	9	4.23	4.23	NUM
ijassa-2051	186	10	)	)	PUNCT
ijassa-2051	186	11	in	in	ADP
ijassa-2051	186	12	order	order	NOUN
ijassa-2051	186	13	to	to	PART
ijassa-2051	186	14	study	study	VERB
ijassa-2051	186	15	non	non	ADJ
ijassa-2051	186	16	-	-	ADJ
ijassa-2051	186	17	oscillating	oscillating	ADJ
ijassa-2051	186	18	solutions	solution	NOUN
ijassa-2051	186	19	of	of	ADP
ijassa-2051	186	20	equation	equation	NOUN
ijassa-2051	186	21	(	(	PUNCT
ijassa-2051	186	22	4.22	4.22	NUM
ijassa-2051	186	23	)	)	PUNCT
ijassa-2051	186	24	entering	enter	VERB
ijassa-2051	186	25	its	its	PRON
ijassa-2051	186	26	singular	singular	ADJ
ijassa-2051	186	27	points	point	NOUN
ijassa-2051	186	28	.	.	PUNCT
ijassa-2051	187	1	first	first	ADV
ijassa-2051	187	2	,	,	PUNCT
ijassa-2051	187	3	remark	remark	VERB
ijassa-2051	187	4	that	that	SCONJ
ijassa-2051	187	5	vector	vector	NOUN
ijassa-2051	187	6	filed	file	VERB
ijassa-2051	187	7	(	(	PUNCT
ijassa-2051	187	8	4.23	4.23	NUM
ijassa-2051	187	9	)	)	PUNCT
ijassa-2051	187	10	has	have	VERB
ijassa-2051	187	11	the	the	DET
ijassa-2051	187	12	form	form	NOUN
ijassa-2051	187	13	(	(	PUNCT
ijassa-2051	187	14	2.5	2.5	NUM
ijassa-2051	187	15	)	)	PUNCT
ijassa-2051	187	16	with	with	ADP
ijassa-2051	187	17	n	n	NOUN
ijassa-2051	187	18	=	=	SYM
ijassa-2051	187	19	1	1	NUM
ijassa-2051	187	20	,	,	PUNCT
ijassa-2051	187	21	where	where	SCONJ
ijassa-2051	187	22	the	the	DET
ijassa-2051	187	23	variables	variable	NOUN
ijassa-2051	187	24	x	x	NOUN
ijassa-2051	187	25	,	,	PUNCT
ijassa-2051	187	26	p	p	NOUN
ijassa-2051	187	27	in	in	ADP
ijassa-2051	187	28	(	(	PUNCT
ijassa-2051	187	29	4.23	4.23	NUM
ijassa-2051	187	30	)	)	PUNCT
ijassa-2051	187	31	correspond	correspond	VERB
ijassa-2051	187	32	to	to	ADP
ijassa-2051	187	33	x	x	PRON
ijassa-2051	187	34	,	,	PUNCT
ijassa-2051	187	35	y	y	PROPN
ijassa-2051	187	36	in	in	ADP
ijassa-2051	187	37	(	(	PUNCT
ijassa-2051	187	38	2.5	2.5	NUM
ijassa-2051	187	39	)	)	PUNCT
ijassa-2051	187	40	,	,	PUNCT
ijassa-2051	187	41	the	the	DET
ijassa-2051	187	42	variable	variable	ADJ
ijassa-2051	187	43	y	y	PROPN
ijassa-2051	187	44	in	in	ADP
ijassa-2051	187	45	(	(	PUNCT
ijassa-2051	187	46	4.23	4.23	NUM
ijassa-2051	187	47	)	)	PUNCT
ijassa-2051	187	48	corresponds	correspond	VERB
ijassa-2051	187	49	to	to	ADP
ijassa-2051	187	50	z1	z1	PROPN
ijassa-2051	187	51	in	in	ADP
ijassa-2051	187	52	(	(	PUNCT
ijassa-2051	187	53	2.5	2.5	NUM
ijassa-2051	187	54	)	)	PUNCT
ijassa-2051	187	55	.	.	PUNCT
ijassa-2051	188	1	let	let	VERB
ijassa-2051	188	2	q0	q0	PROPN
ijassa-2051	188	3	∈	∈	PROPN
ijassa-2051	188	4	γ	γ	NOUN
ijassa-2051	188	5	and	and	CCONJ
ijassa-2051	188	6	m(q0	m(q0	NOUN
ijassa-2051	188	7	,	,	PUNCT
ijassa-2051	188	8	p∗	p∗	PROPN
ijassa-2051	188	9	)	)	PUNCT
ijassa-2051	188	10	=	=	SYM
ijassa-2051	188	11	0	0	NUM
ijassa-2051	188	12	,	,	PUNCT
ijassa-2051	188	13	i.e.	i.e.	X
ijassa-2051	188	14	,	,	PUNCT
ijassa-2051	188	15	p∗	p∗	PROPN
ijassa-2051	188	16	is	be	AUX
ijassa-2051	188	17	an	an	DET
ijassa-2051	188	18	admissible	admissible	ADJ
ijassa-2051	188	19	direction	direction	NOUN
ijassa-2051	188	20	at	at	ADP
ijassa-2051	188	21	q0	q0	PROPN
ijassa-2051	188	22	.	.	PUNCT
ijassa-2051	189	1	the	the	DET
ijassa-2051	189	2	spectrum	spectrum	NOUN
ijassa-2051	189	3	of	of	ADP
ijassa-2051	189	4	the	the	DET
ijassa-2051	189	5	linear	linear	ADJ
ijassa-2051	189	6	part	part	NOUN
ijassa-2051	189	7	of	of	ADP
ijassa-2051	189	8	the	the	DET
ijassa-2051	189	9	field	field	NOUN
ijassa-2051	189	10	(	(	PUNCT
ijassa-2051	189	11	4.23	4.23	NUM
ijassa-2051	189	12	)	)	PUNCT
ijassa-2051	189	13	at	at	ADP
ijassa-2051	189	14	singular	singular	ADJ
ijassa-2051	189	15	point	point	NOUN
ijassa-2051	189	16	(	(	PUNCT
ijassa-2051	189	17	q0	q0	PROPN
ijassa-2051	189	18	,	,	PUNCT
ijassa-2051	189	19	p∗	p∗	PROPN
ijassa-2051	189	20	)	)	PUNCT
ijassa-2051	189	21	is	be	AUX
ijassa-2051	189	22	spec	spec	PROPN
ijassa-2051	189	23	(	(	PUNCT
ijassa-2051	189	24	q0	q0	PROPN
ijassa-2051	189	25	,	,	PUNCT
ijassa-2051	189	26	p∗	p∗	PROPN
ijassa-2051	189	27	)	)	PUNCT
ijassa-2051	189	28	=	=	SYM
ijassa-2051	189	29	(	(	PUNCT
ijassa-2051	189	30	λ1	λ1	ADJ
ijassa-2051	189	31	,	,	PUNCT
ijassa-2051	189	32	λ2	λ2	NOUN
ijassa-2051	189	33	,	,	PUNCT
ijassa-2051	189	34	0	0	NUM
ijassa-2051	189	35	)	)	PUNCT
ijassa-2051	189	36	,	,	PUNCT
ijassa-2051	189	37	copyright	copyright	NOUN
ijassa-2051	189	38	©	©	PROPN
ijassa-2051	189	39	2025	2025	NUM
ijassa-2051	189	40	assa	assa	NOUN
ijassa-2051	189	41	.	.	PUNCT
ijassa-2051	190	1	adv	adv	PROPN
ijassa-2051	190	2	syst	syst	PROPN
ijassa-2051	190	3	sci	sci	PROPN
ijassa-2051	190	4	appl	appl	PROPN
ijassa-2051	190	5	(	(	PUNCT
ijassa-2051	190	6	2025	2025	NUM
ijassa-2051	190	7	)	)	PUNCT
ijassa-2051	190	8	100	100	NUM
ijassa-2051	190	9	n.	n.	NOUN
ijassa-2051	190	10	g.	g.	PROPN
ijassa-2051	190	11	pavlova	pavlova	PROPN
ijassa-2051	190	12	,	,	PUNCT
ijassa-2051	190	13	a.	a.	PROPN
ijassa-2051	190	14	o.	o.	PROPN
ijassa-2051	190	15	remizov	remizov	PROPN
ijassa-2051	190	16	where	where	SCONJ
ijassa-2051	190	17	the	the	DET
ijassa-2051	190	18	eigenvalues	eigenvalue	VERB
ijassa-2051	190	19	λ1	λ1	PROPN
ijassa-2051	190	20	=	=	SYM
ijassa-2051	190	21	(	(	PUNCT
ijassa-2051	190	22	∆x	∆x	PROPN
ijassa-2051	190	23	+	+	CCONJ
ijassa-2051	190	24	p∆y)(q0	p∆y)(q0	NUM
ijassa-2051	190	25	,	,	PUNCT
ijassa-2051	190	26	p∗	p∗	PROPN
ijassa-2051	190	27	)	)	PUNCT
ijassa-2051	190	28	,	,	PUNCT
ijassa-2051	190	29	λ2	λ2	NOUN
ijassa-2051	190	30	=	=	SYM
ijassa-2051	190	31	mp(q0	mp(q0	NUM
ijassa-2051	190	32	,	,	PUNCT
ijassa-2051	190	33	p∗	p∗	PROPN
ijassa-2051	190	34	)	)	PUNCT
ijassa-2051	190	35	.	.	PUNCT
ijassa-2051	191	1	assume	assume	VERB
ijassa-2051	191	2	that	that	SCONJ
ijassa-2051	191	3	λ1,2	λ1,2	PROPN
ijassa-2051	191	4	̸=	̸=	PROPN
ijassa-2051	191	5	0	0	NUM
ijassa-2051	191	6	.	.	PUNCT
ijassa-2051	192	1	then	then	ADV
ijassa-2051	192	2	we	we	PRON
ijassa-2051	192	3	define	define	VERB
ijassa-2051	192	4	the	the	DET
ijassa-2051	192	5	value	value	NOUN
ijassa-2051	192	6	λ	λ	NOUN
ijassa-2051	192	7	=	=	SYM
ijassa-2051	192	8	λ2	λ2	NOUN
ijassa-2051	192	9	:	:	PUNCT
ijassa-2051	192	10	λ1	λ1	PROPN
ijassa-2051	192	11	,	,	PUNCT
ijassa-2051	192	12	which	which	PRON
ijassa-2051	192	13	determines	determine	VERB
ijassa-2051	192	14	the	the	DET
ijassa-2051	192	15	number	number	NOUN
ijassa-2051	192	16	and	and	CCONJ
ijassa-2051	192	17	the	the	DET
ijassa-2051	192	18	behavior	behavior	NOUN
ijassa-2051	192	19	of	of	ADP
ijassa-2051	192	20	solutions	solution	NOUN
ijassa-2051	192	21	of	of	ADP
ijassa-2051	192	22	equation	equation	NOUN
ijassa-2051	192	23	(	(	PUNCT
ijassa-2051	192	24	4.22	4.22	NUM
ijassa-2051	192	25	)	)	PUNCT
ijassa-2051	192	26	that	that	PRON
ijassa-2051	192	27	enter	enter	VERB
ijassa-2051	192	28	q0	q0	VERB
ijassa-2051	192	29	with	with	ADP
ijassa-2051	192	30	the	the	DET
ijassa-2051	192	31	direction	direction	NOUN
ijassa-2051	192	32	p∗.	p∗.	NOUN
ijassa-2051	192	33	namely	namely	ADV
ijassa-2051	192	34	,	,	PUNCT
ijassa-2051	192	35	the	the	DET
ijassa-2051	192	36	following	following	ADJ
ijassa-2051	192	37	result	result	NOUN
ijassa-2051	192	38	is	be	AUX
ijassa-2051	192	39	obtained	obtain	VERB
ijassa-2051	192	40	in	in	ADP
ijassa-2051	192	41	[	[	X
ijassa-2051	192	42	15	15	NUM
ijassa-2051	192	43	]	]	PUNCT
ijassa-2051	192	44	.	.	PUNCT
ijassa-2051	193	1	theorem	theorem	VERB
ijassa-2051	193	2	4.2	4.2	NUM
ijassa-2051	193	3	:	:	PUNCT
ijassa-2051	193	4	if	if	SCONJ
ijassa-2051	193	5	λ	λ	X
ijassa-2051	193	6	<	<	X
ijassa-2051	193	7	0	0	NUM
ijassa-2051	193	8	,	,	PUNCT
ijassa-2051	193	9	then	then	ADV
ijassa-2051	193	10	equation	equation	NOUN
ijassa-2051	193	11	(	(	PUNCT
ijassa-2051	193	12	4.22	4.22	NUM
ijassa-2051	193	13	)	)	PUNCT
ijassa-2051	193	14	has	have	VERB
ijassa-2051	193	15	only	only	ADV
ijassa-2051	193	16	one	one	NUM
ijassa-2051	193	17	solutions	solution	NOUN
ijassa-2051	193	18	passing	pass	VERB
ijassa-2051	193	19	though	though	SCONJ
ijassa-2051	193	20	the	the	DET
ijassa-2051	193	21	point	point	NOUN
ijassa-2051	193	22	q0	q0	VERB
ijassa-2051	193	23	with	with	ADP
ijassa-2051	193	24	the	the	DET
ijassa-2051	193	25	tangential	tangential	ADJ
ijassa-2051	193	26	direction	direction	NOUN
ijassa-2051	193	27	p∗.	p∗.	NOUN
ijassa-2051	193	28	if	if	SCONJ
ijassa-2051	193	29	λ	λ	X
ijassa-2051	193	30	>	>	X
ijassa-2051	193	31	0	0	NUM
ijassa-2051	193	32	,	,	PUNCT
ijassa-2051	193	33	then	then	ADV
ijassa-2051	193	34	equation	equation	NOUN
ijassa-2051	193	35	(	(	PUNCT
ijassa-2051	193	36	4.22	4.22	NUM
ijassa-2051	193	37	)	)	PUNCT
ijassa-2051	193	38	has	have	VERB
ijassa-2051	193	39	an	an	DET
ijassa-2051	193	40	infinite	infinite	ADJ
ijassa-2051	193	41	number	number	NOUN
ijassa-2051	193	42	of	of	ADP
ijassa-2051	193	43	solutions	solution	NOUN
ijassa-2051	193	44	entering	enter	VERB
ijassa-2051	193	45	the	the	DET
ijassa-2051	193	46	point	point	NOUN
ijassa-2051	193	47	q0	q0	NOUN
ijassa-2051	193	48	with	with	ADP
ijassa-2051	193	49	the	the	DET
ijassa-2051	193	50	direction	direction	NOUN
ijassa-2051	193	51	p∗.	p∗.	NOUN
ijassa-2051	193	52	in	in	ADP
ijassa-2051	193	53	appropriate	appropriate	ADJ
ijassa-2051	193	54	local	local	ADJ
ijassa-2051	193	55	coordinates	coordinate	NOUN
ijassa-2051	193	56	,	,	PUNCT
ijassa-2051	193	57	these	these	DET
ijassa-2051	193	58	solutions	solution	NOUN
ijassa-2051	193	59	have	have	VERB
ijassa-2051	193	60	one	one	NUM
ijassa-2051	193	61	of	of	ADP
ijassa-2051	193	62	two	two	NUM
ijassa-2051	193	63	following	follow	VERB
ijassa-2051	193	64	forms	form	NOUN
ijassa-2051	193	65	:	:	PUNCT
ijassa-2051	193	66	y	y	PROPN
ijassa-2051	193	67	=	=	SYM
ijassa-2051	193	68	f	f	PROPN
ijassa-2051	193	69	(	(	PUNCT
ijassa-2051	193	70	x	x	X
ijassa-2051	193	71	,	,	PUNCT
ijassa-2051	193	72	c|x|λ	c|x|λ	PROPN
ijassa-2051	193	73	)	)	PUNCT
ijassa-2051	193	74	,	,	PUNCT
ijassa-2051	193	75	if	if	SCONJ
ijassa-2051	193	76	λ	λ	PROPN
ijassa-2051	193	77	/∈	/∈	PUNCT
ijassa-2051	193	78	n	n	CCONJ
ijassa-2051	193	79	,	,	PUNCT
ijassa-2051	193	80	y	y	PROPN
ijassa-2051	193	81	=	=	SYM
ijassa-2051	193	82	f	f	PROPN
ijassa-2051	193	83	(	(	PUNCT
ijassa-2051	193	84	x	x	X
ijassa-2051	193	85	,	,	PUNCT
ijassa-2051	193	86	xλ(c+	xλ(c+	PROPN
ijassa-2051	193	87	ε	ε	PROPN
ijassa-2051	193	88	ln	ln	ADJ
ijassa-2051	193	89	|x|	|x|	PROPN
ijassa-2051	193	90	)	)	PUNCT
ijassa-2051	193	91	)	)	PUNCT
ijassa-2051	193	92	,	,	PUNCT
ijassa-2051	193	93	ε	ε	PROPN
ijassa-2051	193	94	∈	∈	PROPN
ijassa-2051	193	95	{	{	PUNCT
ijassa-2051	193	96	0	0	NUM
ijassa-2051	193	97	,	,	PUNCT
ijassa-2051	193	98	1	1	NUM
ijassa-2051	193	99	}	}	PUNCT
ijassa-2051	193	100	,	,	PUNCT
ijassa-2051	193	101	if	if	SCONJ
ijassa-2051	193	102	λ	λ	PROPN
ijassa-2051	193	103	∈	∈	PROPN
ijassa-2051	193	104	n	n	CCONJ
ijassa-2051	193	105	,	,	PUNCT
ijassa-2051	193	106	where	where	SCONJ
ijassa-2051	193	107	f	f	PROPN
ijassa-2051	193	108	is	be	AUX
ijassa-2051	193	109	a	a	DET
ijassa-2051	193	110	smooth	smooth	ADJ
ijassa-2051	193	111	function	function	NOUN
ijassa-2051	193	112	,	,	PUNCT
ijassa-2051	193	113	c	c	NOUN
ijassa-2051	193	114	=	=	SYM
ijassa-2051	193	115	const	const	PROPN
ijassa-2051	193	116	.	.	PUNCT
ijassa-2051	194	1	fig	fig	NOUN
ijassa-2051	194	2	.	.	PUNCT
ijassa-2051	195	1	4.3	4.3	NUM
ijassa-2051	195	2	.	.	PUNCT
ijassa-2051	195	3	illustration	illustration	NOUN
ijassa-2051	195	4	for	for	ADP
ijassa-2051	195	5	theorem	theorem	ADJ
ijassa-2051	195	6	4.2	4.2	NUM
ijassa-2051	195	7	:	:	PUNCT
ijassa-2051	195	8	integral	integral	ADJ
ijassa-2051	195	9	curves	curve	NOUN
ijassa-2051	195	10	of	of	ADP
ijassa-2051	195	11	the	the	DET
ijassa-2051	195	12	field	field	NOUN
ijassa-2051	195	13	(	(	PUNCT
ijassa-2051	195	14	4.23	4.23	NUM
ijassa-2051	195	15	)	)	PUNCT
ijassa-2051	195	16	and	and	CCONJ
ijassa-2051	195	17	their	their	PRON
ijassa-2051	195	18	projections	projection	NOUN
ijassa-2051	195	19	to	to	ADP
ijassa-2051	195	20	the	the	DET
ijassa-2051	195	21	(	(	PUNCT
ijassa-2051	195	22	x	x	NOUN
ijassa-2051	195	23	,	,	PUNCT
ijassa-2051	195	24	y)-plane	y)-plane	ADJ
ijassa-2051	195	25	–	–	PUNCT
ijassa-2051	195	26	solutions	solution	NOUN
ijassa-2051	195	27	of	of	ADP
ijassa-2051	195	28	equation	equation	NOUN
ijassa-2051	195	29	(	(	PUNCT
ijassa-2051	195	30	4.22	4.22	NUM
ijassa-2051	195	31	)	)	PUNCT
ijassa-2051	195	32	.	.	PUNCT
ijassa-2051	196	1	from	from	ADP
ijassa-2051	196	2	left	left	ADJ
ijassa-2051	196	3	to	to	ADP
ijassa-2051	196	4	right	right	NOUN
ijassa-2051	196	5	:	:	PUNCT
ijassa-2051	196	6	λ	λ	X
ijassa-2051	196	7	<	<	X
ijassa-2051	196	8	0	0	PUNCT
ijassa-2051	196	9	(	(	PUNCT
ijassa-2051	196	10	a	a	NOUN
ijassa-2051	196	11	)	)	PUNCT
ijassa-2051	196	12	,	,	PUNCT
ijassa-2051	196	13	0	0	PUNCT
ijassa-2051	197	1	<	<	X
ijassa-2051	197	2	λ	λ	X
ijassa-2051	197	3	<	<	X
ijassa-2051	197	4	1	1	NUM
ijassa-2051	197	5	(	(	PUNCT
ijassa-2051	197	6	b	b	NOUN
ijassa-2051	197	7	)	)	PUNCT
ijassa-2051	197	8	,	,	PUNCT
ijassa-2051	197	9	λ	λ	X
ijassa-2051	197	10	>	>	X
ijassa-2051	197	11	1	1	NUM
ijassa-2051	197	12	(	(	PUNCT
ijassa-2051	197	13	c	c	NOUN
ijassa-2051	197	14	)	)	PUNCT
ijassa-2051	197	15	.	.	PUNCT
ijassa-2051	198	1	the	the	DET
ijassa-2051	198	2	curve	curve	NOUN
ijassa-2051	198	3	γ	γ	NOUN
ijassa-2051	198	4	is	be	AUX
ijassa-2051	198	5	depicted	depict	VERB
ijassa-2051	198	6	as	as	ADP
ijassa-2051	198	7	a	a	DET
ijassa-2051	198	8	dashed	dash	VERB
ijassa-2051	198	9	curve	curve	NOUN
ijassa-2051	198	10	on	on	ADP
ijassa-2051	198	11	the	the	DET
ijassa-2051	198	12	(	(	PUNCT
ijassa-2051	198	13	x	x	NOUN
ijassa-2051	198	14	,	,	PUNCT
ijassa-2051	198	15	y)-plane	y)-plane	NOUN
ijassa-2051	198	16	.	.	PROPN
ijassa-2051	198	17	4.1	4.1	NUM
ijassa-2051	198	18	.	.	PUNCT
ijassa-2051	199	1	quasi	quasi	ADJ
ijassa-2051	199	2	-	-	ADJ
ijassa-2051	199	3	linear	linear	ADJ
ijassa-2051	199	4	odes	ode	NOUN
ijassa-2051	199	5	of	of	ADP
ijassa-2051	199	6	the	the	DET
ijassa-2051	199	7	second	second	ADJ
ijassa-2051	199	8	order	order	NOUN
ijassa-2051	199	9	cubic	cubic	ADJ
ijassa-2051	199	10	in	in	ADP
ijassa-2051	199	11	p	p	PROPN
ijassa-2051	199	12	consider	consider	VERB
ijassa-2051	199	13	an	an	DET
ijassa-2051	199	14	important	important	ADJ
ijassa-2051	199	15	class	class	NOUN
ijassa-2051	199	16	of	of	ADP
ijassa-2051	199	17	equations	equation	NOUN
ijassa-2051	199	18	(	(	PUNCT
ijassa-2051	199	19	4.22	4.22	NUM
ijassa-2051	199	20	)	)	PUNCT
ijassa-2051	199	21	,	,	PUNCT
ijassa-2051	199	22	where	where	SCONJ
ijassa-2051	199	23	m(x	m(x	PROPN
ijassa-2051	199	24	,	,	PUNCT
ijassa-2051	199	25	y	y	PROPN
ijassa-2051	199	26	,	,	PUNCT
ijassa-2051	199	27	p	p	NOUN
ijassa-2051	199	28	)	)	PUNCT
ijassa-2051	199	29	is	be	AUX
ijassa-2051	199	30	a	a	DET
ijassa-2051	199	31	cubic	cubic	ADJ
ijassa-2051	199	32	polynomial	polynomial	NOUN
ijassa-2051	199	33	in	in	ADP
ijassa-2051	199	34	p	p	X
ijassa-2051	199	35	:	:	PUNCT
ijassa-2051	199	36	m	m	PROPN
ijassa-2051	199	37	=	=	SYM
ijassa-2051	199	38	µ0	µ0	NOUN
ijassa-2051	200	1	+	+	CCONJ
ijassa-2051	200	2	µ1p+	µ1p+	NOUN
ijassa-2051	200	3	µ2p	µ2p	VERB
ijassa-2051	200	4	2	2	NUM
ijassa-2051	200	5	+	+	CCONJ
ijassa-2051	200	6	µ3p	µ3p	X
ijassa-2051	200	7	3	3	NUM
ijassa-2051	200	8	,	,	PUNCT
ijassa-2051	200	9	µi	µi	ADV
ijassa-2051	200	10	=	=	PUNCT
ijassa-2051	200	11	µi(x	µi(x	NUM
ijassa-2051	200	12	,	,	PUNCT
ijassa-2051	200	13	y	y	NOUN
ijassa-2051	200	14	)	)	PUNCT
ijassa-2051	200	15	.	.	PUNCT
ijassa-2051	201	1	an	an	DET
ijassa-2051	201	2	attention	attention	NOUN
ijassa-2051	201	3	to	to	ADP
ijassa-2051	201	4	such	such	ADJ
ijassa-2051	201	5	equations	equation	NOUN
ijassa-2051	201	6	is	be	AUX
ijassa-2051	201	7	motivated	motivate	VERB
ijassa-2051	201	8	by	by	ADP
ijassa-2051	201	9	their	their	PRON
ijassa-2051	201	10	role	role	NOUN
ijassa-2051	201	11	in	in	ADP
ijassa-2051	201	12	physics	physics	NOUN
ijassa-2051	201	13	and	and	CCONJ
ijassa-2051	201	14	geometry	geometry	NOUN
ijassa-2051	201	15	,	,	PUNCT
ijassa-2051	201	16	for	for	ADP
ijassa-2051	201	17	instance	instance	NOUN
ijassa-2051	201	18	,	,	PUNCT
ijassa-2051	201	19	the	the	DET
ijassa-2051	201	20	description	description	NOUN
ijassa-2051	201	21	of	of	ADP
ijassa-2051	201	22	various	various	ADJ
ijassa-2051	201	23	geometric	geometric	ADJ
ijassa-2051	201	24	structures	structure	NOUN
ijassa-2051	201	25	(	(	PUNCT
ijassa-2051	201	26	geodesic	geodesic	NOUN
ijassa-2051	201	27	flows	flow	VERB
ijassa-2051	201	28	in	in	ADP
ijassa-2051	201	29	affine	affine	NOUN
ijassa-2051	201	30	or	or	CCONJ
ijassa-2051	201	31	projective	projective	ADJ
ijassa-2051	201	32	connection	connection	NOUN
ijassa-2051	201	33	,	,	PUNCT
ijassa-2051	201	34	etc	etc	X
ijassa-2051	201	35	.	.	X
ijassa-2051	201	36	)	)	PUNCT
ijassa-2051	201	37	.	.	PUNCT
ijassa-2051	202	1	equations	equation	NOUN
ijassa-2051	202	2	of	of	ADP
ijassa-2051	202	3	this	this	DET
ijassa-2051	202	4	class	class	NOUN
ijassa-2051	202	5	were	be	AUX
ijassa-2051	202	6	studies	study	NOUN
ijassa-2051	202	7	by	by	ADP
ijassa-2051	202	8	sophus	sophus	PROPN
ijassa-2051	202	9	lie	lie	PROPN
ijassa-2051	202	10	,	,	PUNCT
ijassa-2051	202	11	a.	a.	NOUN
ijassa-2051	202	12	tresse	tresse	PROPN
ijassa-2051	202	13	,	,	PUNCT
ijassa-2051	202	14	j.	j.	PROPN
ijassa-2051	202	15	liouville	liouville	PROPN
ijassa-2051	202	16	,	,	PUNCT
ijassa-2051	202	17	e.	e.	PROPN
ijassa-2051	202	18	cartan	cartan	PROPN
ijassa-2051	202	19	,	,	PUNCT
ijassa-2051	202	20	etc	etc	X
ijassa-2051	202	21	.	.	X
ijassa-2051	203	1	see	see	VERB
ijassa-2051	203	2	also	also	ADV
ijassa-2051	203	3	the	the	DET
ijassa-2051	203	4	recent	recent	ADJ
ijassa-2051	203	5	papers	paper	NOUN
ijassa-2051	203	6	[	[	X
ijassa-2051	203	7	7	7	NUM
ijassa-2051	203	8	,	,	PUNCT
ijassa-2051	203	9	19	19	NUM
ijassa-2051	203	10	,	,	PUNCT
ijassa-2051	203	11	20	20	NUM
ijassa-2051	203	12	]	]	PUNCT
ijassa-2051	203	13	.	.	PUNCT
ijassa-2051	204	1	for	for	ADP
ijassa-2051	204	2	a	a	DET
ijassa-2051	204	3	generic	generic	ADJ
ijassa-2051	204	4	cubic	cubic	ADJ
ijassa-2051	204	5	polynomial	polynomial	ADJ
ijassa-2051	204	6	m(q0	m(q0	NOUN
ijassa-2051	204	7	,	,	PUNCT
ijassa-2051	204	8	p	p	NOUN
ijassa-2051	204	9	)	)	PUNCT
ijassa-2051	204	10	and	and	CCONJ
ijassa-2051	204	11	almost	almost	ADV
ijassa-2051	204	12	all	all	PRON
ijassa-2051	204	13	points	point	NOUN
ijassa-2051	204	14	q0	q0	PROPN
ijassa-2051	204	15	∈	∈	PROPN
ijassa-2051	204	16	γ	γ	NOUN
ijassa-2051	204	17	there	there	PRON
ijassa-2051	204	18	are	be	VERB
ijassa-2051	204	19	4	4	NUM
ijassa-2051	204	20	possible	possible	ADJ
ijassa-2051	204	21	cases	case	NOUN
ijassa-2051	204	22	(	(	PUNCT
ijassa-2051	204	23	the	the	DET
ijassa-2051	204	24	abbreviation	abbreviation	NOUN
ijassa-2051	204	25	ad	ad	NOUN
ijassa-2051	204	26	below	below	ADP
ijassa-2051	204	27	means	mean	VERB
ijassa-2051	204	28	admissible	admissible	ADJ
ijassa-2051	204	29	direction	direction	NOUN
ijassa-2051	204	30	):	):	PUNCT
ijassa-2051	204	31	copyright	copyright	NOUN
ijassa-2051	204	32	©	©	PROPN
ijassa-2051	204	33	2025	2025	NUM
ijassa-2051	204	34	assa	assa	NOUN
ijassa-2051	204	35	.	.	PUNCT
ijassa-2051	205	1	adv	adv	PROPN
ijassa-2051	205	2	syst	syst	PROPN
ijassa-2051	205	3	sci	sci	PROPN
ijassa-2051	205	4	appl	appl	PROPN
ijassa-2051	205	5	(	(	PUNCT
ijassa-2051	205	6	2025	2025	NUM
ijassa-2051	205	7	)	)	PUNCT
ijassa-2051	205	8	vector	vector	NOUN
ijassa-2051	205	9	fields	field	NOUN
ijassa-2051	205	10	with	with	ADP
ijassa-2051	205	11	non	non	ADJ
ijassa-2051	205	12	-	-	ADJ
ijassa-2051	205	13	isolated	isolated	ADJ
ijassa-2051	205	14	singular	singular	ADJ
ijassa-2051	205	15	points	point	NOUN
ijassa-2051	205	16	...	...	PUNCT
ijassa-2051	205	17	101	101	NUM
ijassa-2051	205	18	•	•	NUM
ijassa-2051	205	19	1	1	NUM
ijassa-2051	205	20	ad	ad	NOUN
ijassa-2051	205	21	p0	p0	NOUN
ijassa-2051	205	22	with	with	ADP
ijassa-2051	205	23	λ(q0	λ(q0	NOUN
ijassa-2051	205	24	,	,	PUNCT
ijassa-2051	205	25	p0	p0	NOUN
ijassa-2051	205	26	)	)	PUNCT
ijassa-2051	205	27	>	>	X
ijassa-2051	205	28	0	0	NUM
ijassa-2051	205	29	;	;	PUNCT
ijassa-2051	205	30	•	•	NUM
ijassa-2051	205	31	3	3	NUM
ijassa-2051	205	32	ads	ad	NOUN
ijassa-2051	205	33	p0	p0	NOUN
ijassa-2051	205	34	,	,	PUNCT
ijassa-2051	205	35	p1	p1	NOUN
ijassa-2051	205	36	,	,	PUNCT
ijassa-2051	205	37	p2	p2	PROPN
ijassa-2051	205	38	with	with	ADP
ijassa-2051	205	39	λ(q0	λ(q0	NOUN
ijassa-2051	205	40	,	,	PUNCT
ijassa-2051	205	41	p0	p0	NOUN
ijassa-2051	205	42	)	)	PUNCT
ijassa-2051	205	43	>	>	X
ijassa-2051	205	44	0	0	PUNCT
ijassa-2051	205	45	and	and	CCONJ
ijassa-2051	205	46	λ(q0	λ(q0	NOUN
ijassa-2051	205	47	,	,	PUNCT
ijassa-2051	205	48	pi	pi	NOUN
ijassa-2051	205	49	)	)	PUNCT
ijassa-2051	205	50	<	<	X
ijassa-2051	205	51	0	0	NUM
ijassa-2051	205	52	,	,	PUNCT
ijassa-2051	205	53	i	i	PRON
ijassa-2051	205	54	=	=	NOUN
ijassa-2051	205	55	1	1	NUM
ijassa-2051	205	56	,	,	PUNCT
ijassa-2051	205	57	2	2	NUM
ijassa-2051	205	58	;	;	PUNCT
ijassa-2051	205	59	•	•	NUM
ijassa-2051	205	60	1	1	NUM
ijassa-2051	205	61	ad	ad	NOUN
ijassa-2051	205	62	p0	p0	NOUN
ijassa-2051	205	63	with	with	ADP
ijassa-2051	205	64	λ(q0	λ(q0	NOUN
ijassa-2051	205	65	,	,	PUNCT
ijassa-2051	205	66	p0	p0	NOUN
ijassa-2051	205	67	)	)	PUNCT
ijassa-2051	205	68	<	<	X
ijassa-2051	205	69	0	0	NUM
ijassa-2051	205	70	;	;	PUNCT
ijassa-2051	205	71	•	•	NUM
ijassa-2051	205	72	3	3	NUM
ijassa-2051	205	73	ads	ad	NOUN
ijassa-2051	205	74	p0	p0	NOUN
ijassa-2051	205	75	,	,	PUNCT
ijassa-2051	205	76	p1	p1	NOUN
ijassa-2051	205	77	,	,	PUNCT
ijassa-2051	205	78	p2	p2	PROPN
ijassa-2051	205	79	with	with	ADP
ijassa-2051	205	80	λ(q0	λ(q0	NOUN
ijassa-2051	205	81	,	,	PUNCT
ijassa-2051	205	82	p0	p0	NOUN
ijassa-2051	205	83	)	)	PUNCT
ijassa-2051	205	84	<	<	X
ijassa-2051	205	85	0	0	NUM
ijassa-2051	205	86	and	and	CCONJ
ijassa-2051	205	87	λ(q0	λ(q0	NOUN
ijassa-2051	205	88	,	,	PUNCT
ijassa-2051	205	89	pi	pi	NOUN
ijassa-2051	205	90	)	)	PUNCT
ijassa-2051	205	91	>	>	X
ijassa-2051	206	1	0	0	NUM
ijassa-2051	206	2	,	,	PUNCT
ijassa-2051	206	3	i	i	PRON
ijassa-2051	206	4	=	=	NOUN
ijassa-2051	206	5	1	1	NUM
ijassa-2051	206	6	,	,	PUNCT
ijassa-2051	206	7	2	2	NUM
ijassa-2051	206	8	.	.	PUNCT
ijassa-2051	206	9	example	example	NOUN
ijassa-2051	206	10	4.3	4.3	NUM
ijassa-2051	206	11	:	:	PUNCT
ijassa-2051	206	12	consider	consider	VERB
ijassa-2051	206	13	the	the	DET
ijassa-2051	206	14	equation	equation	NOUN
ijassa-2051	206	15	x	x	PUNCT
ijassa-2051	206	16	dp	dp	NOUN
ijassa-2051	206	17	dx	dx	PROPN
ijassa-2051	206	18	=	=	PUNCT
ijassa-2051	206	19	αp(p2	αp(p2	ADP
ijassa-2051	206	20	−	−	PROPN
ijassa-2051	206	21	1	1	NUM
ijassa-2051	206	22	)	)	PUNCT
ijassa-2051	206	23	,	,	PUNCT
ijassa-2051	206	24	α	α	X
ijassa-2051	206	25	̸=	̸=	PROPN
ijassa-2051	206	26	0	0	NUM
ijassa-2051	206	27	,	,	PUNCT
ijassa-2051	206	28	(	(	PUNCT
ijassa-2051	206	29	4.24	4.24	NUM
ijassa-2051	206	30	)	)	PUNCT
ijassa-2051	206	31	whose	whose	DET
ijassa-2051	206	32	singular	singular	ADJ
ijassa-2051	206	33	points	point	NOUN
ijassa-2051	206	34	fill	fill	VERB
ijassa-2051	206	35	the	the	DET
ijassa-2051	206	36	curve	curve	NOUN
ijassa-2051	206	37	γ	γ	X
ijassa-2051	206	38	=	=	PRON
ijassa-2051	206	39	{	{	PUNCT
ijassa-2051	206	40	x	x	PUNCT
ijassa-2051	206	41	=	=	SYM
ijassa-2051	206	42	0	0	NUM
ijassa-2051	206	43	}	}	PUNCT
ijassa-2051	206	44	.	.	PUNCT
ijassa-2051	207	1	for	for	ADP
ijassa-2051	207	2	every	every	DET
ijassa-2051	207	3	point	point	NOUN
ijassa-2051	207	4	q0	q0	PROPN
ijassa-2051	207	5	∈	∈	PROPN
ijassa-2051	207	6	γ	γ	X
ijassa-2051	207	7	the	the	DET
ijassa-2051	207	8	cubic	cubic	ADJ
ijassa-2051	207	9	polynomial	polynomial	ADJ
ijassa-2051	207	10	m(p	m(p	PROPN
ijassa-2051	207	11	)	)	PUNCT
ijassa-2051	207	12	=	=	SYM
ijassa-2051	207	13	αp(p2	αp(p2	ADP
ijassa-2051	207	14	−	−	PROPN
ijassa-2051	207	15	1	1	NUM
ijassa-2051	207	16	)	)	PUNCT
ijassa-2051	207	17	has	have	VERB
ijassa-2051	207	18	three	three	NUM
ijassa-2051	207	19	different	different	ADJ
ijassa-2051	207	20	real	real	ADJ
ijassa-2051	207	21	roots	root	NOUN
ijassa-2051	207	22	:	:	PUNCT
ijassa-2051	207	23	p0	p0	NOUN
ijassa-2051	207	24	=	=	SYM
ijassa-2051	207	25	0	0	NUM
ijassa-2051	207	26	and	and	CCONJ
ijassa-2051	207	27	p1,2	p1,2	PROPN
ijassa-2051	207	28	=	=	SYM
ijassa-2051	207	29	±1	±1	PROPN
ijassa-2051	207	30	,	,	PUNCT
ijassa-2051	207	31	where	where	SCONJ
ijassa-2051	207	32	λ(q0	λ(q0	NOUN
ijassa-2051	207	33	,	,	PUNCT
ijassa-2051	207	34	0	0	NUM
ijassa-2051	207	35	)	)	PUNCT
ijassa-2051	207	36	=	=	SYM
ijassa-2051	207	37	−α	−α	NOUN
ijassa-2051	207	38	and	and	CCONJ
ijassa-2051	207	39	λ(q0,±1	λ(q0,±1	PROPN
ijassa-2051	207	40	)	)	PUNCT
ijassa-2051	208	1	=	=	PUNCT
ijassa-2051	208	2	2α	2α	NOUN
ijassa-2051	208	3	.	.	PUNCT
ijassa-2051	209	1	solution	solution	NOUN
ijassa-2051	209	2	of	of	ADP
ijassa-2051	209	3	equation	equation	NOUN
ijassa-2051	209	4	(	(	PUNCT
ijassa-2051	209	5	4.24	4.24	NUM
ijassa-2051	209	6	)	)	PUNCT
ijassa-2051	209	7	entering	enter	VERB
ijassa-2051	209	8	the	the	DET
ijassa-2051	209	9	origin	origin	NOUN
ijassa-2051	209	10	are	be	AUX
ijassa-2051	209	11	presented	present	VERB
ijassa-2051	209	12	in	in	ADP
ijassa-2051	209	13	fig	fig	NOUN
ijassa-2051	209	14	.	.	PUNCT
ijassa-2051	210	1	4.4	4.4	NUM
ijassa-2051	210	2	.	.	PUNCT
ijassa-2051	210	3	fig	fig	NOUN
ijassa-2051	210	4	.	.	PUNCT
ijassa-2051	211	1	4.4	4.4	NUM
ijassa-2051	211	2	.	.	PUNCT
ijassa-2051	212	1	on	on	ADP
ijassa-2051	212	2	the	the	DET
ijassa-2051	212	3	left	left	NOUN
ijassa-2051	212	4	:	:	PUNCT
ijassa-2051	212	5	the	the	DET
ijassa-2051	212	6	case	case	NOUN
ijassa-2051	212	7	α	α	X
ijassa-2051	212	8	>	>	X
ijassa-2051	212	9	0	0	NUM
ijassa-2051	212	10	,	,	PUNCT
ijassa-2051	212	11	on	on	ADP
ijassa-2051	212	12	the	the	DET
ijassa-2051	212	13	right	right	NOUN
ijassa-2051	212	14	:	:	PUNCT
ijassa-2051	212	15	the	the	DET
ijassa-2051	212	16	case	case	NOUN
ijassa-2051	212	17	α	α	X
ijassa-2051	212	18	<	<	X
ijassa-2051	212	19	0	0	NUM
ijassa-2051	212	20	.	.	PUNCT
ijassa-2051	213	1	the	the	DET
ijassa-2051	213	2	bold	bold	ADJ
ijassa-2051	213	3	lines	line	NOUN
ijassa-2051	213	4	are	be	AUX
ijassa-2051	213	5	solutions	solution	NOUN
ijassa-2051	213	6	that	that	PRON
ijassa-2051	213	7	are	be	AUX
ijassa-2051	213	8	unique	unique	ADJ
ijassa-2051	213	9	with	with	ADP
ijassa-2051	213	10	given	give	VERB
ijassa-2051	213	11	ad	ad	NOUN
ijassa-2051	213	12	.	.	PUNCT
ijassa-2051	213	13	example	example	NOUN
ijassa-2051	213	14	4.4	4.4	NUM
ijassa-2051	213	15	:	:	PUNCT
ijassa-2051	213	16	consider	consider	VERB
ijassa-2051	213	17	the	the	DET
ijassa-2051	213	18	equation	equation	NOUN
ijassa-2051	213	19	x	x	PUNCT
ijassa-2051	213	20	dp	dp	NOUN
ijassa-2051	213	21	dx	dx	PROPN
ijassa-2051	213	22	=	=	PUNCT
ijassa-2051	213	23	αp(p2	αp(p2	X
ijassa-2051	213	24	+	+	ADJ
ijassa-2051	213	25	1	1	NUM
ijassa-2051	213	26	)	)	PUNCT
ijassa-2051	213	27	,	,	PUNCT
ijassa-2051	213	28	α	α	X
ijassa-2051	213	29	̸=	̸=	PROPN
ijassa-2051	213	30	0	0	NUM
ijassa-2051	213	31	,	,	PUNCT
ijassa-2051	213	32	(	(	PUNCT
ijassa-2051	213	33	4.25	4.25	NUM
ijassa-2051	213	34	)	)	PUNCT
ijassa-2051	213	35	whose	whose	DET
ijassa-2051	213	36	singular	singular	ADJ
ijassa-2051	213	37	points	point	NOUN
ijassa-2051	213	38	fill	fill	VERB
ijassa-2051	213	39	the	the	DET
ijassa-2051	213	40	curve	curve	NOUN
ijassa-2051	213	41	γ	γ	X
ijassa-2051	213	42	=	=	PRON
ijassa-2051	213	43	{	{	PUNCT
ijassa-2051	213	44	x	x	PUNCT
ijassa-2051	213	45	=	=	SYM
ijassa-2051	213	46	0	0	NUM
ijassa-2051	213	47	}	}	PUNCT
ijassa-2051	213	48	.	.	PUNCT
ijassa-2051	214	1	for	for	ADP
ijassa-2051	214	2	every	every	DET
ijassa-2051	214	3	point	point	NOUN
ijassa-2051	214	4	q0	q0	PROPN
ijassa-2051	214	5	∈	∈	PROPN
ijassa-2051	214	6	γ	γ	X
ijassa-2051	214	7	the	the	DET
ijassa-2051	214	8	cubic	cubic	ADJ
ijassa-2051	214	9	polynomial	polynomial	ADJ
ijassa-2051	214	10	m(p	m(p	PROPN
ijassa-2051	214	11	)	)	PUNCT
ijassa-2051	214	12	=	=	SYM
ijassa-2051	214	13	αp(p2	αp(p2	X
ijassa-2051	214	14	+	+	NOUN
ijassa-2051	214	15	1	1	NUM
ijassa-2051	214	16	)	)	PUNCT
ijassa-2051	214	17	has	have	VERB
ijassa-2051	214	18	one	one	NUM
ijassa-2051	214	19	real	real	ADJ
ijassa-2051	214	20	root	root	NOUN
ijassa-2051	214	21	p0	p0	NOUN
ijassa-2051	214	22	=	=	SYM
ijassa-2051	214	23	0	0	NUM
ijassa-2051	214	24	and	and	CCONJ
ijassa-2051	214	25	λ(q0	λ(q0	NOUN
ijassa-2051	214	26	,	,	PUNCT
ijassa-2051	214	27	0	0	NUM
ijassa-2051	214	28	)	)	PUNCT
ijassa-2051	214	29	=	=	SYM
ijassa-2051	214	30	α	α	X
ijassa-2051	214	31	.	.	PUNCT
ijassa-2051	214	32	fig	fig	NOUN
ijassa-2051	214	33	.	.	PUNCT
ijassa-2051	215	1	4.5	4.5	NUM
ijassa-2051	215	2	.	.	PUNCT
ijassa-2051	216	1	on	on	ADP
ijassa-2051	216	2	the	the	DET
ijassa-2051	216	3	left	left	NOUN
ijassa-2051	216	4	:	:	PUNCT
ijassa-2051	216	5	the	the	DET
ijassa-2051	216	6	case	case	NOUN
ijassa-2051	216	7	α	α	X
ijassa-2051	216	8	>	>	X
ijassa-2051	216	9	0	0	NUM
ijassa-2051	216	10	,	,	PUNCT
ijassa-2051	216	11	on	on	ADP
ijassa-2051	216	12	the	the	DET
ijassa-2051	216	13	right	right	NOUN
ijassa-2051	216	14	:	:	PUNCT
ijassa-2051	216	15	the	the	DET
ijassa-2051	216	16	case	case	NOUN
ijassa-2051	216	17	α	α	X
ijassa-2051	216	18	<	<	X
ijassa-2051	216	19	0	0	NUM
ijassa-2051	216	20	.	.	PUNCT
ijassa-2051	217	1	the	the	DET
ijassa-2051	217	2	bold	bold	ADJ
ijassa-2051	217	3	lines	line	NOUN
ijassa-2051	217	4	are	be	AUX
ijassa-2051	217	5	solutions	solution	NOUN
ijassa-2051	217	6	that	that	PRON
ijassa-2051	217	7	are	be	AUX
ijassa-2051	217	8	unique	unique	ADJ
ijassa-2051	217	9	with	with	ADP
ijassa-2051	217	10	given	give	VERB
ijassa-2051	217	11	ad	ad	NOUN
ijassa-2051	217	12	.	.	PUNCT
ijassa-2051	218	1	copyright	copyright	NOUN
ijassa-2051	218	2	©	©	PROPN
ijassa-2051	218	3	2025	2025	NUM
ijassa-2051	218	4	assa	assa	NOUN
ijassa-2051	218	5	.	.	PUNCT
ijassa-2051	219	1	adv	adv	PROPN
ijassa-2051	219	2	syst	syst	PROPN
ijassa-2051	219	3	sci	sci	PROPN
ijassa-2051	219	4	appl	appl	PROPN
ijassa-2051	219	5	(	(	PUNCT
ijassa-2051	219	6	2025	2025	NUM
ijassa-2051	219	7	)	)	PUNCT
ijassa-2051	219	8	102	102	NUM
ijassa-2051	219	9	n.	n.	NOUN
ijassa-2051	219	10	g.	g.	PROPN
ijassa-2051	219	11	pavlova	pavlova	PROPN
ijassa-2051	219	12	,	,	PUNCT
ijassa-2051	219	13	a.	a.	PROPN
ijassa-2051	219	14	o.	o.	PROPN
ijassa-2051	219	15	remizov	remizov	VERB
ijassa-2051	219	16	4.2	4.2	NUM
ijassa-2051	219	17	.	.	PUNCT
ijassa-2051	220	1	equation	equation	NOUN
ijassa-2051	220	2	of	of	ADP
ijassa-2051	220	3	geodesics	geodesic	NOUN
ijassa-2051	220	4	in	in	ADP
ijassa-2051	220	5	signature	signature	NOUN
ijassa-2051	220	6	varying	vary	VERB
ijassa-2051	220	7	metrics	metric	NOUN
ijassa-2051	220	8	consider	consider	VERB
ijassa-2051	220	9	a	a	DET
ijassa-2051	220	10	pseudo	pseudo	NOUN
ijassa-2051	220	11	-	-	ADJ
ijassa-2051	220	12	riemannian	riemannian	ADJ
ijassa-2051	220	13	metric	metric	ADJ
ijassa-2051	220	14	ds2	ds2	PROPN
ijassa-2051	220	15	=	=	SYM
ijassa-2051	220	16	a(x	a(x	PROPN
ijassa-2051	220	17	,	,	PUNCT
ijassa-2051	220	18	y	y	NOUN
ijassa-2051	220	19	)	)	PUNCT
ijassa-2051	220	20	dx2	dx2	PROPN
ijassa-2051	221	1	+	+	CCONJ
ijassa-2051	221	2	2b(x	2b(x	NUM
ijassa-2051	221	3	,	,	PUNCT
ijassa-2051	221	4	y	y	NOUN
ijassa-2051	221	5	)	)	PUNCT
ijassa-2051	221	6	dxdy	dxdy	NOUN
ijassa-2051	221	7	+	+	CCONJ
ijassa-2051	221	8	c(x	c(x	PROPN
ijassa-2051	221	9	,	,	PUNCT
ijassa-2051	221	10	y	y	PROPN
ijassa-2051	221	11	)	)	PUNCT
ijassa-2051	221	12	dy2	dy2	PROPN
ijassa-2051	221	13	,	,	PUNCT
ijassa-2051	221	14	where	where	SCONJ
ijassa-2051	221	15	a	a	DET
ijassa-2051	221	16	,	,	PUNCT
ijassa-2051	221	17	b	b	NOUN
ijassa-2051	221	18	,	,	PUNCT
ijassa-2051	221	19	c	c	PROPN
ijassa-2051	221	20	∈	∈	PROPN
ijassa-2051	221	21	c∞(m	c∞(m	NOUN
ijassa-2051	221	22	)	)	PUNCT
ijassa-2051	221	23	and	and	CCONJ
ijassa-2051	221	24	the	the	DET
ijassa-2051	221	25	discriminant	discriminant	NOUN
ijassa-2051	221	26	function	function	VERB
ijassa-2051	221	27	∆	∆	PROPN
ijassa-2051	221	28	=	=	SYM
ijassa-2051	221	29	ac−	ac−	PROPN
ijassa-2051	221	30	b2	b2	NOUN
ijassa-2051	221	31	vanishes	vanish	VERB
ijassa-2051	221	32	and	and	CCONJ
ijassa-2051	221	33	changes	change	VERB
ijassa-2051	221	34	its	its	PRON
ijassa-2051	221	35	sign	sign	NOUN
ijassa-2051	221	36	on	on	ADP
ijassa-2051	221	37	the	the	DET
ijassa-2051	221	38	regular	regular	ADJ
ijassa-2051	221	39	curve	curve	NOUN
ijassa-2051	221	40	γ	γ	X
ijassa-2051	221	41	⊂	⊂	PROPN
ijassa-2051	221	42	m	m	PROPN
ijassa-2051	221	43	.	.	PUNCT
ijassa-2051	222	1	the	the	DET
ijassa-2051	222	2	latter	latter	ADJ
ijassa-2051	222	3	condition	condition	NOUN
ijassa-2051	222	4	implies	imply	VERB
ijassa-2051	222	5	that	that	SCONJ
ijassa-2051	222	6	the	the	DET
ijassa-2051	222	7	coefficients	coefficient	NOUN
ijassa-2051	222	8	a	a	DET
ijassa-2051	222	9	,	,	PUNCT
ijassa-2051	222	10	b	b	NOUN
ijassa-2051	222	11	,	,	PUNCT
ijassa-2051	222	12	c	c	PRON
ijassa-2051	222	13	do	do	AUX
ijassa-2051	222	14	not	not	PART
ijassa-2051	222	15	vanish	vanish	VERB
ijassa-2051	222	16	simultaneously	simultaneously	ADV
ijassa-2051	222	17	,	,	PUNCT
ijassa-2051	222	18	therefore	therefore	ADV
ijassa-2051	222	19	,	,	PUNCT
ijassa-2051	222	20	the	the	DET
ijassa-2051	222	21	square	square	ADJ
ijassa-2051	222	22	polynomial	polynomial	ADJ
ijassa-2051	222	23	a(q0	a(q0	NOUN
ijassa-2051	222	24	)	)	PUNCT
ijassa-2051	223	1	+	+	CCONJ
ijassa-2051	223	2	2b(q0)p+	2b(q0)p+	NUM
ijassa-2051	223	3	c(q0)p	c(q0)p	PROPN
ijassa-2051	223	4	2	2	NUM
ijassa-2051	223	5	at	at	ADP
ijassa-2051	223	6	every	every	DET
ijassa-2051	223	7	point	point	NOUN
ijassa-2051	223	8	q0	q0	PROPN
ijassa-2051	223	9	∈	∈	PROPN
ijassa-2051	223	10	gamma	gamma	NOUN
ijassa-2051	223	11	has	have	VERB
ijassa-2051	223	12	the	the	DET
ijassa-2051	223	13	double	double	ADJ
ijassa-2051	223	14	root	root	NOUN
ijassa-2051	223	15	p0	p0	NOUN
ijassa-2051	223	16	=	=	SYM
ijassa-2051	223	17	−a	−a	NOUN
ijassa-2051	223	18	b	b	X
ijassa-2051	223	19	=	=	PUNCT
ijassa-2051	223	20	−b	−b	PROPN
ijassa-2051	223	21	c	c	NOUN
ijassa-2051	223	22	,	,	PUNCT
ijassa-2051	223	23	which	which	PRON
ijassa-2051	223	24	defines	define	VERB
ijassa-2051	223	25	the	the	DET
ijassa-2051	223	26	isotropic	isotropic	ADJ
ijassa-2051	223	27	direction	direction	NOUN
ijassa-2051	223	28	of	of	ADP
ijassa-2051	223	29	the	the	DET
ijassa-2051	223	30	metric	metric	NOUN
ijassa-2051	223	31	at	at	ADP
ijassa-2051	223	32	the	the	DET
ijassa-2051	223	33	point	point	NOUN
ijassa-2051	223	34	q0	q0	NOUN
ijassa-2051	223	35	.	.	PUNCT
ijassa-2051	224	1	the	the	DET
ijassa-2051	224	2	equation	equation	NOUN
ijassa-2051	224	3	of	of	ADP
ijassa-2051	224	4	(	(	PUNCT
ijassa-2051	224	5	unparametrized	unparametrized	ADJ
ijassa-2051	224	6	)	)	PUNCT
ijassa-2051	224	7	geodesics	geodesic	NOUN
ijassa-2051	224	8	in	in	ADP
ijassa-2051	224	9	this	this	DET
ijassa-2051	224	10	metric	metric	NOUN
ijassa-2051	224	11	has	have	VERB
ijassa-2051	224	12	the	the	DET
ijassa-2051	224	13	form	form	NOUN
ijassa-2051	224	14	∆(x	∆(x	PROPN
ijassa-2051	224	15	,	,	PUNCT
ijassa-2051	224	16	y	y	NOUN
ijassa-2051	224	17	)	)	PUNCT
ijassa-2051	224	18	dp	dp	NOUN
ijassa-2051	225	1	dx	dx	NOUN
ijassa-2051	225	2	=	=	SYM
ijassa-2051	225	3	1	1	NUM
ijassa-2051	225	4	2	2	NUM
ijassa-2051	225	5	m(x	m(x	PROPN
ijassa-2051	225	6	,	,	PUNCT
ijassa-2051	225	7	y	y	PROPN
ijassa-2051	225	8	,	,	PUNCT
ijassa-2051	225	9	p	p	NOUN
ijassa-2051	225	10	)	)	PUNCT
ijassa-2051	225	11	,	,	PUNCT
ijassa-2051	225	12	p	p	NOUN
ijassa-2051	225	13	=	=	PUNCT
ijassa-2051	225	14	dy	dy	X
ijassa-2051	225	15	/	/	SYM
ijassa-2051	225	16	dx	dx	PROPN
ijassa-2051	225	17	,	,	PUNCT
ijassa-2051	225	18	where	where	SCONJ
ijassa-2051	225	19	m	m	PROPN
ijassa-2051	225	20	is	be	AUX
ijassa-2051	225	21	a	a	DET
ijassa-2051	225	22	cubic	cubic	ADJ
ijassa-2051	225	23	polynomial	polynomial	ADJ
ijassa-2051	225	24	m	m	PROPN
ijassa-2051	225	25	=	=	NOUN
ijassa-2051	225	26	µ0	µ0	NOUN
ijassa-2051	226	1	+	+	CCONJ
ijassa-2051	226	2	µ1p+	µ1p+	NOUN
ijassa-2051	226	3	µ2p	µ2p	VERB
ijassa-2051	226	4	2	2	NUM
ijassa-2051	226	5	+	+	CCONJ
ijassa-2051	226	6	µ3p	µ3p	X
ijassa-2051	226	7	3	3	NUM
ijassa-2051	226	8	with	with	ADP
ijassa-2051	226	9	the	the	DET
ijassa-2051	226	10	coefficients	coefficient	NOUN
ijassa-2051	226	11	µ3	µ3	NOUN
ijassa-2051	226	12	=	=	PUNCT
ijassa-2051	226	13	c(2by	c(2by	NOUN
ijassa-2051	226	14	−	−	PROPN
ijassa-2051	226	15	cx)−	cx)−	NOUN
ijassa-2051	226	16	bcy	bcy	NOUN
ijassa-2051	226	17	,	,	PUNCT
ijassa-2051	226	18	µ2	µ2	PROPN
ijassa-2051	226	19	=	=	PUNCT
ijassa-2051	226	20	b(2by	b(2by	NOUN
ijassa-2051	226	21	−	−	PROPN
ijassa-2051	226	22	3cx	3cx	NOUN
ijassa-2051	226	23	)	)	PUNCT
ijassa-2051	227	1	+	+	NUM
ijassa-2051	227	2	2ayc−	2ayc−	NUM
ijassa-2051	227	3	acy	acy	NOUN
ijassa-2051	227	4	,	,	PUNCT
ijassa-2051	227	5	µ1	µ1	PROPN
ijassa-2051	227	6	=	=	NOUN
ijassa-2051	227	7	b(3ay	b(3ay	VERB
ijassa-2051	227	8	−	−	PROPN
ijassa-2051	227	9	2bx	2bx	ADJ
ijassa-2051	227	10	)	)	PUNCT
ijassa-2051	228	1	+	+	CCONJ
ijassa-2051	228	2	axc−	axc−	PROPN
ijassa-2051	228	3	2acx	2acx	NUM
ijassa-2051	228	4	,	,	PUNCT
ijassa-2051	228	5	µ0	µ0	NOUN
ijassa-2051	228	6	=	=	SYM
ijassa-2051	228	7	a(ay	a(ay	X
ijassa-2051	228	8	−	−	NOUN
ijassa-2051	228	9	2bx	2bx	NOUN
ijassa-2051	228	10	)	)	PUNCT
ijassa-2051	229	1	+	+	CCONJ
ijassa-2051	230	1	axb	axb	PROPN
ijassa-2051	230	2	.	.	PUNCT
ijassa-2051	231	1	this	this	PRON
ijassa-2051	231	2	is	be	AUX
ijassa-2051	231	3	a	a	DET
ijassa-2051	231	4	special	special	ADJ
ijassa-2051	231	5	case	case	NOUN
ijassa-2051	231	6	of	of	ADP
ijassa-2051	231	7	quasi	quasi	ADJ
ijassa-2051	231	8	-	-	ADJ
ijassa-2051	231	9	linear	linear	ADJ
ijassa-2051	231	10	equation	equation	NOUN
ijassa-2051	231	11	of	of	ADP
ijassa-2051	231	12	the	the	DET
ijassa-2051	231	13	second	second	ADJ
ijassa-2051	231	14	order	order	NOUN
ijassa-2051	231	15	.	.	PUNCT
ijassa-2051	232	1	in	in	ADP
ijassa-2051	232	2	this	this	DET
ijassa-2051	232	3	case	case	NOUN
ijassa-2051	232	4	,	,	PUNCT
ijassa-2051	232	5	the	the	DET
ijassa-2051	232	6	isotropic	isotropic	ADJ
ijassa-2051	232	7	direction	direction	NOUN
ijassa-2051	232	8	p0	p0	NOUN
ijassa-2051	232	9	is	be	AUX
ijassa-2051	232	10	always	always	ADV
ijassa-2051	232	11	admissible	admissible	ADJ
ijassa-2051	232	12	,	,	PUNCT
ijassa-2051	232	13	that	that	ADV
ijassa-2051	232	14	is	is	ADV
ijassa-2051	232	15	,	,	PUNCT
ijassa-2051	232	16	m(q0	m(q0	NOUN
ijassa-2051	232	17	,	,	PUNCT
ijassa-2051	232	18	p0	p0	NOUN
ijassa-2051	232	19	)	)	PUNCT
ijassa-2051	232	20	=	=	SYM
ijassa-2051	233	1	0	0	X
ijassa-2051	233	2	.	.	PUNCT
ijassa-2051	234	1	at	at	ADP
ijassa-2051	234	2	almost	almost	ADV
ijassa-2051	234	3	all	all	PRON
ijassa-2051	234	4	points	point	NOUN
ijassa-2051	234	5	of	of	ADP
ijassa-2051	234	6	the	the	DET
ijassa-2051	234	7	curve	curve	NOUN
ijassa-2051	234	8	γ	γ	PROPN
ijassa-2051	234	9	,	,	PUNCT
ijassa-2051	234	10	the	the	DET
ijassa-2051	234	11	cubic	cubic	ADJ
ijassa-2051	234	12	polynomial	polynomial	NOUN
ijassa-2051	234	13	m	m	VERB
ijassa-2051	234	14	has	have	VERB
ijassa-2051	234	15	either	either	CCONJ
ijassa-2051	234	16	one	one	NUM
ijassa-2051	234	17	or	or	CCONJ
ijassa-2051	234	18	three	three	NUM
ijassa-2051	234	19	real	real	ADJ
ijassa-2051	234	20	roots	root	NOUN
ijassa-2051	234	21	,	,	PUNCT
ijassa-2051	234	22	and	and	CCONJ
ijassa-2051	234	23	there	there	PRON
ijassa-2051	234	24	are	be	VERB
ijassa-2051	234	25	only	only	ADV
ijassa-2051	234	26	two	two	NUM
ijassa-2051	234	27	possible	possible	ADJ
ijassa-2051	234	28	combinations	combination	NOUN
ijassa-2051	234	29	:	:	PUNCT
ijassa-2051	234	30	•	•	NUM
ijassa-2051	234	31	one	one	NUM
ijassa-2051	234	32	ad	ad	NOUN
ijassa-2051	234	33	p0	p0	NOUN
ijassa-2051	234	34	with	with	ADP
ijassa-2051	234	35	λ(q0	λ(q0	NOUN
ijassa-2051	234	36	,	,	PUNCT
ijassa-2051	234	37	p0	p0	NOUN
ijassa-2051	234	38	)	)	PUNCT
ijassa-2051	234	39	=	=	SYM
ijassa-2051	234	40	1	1	NUM
ijassa-2051	234	41	2	2	NUM
ijassa-2051	234	42	,	,	PUNCT
ijassa-2051	234	43	•	•	NUM
ijassa-2051	234	44	three	three	NUM
ijassa-2051	234	45	ads	ad	NOUN
ijassa-2051	234	46	p0	p0	NOUN
ijassa-2051	234	47	,	,	PUNCT
ijassa-2051	234	48	p1	p1	NOUN
ijassa-2051	234	49	,	,	PUNCT
ijassa-2051	234	50	p2	p2	PROPN
ijassa-2051	234	51	with	with	ADP
ijassa-2051	234	52	λ(q0	λ(q0	NOUN
ijassa-2051	234	53	,	,	PUNCT
ijassa-2051	234	54	p0	p0	NOUN
ijassa-2051	234	55	)	)	PUNCT
ijassa-2051	234	56	=	=	SYM
ijassa-2051	234	57	1	1	NUM
ijassa-2051	234	58	2	2	NUM
ijassa-2051	234	59	and	and	CCONJ
ijassa-2051	234	60	λ(q0	λ(q0	NOUN
ijassa-2051	234	61	,	,	PUNCT
ijassa-2051	234	62	pi	pi	NOUN
ijassa-2051	234	63	)	)	PUNCT
ijassa-2051	235	1	=	=	SYM
ijassa-2051	235	2	−1	−1	NOUN
ijassa-2051	235	3	,	,	PUNCT
ijassa-2051	235	4	i	i	PRON
ijassa-2051	235	5	=	=	NOUN
ijassa-2051	235	6	1	1	NUM
ijassa-2051	235	7	,	,	PUNCT
ijassa-2051	235	8	2	2	NUM
ijassa-2051	235	9	.	.	PUNCT
ijassa-2051	235	10	a	a	DET
ijassa-2051	235	11	deep	deep	ADJ
ijassa-2051	235	12	explanation	explanation	NOUN
ijassa-2051	235	13	of	of	ADP
ijassa-2051	235	14	this	this	DET
ijassa-2051	235	15	surprising	surprising	ADJ
ijassa-2051	235	16	fact	fact	NOUN
ijassa-2051	235	17	can	can	AUX
ijassa-2051	235	18	be	be	AUX
ijassa-2051	235	19	found	find	VERB
ijassa-2051	235	20	in	in	ADP
ijassa-2051	235	21	[	[	X
ijassa-2051	235	22	5	5	NUM
ijassa-2051	235	23	]	]	PUNCT
ijassa-2051	235	24	.	.	PUNCT
ijassa-2051	236	1	finally	finally	ADV
ijassa-2051	236	2	,	,	PUNCT
ijassa-2051	236	3	we	we	PRON
ijassa-2051	236	4	remark	remark	VERB
ijassa-2051	236	5	one	one	NUM
ijassa-2051	236	6	more	more	ADV
ijassa-2051	236	7	interesting	interesting	ADJ
ijassa-2051	236	8	property	property	NOUN
ijassa-2051	236	9	established	establish	VERB
ijassa-2051	236	10	recently	recently	ADV
ijassa-2051	236	11	.	.	PUNCT
ijassa-2051	237	1	let	let	VERB
ijassa-2051	237	2	q0	q0	PROPN
ijassa-2051	237	3	∈	∈	PROPN
ijassa-2051	237	4	γ	γ	NOUN
ijassa-2051	237	5	and	and	CCONJ
ijassa-2051	237	6	the	the	DET
ijassa-2051	237	7	polynomial	polynomial	ADJ
ijassa-2051	237	8	m	m	NOUN
ijassa-2051	237	9	at	at	ADP
ijassa-2051	237	10	q0	q0	PROPN
ijassa-2051	237	11	has	have	VERB
ijassa-2051	237	12	three	three	NUM
ijassa-2051	237	13	different	different	ADJ
ijassa-2051	237	14	real	real	ADJ
ijassa-2051	237	15	roots	root	NOUN
ijassa-2051	237	16	p0	p0	NOUN
ijassa-2051	237	17	,	,	PUNCT
ijassa-2051	237	18	p1	p1	NOUN
ijassa-2051	237	19	,	,	PUNCT
ijassa-2051	237	20	p2	p2	NOUN
ijassa-2051	237	21	,	,	PUNCT
ijassa-2051	237	22	that	that	ADV
ijassa-2051	237	23	is	is	ADV
ijassa-2051	237	24	,	,	PUNCT
ijassa-2051	237	25	three	three	NUM
ijassa-2051	237	26	different	different	ADJ
ijassa-2051	237	27	admissible	admissible	ADJ
ijassa-2051	237	28	directions	direction	NOUN
ijassa-2051	237	29	at	at	ADP
ijassa-2051	237	30	q0	q0	PROPN
ijassa-2051	237	31	.	.	PUNCT
ijassa-2051	238	1	let	let	VERB
ijassa-2051	238	2	pγ	pγ	PRON
ijassa-2051	238	3	be	be	AUX
ijassa-2051	238	4	the	the	DET
ijassa-2051	238	5	tangent	tangent	ADJ
ijassa-2051	238	6	direction	direction	NOUN
ijassa-2051	238	7	to	to	ADP
ijassa-2051	238	8	the	the	DET
ijassa-2051	238	9	curve	curve	NOUN
ijassa-2051	238	10	γ	γ	NOUN
ijassa-2051	238	11	at	at	ADP
ijassa-2051	238	12	q0	q0	PROPN
ijassa-2051	238	13	.	.	PUNCT
ijassa-2051	239	1	then	then	ADV
ijassa-2051	239	2	the	the	DET
ijassa-2051	239	3	relative	relative	ADJ
ijassa-2051	239	4	position	position	NOUN
ijassa-2051	239	5	of	of	ADP
ijassa-2051	239	6	the	the	DET
ijassa-2051	239	7	directions	direction	NOUN
ijassa-2051	239	8	p0	p0	NOUN
ijassa-2051	239	9	,	,	PUNCT
ijassa-2051	239	10	p1	p1	NOUN
ijassa-2051	239	11	,	,	PUNCT
ijassa-2051	239	12	p2	p2	NOUN
ijassa-2051	239	13	,	,	PUNCT
ijassa-2051	239	14	pγ	pγ	PROPN
ijassa-2051	239	15	is	be	AUX
ijassa-2051	239	16	determined	determine	VERB
ijassa-2051	239	17	by	by	ADP
ijassa-2051	239	18	their	their	PRON
ijassa-2051	239	19	cross	cross	NOUN
ijassa-2051	239	20	-	-	NOUN
ijassa-2051	239	21	ratio	ratio	NOUN
ijassa-2051	239	22	:	:	PUNCT
ijassa-2051	239	23	dv(p0	dv(p0	PROPN
ijassa-2051	239	24	,	,	PUNCT
ijassa-2051	239	25	p1	p1	PROPN
ijassa-2051	239	26	,	,	PUNCT
ijassa-2051	239	27	pγ	pγ	NOUN
ijassa-2051	239	28	,	,	PUNCT
ijassa-2051	239	29	p2	p2	X
ijassa-2051	239	30	)	)	PUNCT
ijassa-2051	239	31	=	=	SYM
ijassa-2051	239	32	2	2	X
ijassa-2051	239	33	.	.	PUNCT
ijassa-2051	240	1	the	the	DET
ijassa-2051	240	2	proof	proof	NOUN
ijassa-2051	240	3	can	can	AUX
ijassa-2051	240	4	be	be	AUX
ijassa-2051	240	5	found	find	VERB
ijassa-2051	240	6	in	in	ADP
ijassa-2051	240	7	[	[	X
ijassa-2051	240	8	12	12	NUM
ijassa-2051	240	9	]	]	PUNCT
ijassa-2051	240	10	.	.	PUNCT
ijassa-2051	241	1	in	in	ADP
ijassa-2051	241	2	fig	fig	NOUN
ijassa-2051	241	3	.	.	PUNCT
ijassa-2051	242	1	4.6	4.6	NUM
ijassa-2051	242	2	,	,	PUNCT
ijassa-2051	242	3	we	we	PRON
ijassa-2051	242	4	present	present	VERB
ijassa-2051	242	5	three	three	NUM
ijassa-2051	242	6	families	family	NOUN
ijassa-2051	242	7	of	of	ADP
ijassa-2051	242	8	geodesics	geodesic	NOUN
ijassa-2051	242	9	issuing	issue	VERB
ijassa-2051	242	10	from	from	ADP
ijassa-2051	242	11	a	a	DET
ijassa-2051	242	12	point	point	NOUN
ijassa-2051	242	13	q0	q0	PROPN
ijassa-2051	242	14	∈	∈	PROPN
ijassa-2051	242	15	γ	γ	NOUN
ijassa-2051	242	16	.	.	PUNCT
ijassa-2051	243	1	here	here	ADV
ijassa-2051	243	2	the	the	DET
ijassa-2051	243	3	curve	curve	NOUN
ijassa-2051	243	4	γ	γ	PROPN
ijassa-2051	243	5	coincides	coincide	NOUN
ijassa-2051	243	6	with	with	ADP
ijassa-2051	243	7	the	the	DET
ijassa-2051	243	8	horizontal	horizontal	ADJ
ijassa-2051	243	9	axis	axis	NOUN
ijassa-2051	243	10	(	(	PUNCT
ijassa-2051	243	11	dashed	dash	VERB
ijassa-2051	243	12	line	line	NOUN
ijassa-2051	243	13	)	)	PUNCT
ijassa-2051	243	14	and	and	CCONJ
ijassa-2051	243	15	the	the	DET
ijassa-2051	243	16	isotropic	isotropic	ADJ
ijassa-2051	243	17	admissible	admissible	ADJ
ijassa-2051	243	18	direction	direction	NOUN
ijassa-2051	243	19	p0	p0	NOUN
ijassa-2051	243	20	at	at	ADV
ijassa-2051	243	21	all	all	DET
ijassa-2051	243	22	points	point	NOUN
ijassa-2051	243	23	q0	q0	PROPN
ijassa-2051	243	24	∈	∈	PROPN
ijassa-2051	243	25	γ	γ	NOUN
ijassa-2051	243	26	is	be	AUX
ijassa-2051	243	27	vertical	vertical	ADJ
ijassa-2051	243	28	.	.	PUNCT
ijassa-2051	244	1	the	the	DET
ijassa-2051	244	2	families	family	NOUN
ijassa-2051	244	3	on	on	ADP
ijassa-2051	244	4	the	the	DET
ijassa-2051	244	5	left	left	NOUN
ijassa-2051	244	6	and	and	CCONJ
ijassa-2051	244	7	in	in	ADP
ijassa-2051	244	8	the	the	DET
ijassa-2051	244	9	center	center	NOUN
ijassa-2051	244	10	correspond	correspond	VERB
ijassa-2051	244	11	to	to	PART
ijassa-2051	244	12	points	point	NOUN
ijassa-2051	244	13	q0	q0	PROPN
ijassa-2051	244	14	with	with	ADP
ijassa-2051	244	15	unique	unique	ADJ
ijassa-2051	244	16	admissible	admissible	ADJ
ijassa-2051	244	17	direction	direction	NOUN
ijassa-2051	244	18	p0	p0	NOUN
ijassa-2051	244	19	.	.	PUNCT
ijassa-2051	245	1	the	the	DET
ijassa-2051	245	2	family	family	NOUN
ijassa-2051	245	3	on	on	ADP
ijassa-2051	245	4	the	the	DET
ijassa-2051	245	5	right	right	ADJ
ijassa-2051	245	6	corresponds	correspond	NOUN
ijassa-2051	245	7	to	to	ADP
ijassa-2051	245	8	a	a	DET
ijassa-2051	245	9	point	point	NOUN
ijassa-2051	245	10	q0	q0	NOUN
ijassa-2051	245	11	with	with	ADP
ijassa-2051	245	12	three	three	NUM
ijassa-2051	245	13	admissible	admissible	ADJ
ijassa-2051	245	14	direction	direction	NOUN
ijassa-2051	245	15	p0	p0	NOUN
ijassa-2051	245	16	,	,	PUNCT
ijassa-2051	245	17	p1	p1	NOUN
ijassa-2051	245	18	,	,	PUNCT
ijassa-2051	245	19	p2	p2	NOUN
ijassa-2051	245	20	;	;	PUNCT
ijassa-2051	245	21	geodesics	geodesic	NOUN
ijassa-2051	245	22	with	with	ADP
ijassa-2051	245	23	non	non	ADJ
ijassa-2051	245	24	-	-	ADJ
ijassa-2051	245	25	isotropic	isotropic	ADJ
ijassa-2051	245	26	tangential	tangential	ADJ
ijassa-2051	245	27	directions	direction	NOUN
ijassa-2051	245	28	p1	p1	NOUN
ijassa-2051	245	29	,	,	PUNCT
ijassa-2051	245	30	p2	p2	PROPN
ijassa-2051	245	31	are	be	AUX
ijassa-2051	245	32	depicted	depict	VERB
ijassa-2051	245	33	as	as	ADP
ijassa-2051	245	34	bold	bold	ADJ
ijassa-2051	245	35	lines	line	NOUN
ijassa-2051	245	36	.	.	PUNCT
ijassa-2051	246	1	copyright	copyright	NOUN
ijassa-2051	246	2	©	©	PROPN
ijassa-2051	246	3	2025	2025	NUM
ijassa-2051	246	4	assa	assa	NOUN
ijassa-2051	246	5	.	.	PUNCT
ijassa-2051	247	1	adv	adv	PROPN
ijassa-2051	247	2	syst	syst	PROPN
ijassa-2051	247	3	sci	sci	PROPN
ijassa-2051	247	4	appl	appl	PROPN
ijassa-2051	247	5	(	(	PUNCT
ijassa-2051	247	6	2025	2025	NUM
ijassa-2051	247	7	)	)	PUNCT
ijassa-2051	247	8	vector	vector	NOUN
ijassa-2051	247	9	fields	field	NOUN
ijassa-2051	247	10	with	with	ADP
ijassa-2051	247	11	non	non	ADJ
ijassa-2051	247	12	-	-	ADJ
ijassa-2051	247	13	isolated	isolated	ADJ
ijassa-2051	247	14	singular	singular	ADJ
ijassa-2051	247	15	points	point	NOUN
ijassa-2051	247	16	...	...	PUNCT
ijassa-2051	247	17	103	103	NUM
ijassa-2051	247	18	fig	fig	NOUN
ijassa-2051	247	19	.	.	PUNCT
ijassa-2051	248	1	4.6	4.6	NUM
ijassa-2051	248	2	.	.	PUNCT
ijassa-2051	249	1	three	three	NUM
ijassa-2051	249	2	families	family	NOUN
ijassa-2051	249	3	of	of	ADP
ijassa-2051	249	4	geodesics	geodesic	NOUN
ijassa-2051	249	5	issuing	issue	VERB
ijassa-2051	249	6	from	from	ADP
ijassa-2051	249	7	a	a	DET
ijassa-2051	249	8	point	point	NOUN
ijassa-2051	249	9	q0	q0	PROPN
ijassa-2051	249	10	∈	∈	PROPN
ijassa-2051	249	11	γ	γ	X
ijassa-2051	249	12	.	.	PROPN
ijassa-2051	249	13	5	5	NUM
ijassa-2051	249	14	.	.	X
ijassa-2051	249	15	conclusion	conclusion	NOUN
ijassa-2051	249	16	we	we	PRON
ijassa-2051	249	17	presented	present	VERB
ijassa-2051	249	18	a	a	DET
ijassa-2051	249	19	survey	survey	NOUN
ijassa-2051	249	20	of	of	ADP
ijassa-2051	249	21	recent	recent	ADJ
ijassa-2051	249	22	results	result	NOUN
ijassa-2051	249	23	about	about	ADP
ijassa-2051	249	24	vector	vector	NOUN
ijassa-2051	249	25	fields	field	NOUN
ijassa-2051	249	26	with	with	ADP
ijassa-2051	249	27	non	non	ADJ
ijassa-2051	249	28	-	-	ADJ
ijassa-2051	249	29	isolated	isolated	ADJ
ijassa-2051	249	30	singular	singular	ADJ
ijassa-2051	249	31	points	point	NOUN
ijassa-2051	249	32	and	and	CCONJ
ijassa-2051	249	33	some	some	DET
ijassa-2051	249	34	their	their	PRON
ijassa-2051	249	35	applications	application	NOUN
ijassa-2051	249	36	.	.	PUNCT
ijassa-2051	250	1	one	one	NUM
ijassa-2051	250	2	of	of	ADP
ijassa-2051	250	3	the	the	DET
ijassa-2051	250	4	most	most	ADV
ijassa-2051	250	5	interesting	interesting	ADJ
ijassa-2051	250	6	and	and	CCONJ
ijassa-2051	250	7	promising	promising	ADJ
ijassa-2051	250	8	application	application	NOUN
ijassa-2051	250	9	is	be	AUX
ijassa-2051	250	10	connected	connect	VERB
ijassa-2051	250	11	with	with	ADP
ijassa-2051	250	12	quasi	quasi	ADJ
ijassa-2051	250	13	-	-	ADJ
ijassa-2051	250	14	linear	linear	ADJ
ijassa-2051	250	15	differential	differential	ADJ
ijassa-2051	250	16	equations	equation	NOUN
ijassa-2051	250	17	of	of	ADP
ijassa-2051	250	18	the	the	DET
ijassa-2051	250	19	second	second	ADJ
ijassa-2051	250	20	order	order	NOUN
ijassa-2051	250	21	,	,	PUNCT
ijassa-2051	250	22	including	include	VERB
ijassa-2051	250	23	the	the	DET
ijassa-2051	250	24	equation	equation	NOUN
ijassa-2051	250	25	of	of	ADP
ijassa-2051	250	26	geodesics	geodesic	NOUN
ijassa-2051	250	27	in	in	ADP
ijassa-2051	250	28	signature	signature	NOUN
ijassa-2051	250	29	varying	vary	VERB
ijassa-2051	250	30	(	(	PUNCT
ijassa-2051	250	31	pseudo	pseudo	NOUN
ijassa-2051	250	32	-	-	ADJ
ijassa-2051	250	33	riemannian	riemannian	ADJ
ijassa-2051	250	34	)	)	PUNCT
ijassa-2051	250	35	metrics	metric	NOUN
ijassa-2051	250	36	.	.	PUNCT
ijassa-2051	251	1	this	this	DET
ijassa-2051	251	2	subject	subject	NOUN
ijassa-2051	251	3	motivates	motivate	VERB
ijassa-2051	251	4	research	research	NOUN
ijassa-2051	251	5	in	in	ADP
ijassa-2051	251	6	various	various	ADJ
ijassa-2051	251	7	directions	direction	NOUN
ijassa-2051	251	8	,	,	PUNCT
ijassa-2051	251	9	see	see	VERB
ijassa-2051	251	10	,	,	PUNCT
ijassa-2051	251	11	for	for	ADP
ijassa-2051	251	12	example	example	NOUN
ijassa-2051	251	13	,	,	PUNCT
ijassa-2051	251	14	the	the	DET
ijassa-2051	251	15	papers	paper	NOUN
ijassa-2051	251	16	[	[	X
ijassa-2051	251	17	9,14,16	9,14,16	NUM
ijassa-2051	251	18	]	]	PUNCT
ijassa-2051	251	19	.	.	PUNCT
ijassa-2051	252	1	applications	application	NOUN
ijassa-2051	252	2	of	of	ADP
ijassa-2051	252	3	different	different	ADJ
ijassa-2051	252	4	types	type	NOUN
ijassa-2051	252	5	can	can	AUX
ijassa-2051	252	6	be	be	AUX
ijassa-2051	252	7	also	also	ADV
ijassa-2051	252	8	found	find	VERB
ijassa-2051	252	9	in	in	ADP
ijassa-2051	252	10	[	[	X
ijassa-2051	252	11	3	3	NUM
ijassa-2051	252	12	,	,	PUNCT
ijassa-2051	252	13	4	4	NUM
ijassa-2051	252	14	]	]	PUNCT
ijassa-2051	252	15	,	,	PUNCT
ijassa-2051	252	16	[	[	X
ijassa-2051	252	17	7	7	NUM
ijassa-2051	252	18	,	,	PUNCT
ijassa-2051	252	19	19	19	NUM
ijassa-2051	252	20	]	]	PUNCT
ijassa-2051	252	21	,	,	PUNCT
ijassa-2051	252	22	and	and	CCONJ
ijassa-2051	252	23	[	[	X
ijassa-2051	252	24	8	8	NUM
ijassa-2051	252	25	]	]	PUNCT
ijassa-2051	252	26	.	.	PUNCT
ijassa-2051	253	1	references	reference	NOUN
ijassa-2051	253	2	1	1	NUM
ijassa-2051	253	3	.	.	PUNCT
ijassa-2051	253	4	arnol’d	arnol’d	PROPN
ijassa-2051	253	5	,	,	PUNCT
ijassa-2051	253	6	v.	v.	PROPN
ijassa-2051	253	7	i.	i.	PROPN
ijassa-2051	253	8	&	&	CCONJ
ijassa-2051	253	9	ilyashenko	ilyashenko	PROPN
ijassa-2051	253	10	,	,	PUNCT
ijassa-2051	253	11	yu	yu	PROPN
ijassa-2051	253	12	.	.	PUNCT
ijassa-2051	253	13	s.	s.	PROPN
ijassa-2051	253	14	(	(	PUNCT
ijassa-2051	253	15	1988	1988	NUM
ijassa-2051	253	16	)	)	PUNCT
ijassa-2051	253	17	ordinary	ordinary	ADJ
ijassa-2051	253	18	differential	differential	ADJ
ijassa-2051	253	19	equations	equation	NOUN
ijassa-2051	253	20	,	,	PUNCT
ijassa-2051	253	21	dynamical	dynamical	ADJ
ijassa-2051	253	22	systems	systems	PROPN
ijassa-2051	253	23	i.	i.	PROPN
ijassa-2051	253	24	encycl	encycl	PROPN
ijassa-2051	253	25	.	.	PUNCT
ijassa-2051	254	1	math	math	PROPN
ijassa-2051	254	2	.	.	PUNCT
ijassa-2051	255	1	sci	sci	PROPN
ijassa-2051	255	2	.	.	PROPN
ijassa-2051	256	1	1	1	NUM
ijassa-2051	256	2	,	,	PUNCT
ijassa-2051	256	3	1–148	1–148	NUM
ijassa-2051	256	4	.	.	NOUN
ijassa-2051	257	1	2	2	NUM
ijassa-2051	257	2	.	.	X
ijassa-2051	257	3	arnol’d	arnol’d	NOUN
ijassa-2051	257	4	,	,	PUNCT
ijassa-2051	257	5	v.	v.	PROPN
ijassa-2051	257	6	i.	i.	PROPN
ijassa-2051	257	7	,	,	PUNCT
ijassa-2051	257	8	gusein	gusein	NOUN
ijassa-2051	257	9	-	-	PUNCT
ijassa-2051	257	10	zade	zade	PROPN
ijassa-2051	257	11	,	,	PUNCT
ijassa-2051	257	12	s.	s.	PROPN
ijassa-2051	257	13	m.	m.	PROPN
ijassa-2051	257	14	,	,	PUNCT
ijassa-2051	257	15	&	&	CCONJ
ijassa-2051	257	16	varchenko	varchenko	PROPN
ijassa-2051	257	17	,	,	PUNCT
ijassa-2051	257	18	a.	a.	NOUN
ijassa-2051	257	19	n.	n.	NOUN
ijassa-2051	257	20	(	(	PUNCT
ijassa-2051	257	21	1988	1988	NUM
ijassa-2051	257	22	)	)	PUNCT
ijassa-2051	257	23	singularities	singularity	NOUN
ijassa-2051	257	24	of	of	ADP
ijassa-2051	257	25	differentiable	differentiable	ADJ
ijassa-2051	257	26	maps	map	NOUN
ijassa-2051	257	27	,	,	PUNCT
ijassa-2051	257	28	vol	vol	NOUN
ijassa-2051	257	29	.	.	PUNCT
ijassa-2051	257	30	ii	ii	PROPN
ijassa-2051	257	31	.	.	PUNCT
ijassa-2051	258	1	monogr	monogr	PROPN
ijassa-2051	258	2	.	.	PUNCT
ijassa-2051	259	1	math	math	NOUN
ijassa-2051	259	2	.	.	PUNCT
ijassa-2051	260	1	83	83	NUM
ijassa-2051	260	2	.	.	PUNCT
ijassa-2051	261	1	birkhauser	birkhauser	PROPN
ijassa-2051	261	2	,	,	PUNCT
ijassa-2051	261	3	boston	boston	PROPN
ijassa-2051	261	4	,	,	PUNCT
ijassa-2051	261	5	ma	ma	PROPN
ijassa-2051	261	6	.	.	PROPN
ijassa-2051	261	7	3	3	NUM
ijassa-2051	261	8	.	.	X
ijassa-2051	261	9	bonnard	bonnard	PROPN
ijassa-2051	261	10	,	,	PUNCT
ijassa-2051	261	11	b.	b.	PROPN
ijassa-2051	261	12	,	,	PUNCT
ijassa-2051	261	13	glaser	glaser	PROPN
ijassa-2051	261	14	,	,	PUNCT
ijassa-2051	261	15	s.	s.	PROPN
ijassa-2051	261	16	j.	j.	PROPN
ijassa-2051	261	17	,	,	PUNCT
ijassa-2051	261	18	&	&	CCONJ
ijassa-2051	261	19	sugny	sugny	PROPN
ijassa-2051	261	20	,	,	PUNCT
ijassa-2051	261	21	d.	d.	PROPN
ijassa-2051	261	22	(	(	PUNCT
ijassa-2051	261	23	2012	2012	NUM
ijassa-2051	261	24	)	)	PUNCT
ijassa-2051	261	25	a	a	DET
ijassa-2051	261	26	review	review	NOUN
ijassa-2051	261	27	of	of	ADP
ijassa-2051	261	28	geometric	geometric	ADJ
ijassa-2051	261	29	optimal	optimal	ADJ
ijassa-2051	261	30	control	control	NOUN
ijassa-2051	261	31	for	for	ADP
ijassa-2051	261	32	quantum	quantum	NOUN
ijassa-2051	261	33	systems	system	NOUN
ijassa-2051	261	34	in	in	ADP
ijassa-2051	261	35	nuclear	nuclear	ADJ
ijassa-2051	261	36	magnetic	magnetic	ADJ
ijassa-2051	261	37	resonance	resonance	NOUN
ijassa-2051	261	38	,	,	PUNCT
ijassa-2051	261	39	adv	adv	PROPN
ijassa-2051	261	40	.	.	PUNCT
ijassa-2051	261	41	math	math	PROPN
ijassa-2051	261	42	.	.	PUNCT
ijassa-2051	262	1	phys	phy	NOUN
ijassa-2051	262	2	.	.	PUNCT
ijassa-2051	262	3	,	,	PUNCT
ijassa-2051	262	4	article	article	NOUN
ijassa-2051	262	5	i	i	PROPN
ijassa-2051	262	6	d	d	PROPN
ijassa-2051	262	7	857493	857493	NUM
ijassa-2051	262	8	,	,	PUNCT
ijassa-2051	262	9	29	29	NUM
ijassa-2051	262	10	p.	p.	NOUN
ijassa-2051	262	11	4	4	NUM
ijassa-2051	262	12	.	.	PUNCT
ijassa-2051	263	1	bonnard	bonnard	PROPN
ijassa-2051	263	2	,	,	PUNCT
ijassa-2051	263	3	b.	b.	PROPN
ijassa-2051	263	4	,	,	PUNCT
ijassa-2051	263	5	chyba	chyba	PROPN
ijassa-2051	263	6	,	,	PUNCT
ijassa-2051	263	7	m.	m.	NOUN
ijassa-2051	263	8	,	,	PUNCT
ijassa-2051	263	9	&	&	CCONJ
ijassa-2051	263	10	marriott	marriott	PROPN
ijassa-2051	263	11	,	,	PUNCT
ijassa-2051	263	12	j.	j.	PROPN
ijassa-2051	263	13	(	(	PUNCT
ijassa-2051	263	14	2013	2013	NUM
ijassa-2051	263	15	)	)	PUNCT
ijassa-2051	263	16	singular	singular	ADJ
ijassa-2051	263	17	trajectories	trajectory	NOUN
ijassa-2051	263	18	and	and	CCONJ
ijassa-2051	263	19	the	the	DET
ijassa-2051	263	20	contrast	contrast	NOUN
ijassa-2051	263	21	imaging	imaging	NOUN
ijassa-2051	263	22	problem	problem	NOUN
ijassa-2051	263	23	in	in	ADP
ijassa-2051	263	24	nuclear	nuclear	ADJ
ijassa-2051	263	25	magnetic	magnetic	ADJ
ijassa-2051	263	26	resonance	resonance	NOUN
ijassa-2051	263	27	,	,	PUNCT
ijassa-2051	263	28	siam	siam	PROPN
ijassa-2051	263	29	j.	j.	PROPN
ijassa-2051	263	30	control	control	PROPN
ijassa-2051	263	31	optim	optim	PROPN
ijassa-2051	263	32	.	.	PROPN
ijassa-2051	263	33	,	,	PUNCT
ijassa-2051	263	34	51(2	51(2	NUM
ijassa-2051	263	35	)	)	PUNCT
ijassa-2051	263	36	,	,	PUNCT
ijassa-2051	263	37	1325	1325	NUM
ijassa-2051	263	38	–	–	PUNCT
ijassa-2051	263	39	1349	1349	NUM
ijassa-2051	263	40	.	.	PUNCT
ijassa-2051	264	1	5	5	NUM
ijassa-2051	264	2	.	.	X
ijassa-2051	264	3	ghezzi	ghezzi	PROPN
ijassa-2051	264	4	,	,	PUNCT
ijassa-2051	264	5	r.	r.	PROPN
ijassa-2051	264	6	&	&	CCONJ
ijassa-2051	264	7	remizov	remizov	PROPN
ijassa-2051	264	8	,	,	PUNCT
ijassa-2051	264	9	a.	a.	NOUN
ijassa-2051	264	10	o.	o.	PROPN
ijassa-2051	264	11	(	(	PUNCT
ijassa-2051	264	12	2012	2012	NUM
ijassa-2051	264	13	)	)	PUNCT
ijassa-2051	264	14	on	on	ADP
ijassa-2051	264	15	a	a	DET
ijassa-2051	264	16	class	class	NOUN
ijassa-2051	264	17	of	of	ADP
ijassa-2051	264	18	vector	vector	NOUN
ijassa-2051	264	19	fields	field	NOUN
ijassa-2051	264	20	with	with	ADP
ijassa-2051	264	21	discontinuities	discontinuity	NOUN
ijassa-2051	264	22	of	of	ADP
ijassa-2051	264	23	divide	divide	NOUN
ijassa-2051	264	24	-	-	PUNCT
ijassa-2051	264	25	by	by	ADP
ijassa-2051	264	26	-	-	PUNCT
ijassa-2051	264	27	zero	zero	NUM
ijassa-2051	264	28	type	type	NOUN
ijassa-2051	264	29	and	and	CCONJ
ijassa-2051	264	30	its	its	PRON
ijassa-2051	264	31	applications	application	NOUN
ijassa-2051	264	32	to	to	ADP
ijassa-2051	264	33	geodesics	geodesic	NOUN
ijassa-2051	264	34	in	in	ADP
ijassa-2051	264	35	singular	singular	ADJ
ijassa-2051	264	36	metrics	metric	NOUN
ijassa-2051	264	37	,	,	PUNCT
ijassa-2051	264	38	j.	j.	PROPN
ijassa-2051	264	39	dyn	dyn	PROPN
ijassa-2051	264	40	.	.	PUNCT
ijassa-2051	265	1	control	control	PROPN
ijassa-2051	265	2	syst	syst	PROPN
ijassa-2051	265	3	.	.	PUNCT
ijassa-2051	265	4	,	,	PUNCT
ijassa-2051	265	5	18(1	18(1	NUM
ijassa-2051	265	6	)	)	PUNCT
ijassa-2051	265	7	,	,	PUNCT
ijassa-2051	265	8	135–158	135–158	NUM
ijassa-2051	265	9	.	.	PUNCT
ijassa-2051	266	1	6	6	NUM
ijassa-2051	266	2	.	.	X
ijassa-2051	266	3	hirsch	hirsch	PROPN
ijassa-2051	266	4	,	,	PUNCT
ijassa-2051	266	5	m.	m.	PROPN
ijassa-2051	266	6	w.	w.	PROPN
ijassa-2051	266	7	,	,	PUNCT
ijassa-2051	266	8	pugh	pugh	PROPN
ijassa-2051	266	9	,	,	PUNCT
ijassa-2051	266	10	c.	c.	PROPN
ijassa-2051	266	11	c.	c.	PROPN
ijassa-2051	266	12	,	,	PUNCT
ijassa-2051	266	13	&	&	CCONJ
ijassa-2051	266	14	shub	shub	PROPN
ijassa-2051	266	15	,	,	PUNCT
ijassa-2051	266	16	m.	m.	NOUN
ijassa-2051	266	17	(	(	PUNCT
ijassa-2051	266	18	1977	1977	NUM
ijassa-2051	266	19	)	)	PUNCT
ijassa-2051	266	20	invariant	invariant	ADJ
ijassa-2051	266	21	manifolds	manifold	NOUN
ijassa-2051	266	22	,	,	PUNCT
ijassa-2051	266	23	lect	lect	ADJ
ijassa-2051	266	24	.	.	PUNCT
ijassa-2051	266	25	notes	note	VERB
ijassa-2051	266	26	math	math	PROPN
ijassa-2051	266	27	.	.	PUNCT
ijassa-2051	267	1	583	583	NUM
ijassa-2051	267	2	,	,	PUNCT
ijassa-2051	267	3	berlin	berlin	PROPN
ijassa-2051	267	4	:	:	PUNCT
ijassa-2051	267	5	springer	springer	NOUN
ijassa-2051	267	6	.	.	PUNCT
ijassa-2051	268	1	7	7	X
ijassa-2051	268	2	.	.	X
ijassa-2051	268	3	liang	liang	PROPN
ijassa-2051	268	4	,	,	PUNCT
ijassa-2051	268	5	j.	j.	PROPN
ijassa-2051	268	6	(	(	PUNCT
ijassa-2051	268	7	2009	2009	NUM
ijassa-2051	268	8	)	)	PUNCT
ijassa-2051	268	9	a	a	DET
ijassa-2051	268	10	singular	singular	ADJ
ijassa-2051	268	11	initial	initial	ADJ
ijassa-2051	268	12	value	value	NOUN
ijassa-2051	268	13	problem	problem	NOUN
ijassa-2051	268	14	and	and	CCONJ
ijassa-2051	268	15	self	self	NOUN
ijassa-2051	268	16	-	-	PUNCT
ijassa-2051	268	17	similar	similar	ADJ
ijassa-2051	268	18	solutions	solution	NOUN
ijassa-2051	268	19	of	of	ADP
ijassa-2051	268	20	a	a	DET
ijassa-2051	268	21	nonlinear	nonlinear	ADJ
ijassa-2051	268	22	dissipative	dissipative	ADJ
ijassa-2051	268	23	wave	wave	NOUN
ijassa-2051	268	24	equation	equation	NOUN
ijassa-2051	268	25	,	,	PUNCT
ijassa-2051	268	26	j.	j.	PROPN
ijassa-2051	268	27	differ	differ	VERB
ijassa-2051	268	28	.	.	PUNCT
ijassa-2051	269	1	equations	equation	NOUN
ijassa-2051	269	2	,	,	PUNCT
ijassa-2051	269	3	246	246	NUM
ijassa-2051	269	4	,	,	PUNCT
ijassa-2051	269	5	819–844	819–844	NUM
ijassa-2051	269	6	.	.	PUNCT
ijassa-2051	269	7	8	8	NUM
ijassa-2051	269	8	.	.	X
ijassa-2051	270	1	panov	panov	PROPN
ijassa-2051	270	2	,	,	PUNCT
ijassa-2051	270	3	a.	a.	PROPN
ijassa-2051	270	4	v.	v.	PROPN
ijassa-2051	270	5	(	(	PUNCT
ijassa-2051	270	6	2024	2024	NUM
ijassa-2051	270	7	)	)	PUNCT
ijassa-2051	270	8	on	on	ADP
ijassa-2051	270	9	bifurcation	bifurcation	NOUN
ijassa-2051	270	10	of	of	ADP
ijassa-2051	270	11	non	non	ADJ
ijassa-2051	270	12	-	-	ADJ
ijassa-2051	270	13	isolated	isolated	ADJ
ijassa-2051	270	14	singular	singular	ADJ
ijassa-2051	270	15	points	point	NOUN
ijassa-2051	270	16	arising	arise	VERB
ijassa-2051	270	17	in	in	ADP
ijassa-2051	270	18	a	a	DET
ijassa-2051	270	19	problem	problem	NOUN
ijassa-2051	270	20	of	of	ADP
ijassa-2051	270	21	two	two	NUM
ijassa-2051	270	22	-	-	PUNCT
ijassa-2051	270	23	phase	phase	NOUN
ijassa-2051	270	24	fluid	fluid	NOUN
ijassa-2051	270	25	motion	motion	NOUN
ijassa-2051	270	26	in	in	ADP
ijassa-2051	270	27	a	a	DET
ijassa-2051	270	28	pipe	pipe	NOUN
ijassa-2051	270	29	,	,	PUNCT
ijassa-2051	270	30	physica	physica	NOUN
ijassa-2051	270	31	d	d	PROPN
ijassa-2051	270	32	,	,	PUNCT
ijassa-2051	270	33	470	470	NUM
ijassa-2051	270	34	,	,	PUNCT
ijassa-2051	270	35	part	part	NOUN
ijassa-2051	270	36	a	a	X
ijassa-2051	270	37	,	,	PUNCT
ijassa-2051	270	38	article	article	NOUN
ijassa-2051	270	39	i	i	PROPN
ijassa-2051	270	40	d	d	PROPN
ijassa-2051	270	41	134408	134408	NUM
ijassa-2051	270	42	,	,	PUNCT
ijassa-2051	270	43	12	12	NUM
ijassa-2051	270	44	p.	p.	NOUN
ijassa-2051	270	45	9	9	NUM
ijassa-2051	270	46	.	.	PUNCT
ijassa-2051	271	1	pavlova	pavlova	PROPN
ijassa-2051	271	2	,	,	PUNCT
ijassa-2051	271	3	n.	n.	PROPN
ijassa-2051	271	4	g.	g.	PROPN
ijassa-2051	271	5	&	&	CCONJ
ijassa-2051	271	6	remizov	remizov	PROPN
ijassa-2051	271	7	,	,	PUNCT
ijassa-2051	271	8	a.	a.	NOUN
ijassa-2051	271	9	o.	o.	PROPN
ijassa-2051	271	10	(	(	PUNCT
ijassa-2051	271	11	2018	2018	NUM
ijassa-2051	271	12	)	)	PUNCT
ijassa-2051	271	13	a	a	DET
ijassa-2051	271	14	brief	brief	ADJ
ijassa-2051	271	15	survey	survey	NOUN
ijassa-2051	271	16	on	on	ADP
ijassa-2051	271	17	singularities	singularity	NOUN
ijassa-2051	271	18	of	of	ADP
ijassa-2051	271	19	geodesic	geodesic	ADJ
ijassa-2051	271	20	flows	flow	NOUN
ijassa-2051	271	21	in	in	ADP
ijassa-2051	271	22	smooth	smooth	ADJ
ijassa-2051	271	23	signature	signature	NOUN
ijassa-2051	271	24	changing	change	VERB
ijassa-2051	271	25	metrics	metric	NOUN
ijassa-2051	271	26	on	on	ADP
ijassa-2051	271	27	2	2	NUM
ijassa-2051	271	28	-	-	PUNCT
ijassa-2051	271	29	surfaces	surface	NOUN
ijassa-2051	271	30	,	,	PUNCT
ijassa-2051	271	31	springer	springer	NOUN
ijassa-2051	271	32	proc	proc	NOUN
ijassa-2051	271	33	.	.	PUNCT
ijassa-2051	272	1	math	math	NOUN
ijassa-2051	272	2	.	.	PUNCT
ijassa-2051	273	1	stat	stat	PROPN
ijassa-2051	273	2	.	.	PUNCT
ijassa-2051	273	3	,	,	PUNCT
ijassa-2051	273	4	222	222	NUM
ijassa-2051	273	5	,	,	PUNCT
ijassa-2051	273	6	135–155	135–155	NUM
ijassa-2051	273	7	.	.	NOUN
ijassa-2051	274	1	10	10	NUM
ijassa-2051	274	2	.	.	PUNCT
ijassa-2051	275	1	pavlova	pavlova	PROPN
ijassa-2051	275	2	,	,	PUNCT
ijassa-2051	275	3	n.	n.	PROPN
ijassa-2051	275	4	g.	g.	PROPN
ijassa-2051	275	5	&	&	CCONJ
ijassa-2051	275	6	remizov	remizov	PROPN
ijassa-2051	275	7	,	,	PUNCT
ijassa-2051	275	8	a.	a.	NOUN
ijassa-2051	275	9	o.	o.	NOUN
ijassa-2051	275	10	(	(	PUNCT
ijassa-2051	275	11	2021	2021	NUM
ijassa-2051	275	12	)	)	PUNCT
ijassa-2051	275	13	smooth	smooth	ADJ
ijassa-2051	275	14	local	local	ADJ
ijassa-2051	275	15	normal	normal	ADJ
ijassa-2051	275	16	forms	form	NOUN
ijassa-2051	275	17	of	of	ADP
ijassa-2051	275	18	hyperbolic	hyperbolic	ADJ
ijassa-2051	275	19	roussarie	roussarie	NOUN
ijassa-2051	275	20	vector	vector	NOUN
ijassa-2051	275	21	fields	field	NOUN
ijassa-2051	275	22	,	,	PUNCT
ijassa-2051	275	23	moscow	moscow	PROPN
ijassa-2051	275	24	math	math	NOUN
ijassa-2051	275	25	.	.	PUNCT
ijassa-2051	276	1	j.	j.	PROPN
ijassa-2051	276	2	,	,	PUNCT
ijassa-2051	276	3	21(2	21(2	NUM
ijassa-2051	276	4	)	)	PUNCT
ijassa-2051	276	5	,	,	PUNCT
ijassa-2051	276	6	413–426	413–426	NUM
ijassa-2051	276	7	.	.	PUNCT
ijassa-2051	276	8	11	11	NUM
ijassa-2051	276	9	.	.	PUNCT
ijassa-2051	277	1	pavlova	pavlova	PROPN
ijassa-2051	277	2	,	,	PUNCT
ijassa-2051	277	3	n.	n.	PROPN
ijassa-2051	277	4	g.	g.	PROPN
ijassa-2051	277	5	&	&	CCONJ
ijassa-2051	277	6	remizov	remizov	PROPN
ijassa-2051	277	7	,	,	PUNCT
ijassa-2051	277	8	a.	a.	NOUN
ijassa-2051	277	9	o.	o.	NOUN
ijassa-2051	277	10	(	(	PUNCT
ijassa-2051	277	11	2022	2022	NUM
ijassa-2051	277	12	)	)	PUNCT
ijassa-2051	277	13	oscillating	oscillating	NOUN
ijassa-2051	277	14	and	and	CCONJ
ijassa-2051	277	15	proper	proper	ADJ
ijassa-2051	277	16	solutions	solution	NOUN
ijassa-2051	277	17	of	of	ADP
ijassa-2051	277	18	singular	singular	ADJ
ijassa-2051	277	19	quasi	quasi	ADJ
ijassa-2051	277	20	-	-	ADJ
ijassa-2051	277	21	linear	linear	ADJ
ijassa-2051	277	22	differential	differential	NOUN
ijassa-2051	277	23	equations	equation	NOUN
ijassa-2051	277	24	,	,	PUNCT
ijassa-2051	277	25	adv	adv	PROPN
ijassa-2051	277	26	.	.	PUNCT
ijassa-2051	277	27	syst	syst	PROPN
ijassa-2051	277	28	.	.	PUNCT
ijassa-2051	278	1	sci	sci	PROPN
ijassa-2051	278	2	.	.	PUNCT
ijassa-2051	278	3	appl	appl	PROPN
ijassa-2051	278	4	.	.	PROPN
ijassa-2051	278	5	,	,	PUNCT
ijassa-2051	278	6	22(4	22(4	NUM
ijassa-2051	278	7	)	)	PUNCT
ijassa-2051	278	8	,	,	PUNCT
ijassa-2051	278	9	51–64	51–64	PROPN
ijassa-2051	278	10	.	.	PROPN
ijassa-2051	278	11	12	12	NUM
ijassa-2051	278	12	.	.	PUNCT
ijassa-2051	279	1	pavlova	pavlova	PROPN
ijassa-2051	279	2	,	,	PUNCT
ijassa-2051	279	3	n.	n.	PROPN
ijassa-2051	279	4	g.	g.	PROPN
ijassa-2051	279	5	&	&	CCONJ
ijassa-2051	279	6	remizov	remizov	PROPN
ijassa-2051	279	7	,	,	PUNCT
ijassa-2051	279	8	a.	a.	NOUN
ijassa-2051	279	9	o.	o.	PROPN
ijassa-2051	279	10	(	(	PUNCT
ijassa-2051	279	11	2025	2025	NUM
ijassa-2051	279	12	)	)	PUNCT
ijassa-2051	279	13	the	the	DET
ijassa-2051	279	14	cross	cross	NOUN
ijassa-2051	279	15	-	-	NOUN
ijassa-2051	279	16	ratio	ratio	NOUN
ijassa-2051	279	17	at	at	ADP
ijassa-2051	279	18	singular	singular	ADJ
ijassa-2051	279	19	points	point	NOUN
ijassa-2051	279	20	of	of	ADP
ijassa-2051	279	21	geodesic	geodesic	NOUN
ijassa-2051	279	22	flows	flow	NOUN
ijassa-2051	279	23	in	in	ADP
ijassa-2051	279	24	signature	signature	NOUN
ijassa-2051	279	25	changing	change	VERB
ijassa-2051	279	26	metrics	metric	NOUN
ijassa-2051	279	27	,	,	PUNCT
ijassa-2051	279	28	lobachevskii	lobachevskii	VERB
ijassa-2051	279	29	j.	j.	PROPN
ijassa-2051	279	30	math	math	PROPN
ijassa-2051	279	31	.	.	PUNCT
ijassa-2051	279	32	,	,	PUNCT
ijassa-2051	279	33	to	to	PART
ijassa-2051	279	34	appear	appear	VERB
ijassa-2051	279	35	.	.	PUNCT
ijassa-2051	280	1	copyright	copyright	NOUN
ijassa-2051	280	2	©	©	PROPN
ijassa-2051	280	3	2025	2025	NUM
ijassa-2051	280	4	assa	assa	NOUN
ijassa-2051	280	5	.	.	PUNCT
ijassa-2051	281	1	adv	adv	PROPN
ijassa-2051	281	2	syst	syst	PROPN
ijassa-2051	281	3	sci	sci	PROPN
ijassa-2051	281	4	appl	appl	PROPN
ijassa-2051	281	5	(	(	PUNCT
ijassa-2051	281	6	2025	2025	NUM
ijassa-2051	281	7	)	)	PUNCT
ijassa-2051	281	8	104	104	NUM
ijassa-2051	281	9	n.	n.	NOUN
ijassa-2051	281	10	g.	g.	PROPN
ijassa-2051	281	11	pavlova	pavlova	PROPN
ijassa-2051	281	12	,	,	PUNCT
ijassa-2051	281	13	a.	a.	PROPN
ijassa-2051	281	14	o.	o.	PROPN
ijassa-2051	281	15	remizov	remizov	PROPN
ijassa-2051	281	16	13	13	NUM
ijassa-2051	281	17	.	.	PUNCT
ijassa-2051	282	1	remizov	remizov	NOUN
ijassa-2051	282	2	,	,	PUNCT
ijassa-2051	282	3	a.	a.	NOUN
ijassa-2051	282	4	o.	o.	PROPN
ijassa-2051	282	5	(	(	PUNCT
ijassa-2051	282	6	2008	2008	NUM
ijassa-2051	282	7	)	)	PUNCT
ijassa-2051	282	8	multidimensional	multidimensional	ADJ
ijassa-2051	282	9	poincaré	poincaré	ADJ
ijassa-2051	282	10	construction	construction	NOUN
ijassa-2051	282	11	and	and	CCONJ
ijassa-2051	282	12	singularities	singularity	NOUN
ijassa-2051	282	13	of	of	ADP
ijassa-2051	282	14	lifted	lift	VERB
ijassa-2051	282	15	fields	field	NOUN
ijassa-2051	282	16	for	for	ADP
ijassa-2051	282	17	implicit	implicit	ADJ
ijassa-2051	282	18	differential	differential	ADJ
ijassa-2051	282	19	equations	equation	NOUN
ijassa-2051	282	20	,	,	PUNCT
ijassa-2051	282	21	j.	j.	PROPN
ijassa-2051	282	22	math	math	PROPN
ijassa-2051	282	23	.	.	PUNCT
ijassa-2051	283	1	sci	sci	PROPN
ijassa-2051	283	2	.	.	PROPN
ijassa-2051	283	3	,	,	PUNCT
ijassa-2051	283	4	151(6	151(6	NUM
ijassa-2051	283	5	)	)	PUNCT
ijassa-2051	283	6	,	,	PUNCT
ijassa-2051	283	7	3561–3602	3561–3602	NUM
ijassa-2051	283	8	.	.	PUNCT
ijassa-2051	284	1	14	14	NUM
ijassa-2051	284	2	.	.	PUNCT
ijassa-2051	285	1	remizov	remizov	NOUN
ijassa-2051	285	2	,	,	PUNCT
ijassa-2051	285	3	a.	a.	NOUN
ijassa-2051	285	4	o.	o.	PROPN
ijassa-2051	285	5	(	(	PUNCT
ijassa-2051	285	6	2015	2015	NUM
ijassa-2051	285	7	)	)	PUNCT
ijassa-2051	285	8	on	on	ADP
ijassa-2051	285	9	the	the	DET
ijassa-2051	285	10	local	local	ADJ
ijassa-2051	285	11	and	and	CCONJ
ijassa-2051	285	12	global	global	ADJ
ijassa-2051	285	13	properties	property	NOUN
ijassa-2051	285	14	of	of	ADP
ijassa-2051	285	15	geodesics	geodesic	NOUN
ijassa-2051	285	16	in	in	ADP
ijassa-2051	285	17	pseudoriemannian	pseudoriemannian	ADJ
ijassa-2051	285	18	metrics	metric	NOUN
ijassa-2051	285	19	,	,	PUNCT
ijassa-2051	285	20	diff	diff	PROPN
ijassa-2051	285	21	.	.	PUNCT
ijassa-2051	286	1	geom	geom	PROPN
ijassa-2051	286	2	.	.	PUNCT
ijassa-2051	287	1	appl	appl	PROPN
ijassa-2051	287	2	.	.	PROPN
ijassa-2051	287	3	,	,	PUNCT
ijassa-2051	287	4	39	39	NUM
ijassa-2051	287	5	,	,	PUNCT
ijassa-2051	287	6	36–58	36–58	NUM
ijassa-2051	287	7	.	.	PUNCT
ijassa-2051	288	1	15	15	NUM
ijassa-2051	288	2	.	.	X
ijassa-2051	289	1	remizov	remizov	NOUN
ijassa-2051	289	2	,	,	PUNCT
ijassa-2051	289	3	a.	a.	NOUN
ijassa-2051	289	4	o.	o.	NOUN
ijassa-2051	289	5	(	(	PUNCT
ijassa-2051	289	6	2023	2023	NUM
ijassa-2051	289	7	)	)	PUNCT
ijassa-2051	289	8	singularities	singularity	NOUN
ijassa-2051	289	9	of	of	ADP
ijassa-2051	289	10	quasi	quasi	ADJ
ijassa-2051	289	11	-	-	ADJ
ijassa-2051	289	12	linear	linear	ADJ
ijassa-2051	289	13	differential	differential	ADJ
ijassa-2051	289	14	equations	equation	NOUN
ijassa-2051	289	15	,	,	PUNCT
ijassa-2051	290	1	dal’nevost	dal’nevost	PROPN
ijassa-2051	290	2	.	.	PUNCT
ijassa-2051	290	3	mat	mat	PROPN
ijassa-2051	290	4	.	.	PUNCT
ijassa-2051	291	1	zh	zh	PROPN
ijassa-2051	291	2	.	.	PROPN
ijassa-2051	291	3	,	,	PUNCT
ijassa-2051	291	4	23(1	23(1	X
ijassa-2051	291	5	)	)	PUNCT
ijassa-2051	291	6	,	,	PUNCT
ijassa-2051	291	7	85–105	85–105	NOUN
ijassa-2051	291	8	.	.	PUNCT
ijassa-2051	292	1	16	16	NUM
ijassa-2051	292	2	.	.	PUNCT
ijassa-2051	293	1	remizov	remizov	PROPN
ijassa-2051	293	2	,	,	PUNCT
ijassa-2051	293	3	a.	a.	PROPN
ijassa-2051	293	4	o.	o.	PROPN
ijassa-2051	293	5	&	&	CCONJ
ijassa-2051	293	6	tari	tari	PROPN
ijassa-2051	293	7	,	,	PUNCT
ijassa-2051	293	8	f.	f.	PROPN
ijassa-2051	293	9	(	(	PUNCT
ijassa-2051	293	10	2016	2016	NUM
ijassa-2051	293	11	)	)	PUNCT
ijassa-2051	293	12	singularities	singularity	NOUN
ijassa-2051	293	13	of	of	ADP
ijassa-2051	293	14	the	the	DET
ijassa-2051	293	15	geodesic	geodesic	ADJ
ijassa-2051	293	16	flow	flow	NOUN
ijassa-2051	293	17	on	on	ADP
ijassa-2051	293	18	surfaces	surface	NOUN
ijassa-2051	293	19	with	with	ADP
ijassa-2051	293	20	pseudo	pseudo	NOUN
ijassa-2051	293	21	-	-	ADJ
ijassa-2051	293	22	riemannian	riemannian	ADJ
ijassa-2051	293	23	metrics	metric	NOUN
ijassa-2051	293	24	,	,	PUNCT
ijassa-2051	293	25	geom	geom	PROPN
ijassa-2051	293	26	.	.	PUNCT
ijassa-2051	293	27	dedicata	dedicata	PROPN
ijassa-2051	293	28	,	,	PUNCT
ijassa-2051	293	29	185(1	185(1	NUM
ijassa-2051	293	30	)	)	PUNCT
ijassa-2051	293	31	,	,	PUNCT
ijassa-2051	293	32	131–153	131–153	NUM
ijassa-2051	293	33	.	.	PUNCT
ijassa-2051	294	1	17	17	NUM
ijassa-2051	294	2	.	.	PUNCT
ijassa-2051	295	1	roussarie	roussarie	PROPN
ijassa-2051	295	2	,	,	PUNCT
ijassa-2051	295	3	r.	r.	PROPN
ijassa-2051	295	4	(	(	PUNCT
ijassa-2051	295	5	1975	1975	NUM
ijassa-2051	295	6	)	)	PUNCT
ijassa-2051	295	7	modèles	modèle	VERB
ijassa-2051	295	8	locaux	locaux	PROPN
ijassa-2051	295	9	de	de	X
ijassa-2051	295	10	champs	champs	PROPN
ijassa-2051	295	11	et	et	PROPN
ijassa-2051	295	12	de	de	X
ijassa-2051	295	13	formes	forme	NOUN
ijassa-2051	295	14	,	,	PUNCT
ijassa-2051	295	15	asterisque	asterisque	ADJ
ijassa-2051	295	16	,	,	PUNCT
ijassa-2051	295	17	30	30	NUM
ijassa-2051	295	18	,	,	PUNCT
ijassa-2051	295	19	1–181	1–181	NUM
ijassa-2051	295	20	.	.	NOUN
ijassa-2051	295	21	18	18	NUM
ijassa-2051	295	22	.	.	X
ijassa-2051	295	23	samovol	samovol	NOUN
ijassa-2051	295	24	,	,	PUNCT
ijassa-2051	295	25	v.	v.	CCONJ
ijassa-2051	295	26	s.	s.	PROPN
ijassa-2051	295	27	(	(	PUNCT
ijassa-2051	295	28	1983	1983	NUM
ijassa-2051	295	29	)	)	PUNCT
ijassa-2051	295	30	equivalence	equivalence	NOUN
ijassa-2051	295	31	of	of	ADP
ijassa-2051	295	32	systems	system	NOUN
ijassa-2051	295	33	of	of	ADP
ijassa-2051	295	34	differential	differential	ADJ
ijassa-2051	295	35	equations	equation	NOUN
ijassa-2051	295	36	in	in	ADP
ijassa-2051	295	37	a	a	DET
ijassa-2051	295	38	neighborhood	neighborhood	NOUN
ijassa-2051	295	39	of	of	ADP
ijassa-2051	295	40	a	a	DET
ijassa-2051	295	41	singular	singular	ADJ
ijassa-2051	295	42	point	point	NOUN
ijassa-2051	295	43	,	,	PUNCT
ijassa-2051	295	44	trans	trans	PROPN
ijassa-2051	295	45	.	.	PUNCT
ijassa-2051	296	1	mosc	mosc	PROPN
ijassa-2051	296	2	.	.	PUNCT
ijassa-2051	297	1	math	math	PROPN
ijassa-2051	297	2	.	.	PUNCT
ijassa-2051	298	1	soc	soc	PROPN
ijassa-2051	298	2	.	.	PUNCT
ijassa-2051	298	3	,	,	PUNCT
ijassa-2051	298	4	2	2	NUM
ijassa-2051	298	5	,	,	PUNCT
ijassa-2051	298	6	217–237	217–237	NUM
ijassa-2051	298	7	.	.	PUNCT
ijassa-2051	299	1	19	19	NUM
ijassa-2051	299	2	.	.	X
ijassa-2051	299	3	seiler	seiler	PROPN
ijassa-2051	299	4	,	,	PUNCT
ijassa-2051	299	5	w.	w.	PROPN
ijassa-2051	299	6	m.	m.	PROPN
ijassa-2051	299	7	&	&	CCONJ
ijassa-2051	299	8	seiss	seiss	PROPN
ijassa-2051	299	9	,	,	PUNCT
ijassa-2051	299	10	m.	m.	NOUN
ijassa-2051	299	11	(	(	PUNCT
ijassa-2051	299	12	2021	2021	NUM
ijassa-2051	299	13	)	)	PUNCT
ijassa-2051	299	14	singular	singular	PROPN
ijassa-2051	299	15	initial	initial	ADJ
ijassa-2051	299	16	value	value	NOUN
ijassa-2051	299	17	problems	problem	NOUN
ijassa-2051	299	18	for	for	ADP
ijassa-2051	299	19	scalar	scalar	ADJ
ijassa-2051	299	20	quasi	quasi	ADJ
ijassa-2051	299	21	-	-	ADJ
ijassa-2051	299	22	linear	linear	ADJ
ijassa-2051	299	23	ordinary	ordinary	ADJ
ijassa-2051	299	24	differential	differential	ADJ
ijassa-2051	299	25	equations	equation	NOUN
ijassa-2051	299	26	,	,	PUNCT
ijassa-2051	299	27	j.	j.	PROPN
ijassa-2051	299	28	differ	differ	VERB
ijassa-2051	299	29	.	.	PUNCT
ijassa-2051	300	1	equations	equation	NOUN
ijassa-2051	300	2	,	,	PUNCT
ijassa-2051	300	3	281	281	NUM
ijassa-2051	300	4	,	,	PUNCT
ijassa-2051	300	5	258–288	258–288	NUM
ijassa-2051	300	6	.	.	PUNCT
ijassa-2051	301	1	20	20	NUM
ijassa-2051	301	2	.	.	PUNCT
ijassa-2051	301	3	tunitsky	tunitsky	NOUN
ijassa-2051	301	4	,	,	PUNCT
ijassa-2051	301	5	d.	d.	PROPN
ijassa-2051	301	6	v.	v.	PROPN
ijassa-2051	301	7	(	(	PUNCT
ijassa-2051	301	8	2021	2021	NUM
ijassa-2051	301	9	)	)	PUNCT
ijassa-2051	301	10	on	on	ADP
ijassa-2051	301	11	some	some	DET
ijassa-2051	301	12	global	global	ADJ
ijassa-2051	301	13	properties	property	NOUN
ijassa-2051	301	14	of	of	ADP
ijassa-2051	301	15	multivalued	multivalued	ADJ
ijassa-2051	301	16	simple	simple	ADJ
ijassa-2051	301	17	waves	wave	NOUN
ijassa-2051	301	18	,	,	PUNCT
ijassa-2051	302	1	adv	adv	PROPN
ijassa-2051	302	2	.	.	PUNCT
ijassa-2051	302	3	syst	syst	PROPN
ijassa-2051	302	4	.	.	PUNCT
ijassa-2051	303	1	sci	sci	PROPN
ijassa-2051	303	2	.	.	PUNCT
ijassa-2051	303	3	appl	appl	PROPN
ijassa-2051	303	4	.	.	PROPN
ijassa-2051	303	5	,	,	PUNCT
ijassa-2051	303	6	20(4	20(4	NOUN
ijassa-2051	303	7	)	)	PUNCT
ijassa-2051	303	8	,	,	PUNCT
ijassa-2051	303	9	125–131	125–131	NUM
ijassa-2051	303	10	.	.	PUNCT
ijassa-2051	304	1	copyright	copyright	NOUN
ijassa-2051	304	2	©	©	PROPN
ijassa-2051	304	3	2025	2025	NUM
ijassa-2051	304	4	assa	assa	NOUN
ijassa-2051	304	5	.	.	PUNCT
ijassa-2051	305	1	adv	adv	PROPN
ijassa-2051	305	2	syst	syst	PROPN
ijassa-2051	305	3	sci	sci	PROPN
ijassa-2051	305	4	appl	appl	PROPN
ijassa-2051	305	5	(	(	PUNCT
ijassa-2051	305	6	2025	2025	NUM
ijassa-2051	305	7	)	)	PUNCT
ijassa-2051	305	8	introduction	introduction	NOUN
ijassa-2051	305	9	the	the	DET
ijassa-2051	305	10	main	main	ADJ
ijassa-2051	305	11	results	result	NOUN
ijassa-2051	305	12	roussarie	roussarie	VERB
ijassa-2051	305	13	vector	vector	NOUN
ijassa-2051	305	14	fields	field	NOUN
ijassa-2051	305	15	applications	application	NOUN
ijassa-2051	305	16	:	:	PUNCT
ijassa-2051	305	17	quasi	quasi	ADJ
ijassa-2051	305	18	-	-	ADJ
ijassa-2051	305	19	linear	linear	ADJ
ijassa-2051	305	20	odes	ode	NOUN
ijassa-2051	305	21	of	of	ADP
ijassa-2051	305	22	the	the	DET
ijassa-2051	305	23	second	second	ADJ
ijassa-2051	305	24	order	order	NOUN
ijassa-2051	305	25	quasi	quasi	ADJ
ijassa-2051	305	26	-	-	ADJ
ijassa-2051	305	27	linear	linear	ADJ
ijassa-2051	305	28	odes	ode	NOUN
ijassa-2051	305	29	of	of	ADP
ijassa-2051	305	30	the	the	DET
ijassa-2051	305	31	second	second	ADJ
ijassa-2051	305	32	order	order	NOUN
ijassa-2051	305	33	cubic	cubic	ADJ
ijassa-2051	305	34	in	in	ADP
ijassa-2051	305	35	p	p	NOUN
ijassa-2051	305	36	equation	equation	NOUN
ijassa-2051	305	37	of	of	ADP
ijassa-2051	305	38	geodesics	geodesic	NOUN
ijassa-2051	305	39	in	in	ADP
ijassa-2051	305	40	signature	signature	NOUN
ijassa-2051	305	41	varying	vary	VERB
ijassa-2051	305	42	metrics	metric	NOUN
ijassa-2051	305	43	conclusion	conclusion	NOUN