id	sid	tid	token	lemma	pos
ejpam-5293	1	1	european	european	PROPN
ejpam-5293	1	2	journal	journal	PROPN
ejpam-5293	1	3	of	of	ADP
ejpam-5293	1	4	pure	pure	ADJ
ejpam-5293	1	5	and	and	CCONJ
ejpam-5293	1	6	applied	apply	VERB
ejpam-5293	1	7	mathematics	mathematic	NOUN
ejpam-5293	1	8	vol	vol	NOUN
ejpam-5293	1	9	.	.	PROPN
ejpam-5293	2	1	17	17	NUM
ejpam-5293	2	2	,	,	PUNCT
ejpam-5293	2	3	no	no	INTJ
ejpam-5293	2	4	.	.	NOUN
ejpam-5293	2	5	3	3	NUM
ejpam-5293	2	6	,	,	PUNCT
ejpam-5293	2	7	2024	2024	NUM
ejpam-5293	2	8	,	,	PUNCT
ejpam-5293	2	9	1403	1403	NUM
ejpam-5293	2	10	-	-	SYM
ejpam-5293	2	11	1416	1416	NUM
ejpam-5293	2	12	issn	issn	PROPN
ejpam-5293	2	13	1307	1307	NUM
ejpam-5293	2	14	-	-	SYM
ejpam-5293	2	15	5543	5543	NUM
ejpam-5293	2	16	–	–	PUNCT
ejpam-5293	2	17	ejpam.com	ejpam.com	X
ejpam-5293	2	18	published	publish	VERB
ejpam-5293	2	19	by	by	ADP
ejpam-5293	2	20	new	new	PROPN
ejpam-5293	2	21	york	york	PROPN
ejpam-5293	2	22	business	business	PROPN
ejpam-5293	2	23	global	global	PROPN
ejpam-5293	2	24	from	from	ADP
ejpam-5293	2	25	anosov	anosov	NOUN
ejpam-5293	2	26	closing	close	VERB
ejpam-5293	2	27	lemma	lemma	PROPN
ejpam-5293	2	28	to	to	ADP
ejpam-5293	2	29	global	global	ADJ
ejpam-5293	2	30	data	datum	NOUN
ejpam-5293	2	31	of	of	ADP
ejpam-5293	2	32	cohomological	cohomological	ADJ
ejpam-5293	2	33	nature	nature	NOUN
ejpam-5293	2	34	rosário	rosário	X
ejpam-5293	2	35	d.	d.	PROPN
ejpam-5293	2	36	laureano	laureano	PROPN
ejpam-5293	2	37	istar	istar	PROPN
ejpam-5293	2	38	information	information	PROPN
ejpam-5293	2	39	sciences	sciences	PROPN
ejpam-5293	2	40	,	,	PUNCT
ejpam-5293	2	41	technologies	technology	NOUN
ejpam-5293	2	42	and	and	CCONJ
ejpam-5293	2	43	architecture	architecture	NOUN
ejpam-5293	2	44	research	research	NOUN
ejpam-5293	2	45	center	center	NOUN
ejpam-5293	2	46	,	,	PUNCT
ejpam-5293	2	47	department	department	NOUN
ejpam-5293	2	48	of	of	ADP
ejpam-5293	2	49	mathematics	mathematic	NOUN
ejpam-5293	2	50	,	,	PUNCT
ejpam-5293	2	51	iscte	iscte	NOUN
ejpam-5293	2	52	-	-	PUNCT
ejpam-5293	2	53	iul	iul	NOUN
ejpam-5293	2	54	instituto	instituto	PROPN
ejpam-5293	2	55	universitário	universitário	PROPN
ejpam-5293	2	56	de	de	PROPN
ejpam-5293	2	57	lisboa	lisboa	PROPN
ejpam-5293	2	58	,	,	PUNCT
ejpam-5293	2	59	av	av	PROPN
ejpam-5293	2	60	.	.	PUNCT
ejpam-5293	3	1	das	das	PROPN
ejpam-5293	3	2	forças	forças	ADP
ejpam-5293	3	3	armadas	armada	NOUN
ejpam-5293	3	4	,	,	PUNCT
ejpam-5293	3	5	lisboa	lisboa	PROPN
ejpam-5293	3	6	1649	1649	NUM
ejpam-5293	3	7	-	-	SYM
ejpam-5293	3	8	026	026	NUM
ejpam-5293	3	9	,	,	PUNCT
ejpam-5293	3	10	portugal	portugal	PROPN
ejpam-5293	3	11	abstract	abstract	NOUN
ejpam-5293	3	12	.	.	PUNCT
ejpam-5293	4	1	for	for	ADP
ejpam-5293	4	2	diffeomorphisms	diffeomorphism	NOUN
ejpam-5293	4	3	with	with	ADP
ejpam-5293	4	4	hyperbolic	hyperbolic	ADJ
ejpam-5293	4	5	sets	set	NOUN
ejpam-5293	4	6	,	,	PUNCT
ejpam-5293	4	7	the	the	DET
ejpam-5293	4	8	anosov	anosov	NOUN
ejpam-5293	4	9	closing	close	VERB
ejpam-5293	4	10	lemma	lemma	PROPN
ejpam-5293	4	11	ensures	ensure	VERB
ejpam-5293	4	12	the	the	DET
ejpam-5293	4	13	existence	existence	NOUN
ejpam-5293	4	14	of	of	ADP
ejpam-5293	4	15	periodic	periodic	ADJ
ejpam-5293	4	16	orbits	orbit	NOUN
ejpam-5293	4	17	in	in	ADP
ejpam-5293	4	18	the	the	DET
ejpam-5293	4	19	neighbourhood	neighbourhood	NOUN
ejpam-5293	4	20	of	of	ADP
ejpam-5293	4	21	orbits	orbit	NOUN
ejpam-5293	4	22	that	that	PRON
ejpam-5293	4	23	return	return	VERB
ejpam-5293	4	24	close	close	ADV
ejpam-5293	4	25	enough	enough	ADV
ejpam-5293	4	26	to	to	ADP
ejpam-5293	4	27	themselves	themselves	PRON
ejpam-5293	4	28	.	.	PUNCT
ejpam-5293	5	1	moreover	moreover	ADV
ejpam-5293	5	2	,	,	PUNCT
ejpam-5293	5	3	it	it	PRON
ejpam-5293	5	4	defines	define	VERB
ejpam-5293	5	5	how	how	SCONJ
ejpam-5293	5	6	the	the	DET
ejpam-5293	5	7	distance	distance	NOUN
ejpam-5293	5	8	between	between	ADP
ejpam-5293	5	9	the	the	DET
ejpam-5293	5	10	corresponding	corresponding	ADJ
ejpam-5293	5	11	points	point	NOUN
ejpam-5293	5	12	of	of	ADP
ejpam-5293	5	13	an	an	DET
ejpam-5293	5	14	initial	initial	ADJ
ejpam-5293	5	15	orbit	orbit	NOUN
ejpam-5293	5	16	and	and	CCONJ
ejpam-5293	5	17	the	the	DET
ejpam-5293	5	18	constructed	construct	VERB
ejpam-5293	5	19	periodic	periodic	ADJ
ejpam-5293	5	20	orbits	orbit	NOUN
ejpam-5293	5	21	is	be	AUX
ejpam-5293	5	22	controlled	control	VERB
ejpam-5293	5	23	.	.	PUNCT
ejpam-5293	6	1	in	in	ADP
ejpam-5293	6	2	the	the	DET
ejpam-5293	6	3	essential	essential	ADJ
ejpam-5293	6	4	,	,	PUNCT
ejpam-5293	6	5	this	this	DET
ejpam-5293	6	6	article	article	NOUN
ejpam-5293	6	7	presents	present	VERB
ejpam-5293	6	8	proof	proof	NOUN
ejpam-5293	6	9	of	of	ADP
ejpam-5293	6	10	the	the	DET
ejpam-5293	6	11	estimate	estimate	NOUN
ejpam-5293	6	12	of	of	ADP
ejpam-5293	6	13	this	this	DET
ejpam-5293	6	14	distance	distance	NOUN
ejpam-5293	6	15	.	.	PUNCT
ejpam-5293	7	1	the	the	DET
ejpam-5293	7	2	anosov	anosov	NOUN
ejpam-5293	7	3	closing	close	VERB
ejpam-5293	7	4	lemma	lemma	PROPN
ejpam-5293	7	5	is	be	AUX
ejpam-5293	7	6	crucial	crucial	ADJ
ejpam-5293	7	7	in	in	ADP
ejpam-5293	7	8	the	the	DET
ejpam-5293	7	9	statement	statement	NOUN
ejpam-5293	7	10	of	of	ADP
ejpam-5293	7	11	livschitz	livschitz	PROPN
ejpam-5293	7	12	theorem	theorem	ADJ
ejpam-5293	7	13	that	that	SCONJ
ejpam-5293	7	14	,	,	PUNCT
ejpam-5293	7	15	based	base	VERB
ejpam-5293	7	16	only	only	ADV
ejpam-5293	7	17	on	on	ADP
ejpam-5293	7	18	the	the	DET
ejpam-5293	7	19	periodic	periodic	ADJ
ejpam-5293	7	20	data	datum	NOUN
ejpam-5293	7	21	,	,	PUNCT
ejpam-5293	7	22	provides	provide	VERB
ejpam-5293	7	23	a	a	DET
ejpam-5293	7	24	necessary	necessary	ADJ
ejpam-5293	7	25	and	and	CCONJ
ejpam-5293	7	26	sufficient	sufficient	ADJ
ejpam-5293	7	27	condition	condition	NOUN
ejpam-5293	7	28	so	so	SCONJ
ejpam-5293	7	29	that	that	SCONJ
ejpam-5293	7	30	cohomological	cohomological	ADJ
ejpam-5293	7	31	equations	equation	NOUN
ejpam-5293	7	32	have	have	VERB
ejpam-5293	7	33	sufficiently	sufficiently	ADV
ejpam-5293	7	34	regular	regular	ADJ
ejpam-5293	7	35	solutions	solution	NOUN
ejpam-5293	7	36	,	,	PUNCT
ejpam-5293	7	37	hölder	hölder	NOUN
ejpam-5293	7	38	solutions	solution	NOUN
ejpam-5293	7	39	.	.	PUNCT
ejpam-5293	8	1	it	it	PRON
ejpam-5293	8	2	is	be	AUX
ejpam-5293	8	3	one	one	NUM
ejpam-5293	8	4	of	of	ADP
ejpam-5293	8	5	the	the	DET
ejpam-5293	8	6	main	main	ADJ
ejpam-5293	8	7	tools	tool	NOUN
ejpam-5293	8	8	to	to	PART
ejpam-5293	8	9	obtain	obtain	VERB
ejpam-5293	8	10	global	global	ADJ
ejpam-5293	8	11	data	datum	NOUN
ejpam-5293	8	12	of	of	ADP
ejpam-5293	8	13	a	a	DET
ejpam-5293	8	14	cohomological	cohomological	ADJ
ejpam-5293	8	15	nature	nature	NOUN
ejpam-5293	8	16	based	base	VERB
ejpam-5293	8	17	only	only	ADV
ejpam-5293	8	18	on	on	ADP
ejpam-5293	8	19	periodic	periodic	ADJ
ejpam-5293	8	20	data	datum	NOUN
ejpam-5293	8	21	.	.	PUNCT
ejpam-5293	9	1	as	as	SCONJ
ejpam-5293	9	2	suggested	suggest	VERB
ejpam-5293	9	3	by	by	ADP
ejpam-5293	9	4	katok	katok	NOUN
ejpam-5293	9	5	and	and	CCONJ
ejpam-5293	9	6	hasselblat	hasselblat	ADJ
ejpam-5293	9	7	in	in	ADP
ejpam-5293	9	8	[	[	X
ejpam-5293	9	9	2	2	NUM
ejpam-5293	9	10	]	]	PUNCT
ejpam-5293	9	11	,	,	PUNCT
ejpam-5293	9	12	it	it	PRON
ejpam-5293	9	13	is	be	AUX
ejpam-5293	9	14	demonstrated	demonstrate	VERB
ejpam-5293	9	15	,	,	PUNCT
ejpam-5293	9	16	in	in	ADP
ejpam-5293	9	17	detail	detail	NOUN
ejpam-5293	9	18	and	and	CCONJ
ejpam-5293	9	19	the	the	DET
ejpam-5293	9	20	cohomology	cohomology	NOUN
ejpam-5293	9	21	context	context	NOUN
ejpam-5293	9	22	,	,	PUNCT
ejpam-5293	9	23	the	the	DET
ejpam-5293	9	24	livschitz	livschitz	NOUN
ejpam-5293	9	25	theorem	theorem	VERB
ejpam-5293	9	26	for	for	ADP
ejpam-5293	9	27	hyperbolic	hyperbolic	ADJ
ejpam-5293	9	28	diffeomorphisms	diffeomorphism	NOUN
ejpam-5293	9	29	,	,	PUNCT
ejpam-5293	9	30	where	where	SCONJ
ejpam-5293	9	31	the	the	DET
ejpam-5293	9	32	mentioned	mention	VERB
ejpam-5293	9	33	distance	distance	NOUN
ejpam-5293	9	34	control	control	NOUN
ejpam-5293	9	35	inequality	inequality	NOUN
ejpam-5293	9	36	is	be	AUX
ejpam-5293	9	37	essential	essential	ADJ
ejpam-5293	9	38	.	.	PUNCT
ejpam-5293	10	1	2020	2020	NUM
ejpam-5293	10	2	mathematics	mathematic	NOUN
ejpam-5293	10	3	subject	subject	NOUN
ejpam-5293	10	4	classifications	classification	NOUN
ejpam-5293	10	5	:	:	PUNCT
ejpam-5293	10	6	37a20	37a20	NUM
ejpam-5293	10	7	,	,	PUNCT
ejpam-5293	10	8	37c05	37c05	NUM
ejpam-5293	10	9	,	,	PUNCT
ejpam-5293	10	10	37c50	37c50	NUM
ejpam-5293	10	11	,	,	PUNCT
ejpam-5293	10	12	37c55	37c55	NUM
ejpam-5293	10	13	,	,	PUNCT
ejpam-5293	10	14	37d05	37d05	NUM
ejpam-5293	10	15	,	,	PUNCT
ejpam-5293	10	16	37d20	37d20	NUM
ejpam-5293	10	17	.	.	PUNCT
ejpam-5293	11	1	key	key	ADJ
ejpam-5293	11	2	words	word	NOUN
ejpam-5293	11	3	and	and	CCONJ
ejpam-5293	11	4	phrases	phrase	NOUN
ejpam-5293	11	5	:	:	PUNCT
ejpam-5293	11	6	livschitz	livschitz	NOUN
ejpam-5293	11	7	theorem	theorem	NOUN
ejpam-5293	11	8	,	,	PUNCT
ejpam-5293	11	9	periodic	periodic	ADJ
ejpam-5293	11	10	data	datum	NOUN
ejpam-5293	11	11	,	,	PUNCT
ejpam-5293	11	12	hyperbolic	hyperbolic	ADJ
ejpam-5293	11	13	diffeomorphisms	diffeomorphism	NOUN
ejpam-5293	11	14	,	,	PUNCT
ejpam-5293	11	15	distance	distance	NOUN
ejpam-5293	11	16	control	control	NOUN
ejpam-5293	11	17	,	,	PUNCT
ejpam-5293	11	18	anosov	anosov	PROPN
ejpam-5293	11	19	closing	close	VERB
ejpam-5293	11	20	lemma	lemma	PROPN
ejpam-5293	11	21	,	,	PUNCT
ejpam-5293	11	22	coboundary	coboundary	ADJ
ejpam-5293	11	23	,	,	PUNCT
ejpam-5293	11	24	cohomological	cohomological	ADJ
ejpam-5293	11	25	equations	equation	NOUN
ejpam-5293	11	26	1	1	NUM
ejpam-5293	11	27	.	.	PUNCT
ejpam-5293	12	1	introduction	introduction	NOUN
ejpam-5293	12	2	h.	h.	PROPN
ejpam-5293	12	3	poincaré	poincaré	PROPN
ejpam-5293	12	4	found	find	VERB
ejpam-5293	12	5	the	the	DET
ejpam-5293	12	6	modern	modern	ADJ
ejpam-5293	12	7	theory	theory	NOUN
ejpam-5293	12	8	of	of	ADP
ejpam-5293	12	9	dynamical	dynamical	ADJ
ejpam-5293	12	10	systems	system	NOUN
ejpam-5293	12	11	when	when	SCONJ
ejpam-5293	12	12	he	he	PRON
ejpam-5293	12	13	emphasised	emphasise	VERB
ejpam-5293	12	14	the	the	DET
ejpam-5293	12	15	qualitative	qualitative	ADJ
ejpam-5293	12	16	approach	approach	NOUN
ejpam-5293	12	17	instead	instead	ADV
ejpam-5293	12	18	of	of	ADP
ejpam-5293	12	19	the	the	DET
ejpam-5293	12	20	traditional	traditional	ADJ
ejpam-5293	12	21	emphasis	emphasis	NOUN
ejpam-5293	12	22	on	on	ADP
ejpam-5293	12	23	explicit	explicit	ADJ
ejpam-5293	12	24	solutions	solution	NOUN
ejpam-5293	12	25	of	of	ADP
ejpam-5293	12	26	differential	differential	ADJ
ejpam-5293	12	27	equations	equation	NOUN
ejpam-5293	12	28	.	.	PUNCT
ejpam-5293	13	1	in	in	ADP
ejpam-5293	13	2	particular	particular	ADJ
ejpam-5293	13	3	,	,	PUNCT
ejpam-5293	13	4	when	when	SCONJ
ejpam-5293	13	5	he	he	PRON
ejpam-5293	13	6	considers	consider	VERB
ejpam-5293	13	7	the	the	DET
ejpam-5293	13	8	local	local	ADJ
ejpam-5293	13	9	theory	theory	NOUN
ejpam-5293	13	10	of	of	ADP
ejpam-5293	13	11	maps	map	NOUN
ejpam-5293	13	12	and	and	CCONJ
ejpam-5293	13	13	vector	vector	NOUN
ejpam-5293	13	14	fields	field	NOUN
ejpam-5293	13	15	near	near	ADP
ejpam-5293	13	16	fixed	fix	VERB
ejpam-5293	13	17	and	and	CCONJ
ejpam-5293	13	18	periodic	periodic	ADJ
ejpam-5293	13	19	orbits	orbit	NOUN
ejpam-5293	13	20	in	in	ADP
ejpam-5293	13	21	the	the	DET
ejpam-5293	13	22	context	context	NOUN
ejpam-5293	13	23	of	of	ADP
ejpam-5293	13	24	differentiable	differentiable	ADJ
ejpam-5293	13	25	dynamics	dynamic	NOUN
ejpam-5293	13	26	[	[	X
ejpam-5293	13	27	16	16	NUM
ejpam-5293	13	28	]	]	PUNCT
ejpam-5293	13	29	.	.	PUNCT
ejpam-5293	14	1	other	other	ADJ
ejpam-5293	14	2	leading	lead	VERB
ejpam-5293	14	3	researchers	researcher	NOUN
ejpam-5293	14	4	on	on	ADP
ejpam-5293	14	5	this	this	DET
ejpam-5293	14	6	broad	broad	ADJ
ejpam-5293	14	7	subject	subject	NOUN
ejpam-5293	14	8	were	be	AUX
ejpam-5293	14	9	a.	a.	NOUN
ejpam-5293	14	10	lyapunov	lyapunov	NOUN
ejpam-5293	14	11	and	and	CCONJ
ejpam-5293	14	12	j.	j.	PROPN
ejpam-5293	14	13	hadamard	hadamard	PROPN
ejpam-5293	14	14	introduced	introduce	VERB
ejpam-5293	14	15	several	several	ADJ
ejpam-5293	14	16	concepts	concept	NOUN
ejpam-5293	14	17	of	of	ADP
ejpam-5293	14	18	stability	stability	NOUN
ejpam-5293	14	19	and	and	CCONJ
ejpam-5293	14	20	developed	develop	VERB
ejpam-5293	14	21	analytic	analytic	ADJ
ejpam-5293	14	22	tools	tool	NOUN
ejpam-5293	14	23	such	such	ADJ
ejpam-5293	14	24	as	as	ADP
ejpam-5293	14	25	,	,	PUNCT
ejpam-5293	14	26	for	for	ADP
ejpam-5293	14	27	instance	instance	NOUN
ejpam-5293	14	28	,	,	PUNCT
ejpam-5293	14	29	the	the	DET
ejpam-5293	14	30	hadamardperron	hadamardperron	PROPN
ejpam-5293	14	31	theorem	theorem	VERB
ejpam-5293	14	32	[	[	X
ejpam-5293	14	33	6	6	NUM
ejpam-5293	14	34	]	]	PUNCT
ejpam-5293	14	35	.	.	PUNCT
ejpam-5293	15	1	another	another	DET
ejpam-5293	15	2	essential	essential	ADJ
ejpam-5293	15	3	advance	advance	NOUN
ejpam-5293	15	4	in	in	ADP
ejpam-5293	15	5	the	the	DET
ejpam-5293	15	6	study	study	NOUN
ejpam-5293	15	7	of	of	ADP
ejpam-5293	15	8	differentiable	differentiable	ADJ
ejpam-5293	15	9	dynamics	dynamic	NOUN
ejpam-5293	15	10	was	be	AUX
ejpam-5293	15	11	the	the	DET
ejpam-5293	15	12	concept	concept	NOUN
ejpam-5293	15	13	of	of	ADP
ejpam-5293	15	14	structural	structural	ADJ
ejpam-5293	15	15	stability	stability	NOUN
ejpam-5293	15	16	,	,	PUNCT
ejpam-5293	15	17	particularly	particularly	ADV
ejpam-5293	15	18	with	with	ADP
ejpam-5293	15	19	the	the	DET
ejpam-5293	15	20	founding	founding	NOUN
ejpam-5293	15	21	by	by	ADP
ejpam-5293	15	22	s.	s.	PROPN
ejpam-5293	15	23	smale	smale	PROPN
ejpam-5293	15	24	that	that	SCONJ
ejpam-5293	15	25	systems	system	NOUN
ejpam-5293	15	26	with	with	ADP
ejpam-5293	15	27	complicated	complicated	ADJ
ejpam-5293	15	28	orbit	orbit	NOUN
ejpam-5293	15	29	behaviour	behaviour	NOUN
ejpam-5293	15	30	can	can	AUX
ejpam-5293	15	31	be	be	AUX
ejpam-5293	15	32	structurally	structurally	ADV
ejpam-5293	15	33	stable	stable	ADJ
ejpam-5293	15	34	.	.	PUNCT
ejpam-5293	16	1	afterwards	afterwards	ADV
ejpam-5293	16	2	,	,	PUNCT
ejpam-5293	16	3	s.	s.	PROPN
ejpam-5293	16	4	smale	smale	PROPN
ejpam-5293	16	5	,	,	PUNCT
ejpam-5293	16	6	d.	d.	PROPN
ejpam-5293	16	7	anosov	anosov	PROPN
ejpam-5293	16	8	,	,	PUNCT
ejpam-5293	16	9	y.	y.	PROPN
ejpam-5293	16	10	sinai	sinai	PROPN
ejpam-5293	16	11	,	,	PUNCT
ejpam-5293	16	12	r.	r.	PROPN
ejpam-5293	16	13	bowen	bowen	PROPN
ejpam-5293	16	14	and	and	CCONJ
ejpam-5293	16	15	d.	d.	PROPN
ejpam-5293	16	16	ruelle	ruelle	PROPN
ejpam-5293	16	17	developed	develop	VERB
ejpam-5293	16	18	the	the	DET
ejpam-5293	16	19	core	core	NOUN
ejpam-5293	16	20	of	of	ADP
ejpam-5293	16	21	the	the	DET
ejpam-5293	16	22	hyperbolic	hyperbolic	ADJ
ejpam-5293	16	23	dynamics	dynamic	NOUN
ejpam-5293	16	24	theory	theory	NOUN
ejpam-5293	16	25	[	[	X
ejpam-5293	16	26	6	6	NUM
ejpam-5293	16	27	]	]	PUNCT
ejpam-5293	16	28	.	.	PUNCT
ejpam-5293	17	1	some	some	DET
ejpam-5293	17	2	results	result	NOUN
ejpam-5293	17	3	established	establish	VERB
ejpam-5293	17	4	by	by	ADP
ejpam-5293	17	5	a.	a.	NOUN
ejpam-5293	17	6	livschitz	livschitz	NOUN
ejpam-5293	17	7	in	in	ADP
ejpam-5293	17	8	the	the	DET
ejpam-5293	17	9	1970s	1970	NOUN
ejpam-5293	17	10	[	[	X
ejpam-5293	17	11	11	11	NUM
ejpam-5293	17	12	,	,	PUNCT
ejpam-5293	17	13	12	12	NUM
ejpam-5293	17	14	]	]	PUNCT
ejpam-5293	17	15	address	address	NOUN
ejpam-5293	17	16	the	the	DET
ejpam-5293	17	17	doi	doi	NOUN
ejpam-5293	17	18	:	:	PUNCT
ejpam-5293	17	19	https://doi.org/10.29020/nybg.ejpam.v17i3.5293	https://doi.org/10.29020/nybg.ejpam.v17i3.5293	PRON
ejpam-5293	17	20	email	email	NOUN
ejpam-5293	17	21	address	address	NOUN
ejpam-5293	17	22	:	:	PUNCT
ejpam-5293	17	23	maria.laureano@iscte-iul.pt	maria.laureano@iscte-iul.pt	PROPN
ejpam-5293	17	24	(	(	PUNCT
ejpam-5293	17	25	r.	r.	PROPN
ejpam-5293	17	26	d.	d.	PROPN
ejpam-5293	17	27	laureano	laureano	PROPN
ejpam-5293	17	28	)	)	PUNCT
ejpam-5293	17	29	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5293	17	30	1403	1403	NUM
ejpam-5293	17	31	©	©	PROPN
ejpam-5293	17	32	2024	2024	NUM
ejpam-5293	17	33	ejpam	ejpam	NOUN
ejpam-5293	17	34	all	all	DET
ejpam-5293	17	35	rights	right	NOUN
ejpam-5293	17	36	reserved	reserve	VERB
ejpam-5293	17	37	.	.	PUNCT
ejpam-5293	18	1	r.	r.	PROPN
ejpam-5293	18	2	d.	d.	PROPN
ejpam-5293	18	3	laureano	laureano	PROPN
ejpam-5293	18	4	/	/	SYM
ejpam-5293	18	5	eur	eur	PROPN
ejpam-5293	18	6	.	.	PUNCT
ejpam-5293	19	1	j.	j.	PROPN
ejpam-5293	19	2	pure	pure	PROPN
ejpam-5293	19	3	appl	appl	PROPN
ejpam-5293	19	4	.	.	PROPN
ejpam-5293	19	5	math	math	PROPN
ejpam-5293	19	6	,	,	PUNCT
ejpam-5293	19	7	17	17	NUM
ejpam-5293	19	8	(	(	PUNCT
ejpam-5293	19	9	3	3	NUM
ejpam-5293	19	10	)	)	PUNCT
ejpam-5293	19	11	(	(	PUNCT
ejpam-5293	19	12	2024	2024	NUM
ejpam-5293	19	13	)	)	PUNCT
ejpam-5293	19	14	,	,	PUNCT
ejpam-5293	19	15	1403	1403	NUM
ejpam-5293	19	16	-	-	SYM
ejpam-5293	19	17	1416	1416	NUM
ejpam-5293	19	18	1404	1404	NUM
ejpam-5293	19	19	possibility	possibility	NOUN
ejpam-5293	19	20	of	of	ADP
ejpam-5293	19	21	obtaining	obtain	VERB
ejpam-5293	19	22	solutions	solution	NOUN
ejpam-5293	19	23	of	of	ADP
ejpam-5293	19	24	cohomological	cohomological	ADJ
ejpam-5293	19	25	equations	equation	NOUN
ejpam-5293	19	26	in	in	ADP
ejpam-5293	19	27	the	the	DET
ejpam-5293	19	28	hyperbolic	hyperbolic	ADJ
ejpam-5293	19	29	dynamics	dynamic	NOUN
ejpam-5293	19	30	context	context	NOUN
ejpam-5293	19	31	.	.	PUNCT
ejpam-5293	20	1	in	in	ADP
ejpam-5293	20	2	turn	turn	NOUN
ejpam-5293	20	3	,	,	PUNCT
ejpam-5293	20	4	the	the	DET
ejpam-5293	20	5	anosov	anosov	NOUN
ejpam-5293	20	6	closing	close	VERB
ejpam-5293	20	7	lemma	lemma	PROPN
ejpam-5293	20	8	(	(	PUNCT
ejpam-5293	20	9	acl	acl	PROPN
ejpam-5293	20	10	)	)	PUNCT
ejpam-5293	20	11	is	be	AUX
ejpam-5293	20	12	used	use	VERB
ejpam-5293	20	13	to	to	PART
ejpam-5293	20	14	prove	prove	VERB
ejpam-5293	20	15	these	these	DET
ejpam-5293	20	16	results	result	NOUN
ejpam-5293	20	17	[	[	X
ejpam-5293	20	18	6	6	NUM
ejpam-5293	20	19	]	]	PUNCT
ejpam-5293	20	20	.	.	PUNCT
ejpam-5293	21	1	acl	acl	PROPN
ejpam-5293	21	2	formalizes	formalize	VERB
ejpam-5293	21	3	how	how	SCONJ
ejpam-5293	21	4	the	the	DET
ejpam-5293	21	5	combination	combination	NOUN
ejpam-5293	21	6	of	of	ADP
ejpam-5293	21	7	local	local	ADJ
ejpam-5293	21	8	hyperbolicity	hyperbolicity	NOUN
ejpam-5293	21	9	(	(	PUNCT
ejpam-5293	21	10	from	from	ADP
ejpam-5293	21	11	the	the	DET
ejpam-5293	21	12	linearized	linearize	VERB
ejpam-5293	21	13	dynamical	dynamical	ADJ
ejpam-5293	21	14	systems	system	NOUN
ejpam-5293	21	15	analysis	analysis	NOUN
ejpam-5293	21	16	)	)	PUNCT
ejpam-5293	21	17	with	with	ADP
ejpam-5293	21	18	nontrivial	nontrivial	ADJ
ejpam-5293	21	19	recurrence	recurrence	NOUN
ejpam-5293	21	20	tends	tend	VERB
ejpam-5293	21	21	to	to	PART
ejpam-5293	21	22	produce	produce	VERB
ejpam-5293	21	23	an	an	DET
ejpam-5293	21	24	abundance	abundance	NOUN
ejpam-5293	21	25	of	of	ADP
ejpam-5293	21	26	periodic	periodic	ADJ
ejpam-5293	21	27	orbits	orbit	NOUN
ejpam-5293	21	28	.	.	PUNCT
ejpam-5293	22	1	given	give	VERB
ejpam-5293	22	2	a	a	DET
ejpam-5293	22	3	dynamical	dynamical	ADJ
ejpam-5293	22	4	system	system	NOUN
ejpam-5293	22	5	with	with	ADP
ejpam-5293	22	6	phase	phase	NOUN
ejpam-5293	22	7	space	space	NOUN
ejpam-5293	22	8	x	x	NOUN
ejpam-5293	22	9	,	,	PUNCT
ejpam-5293	22	10	f	f	X
ejpam-5293	22	11	:	:	PUNCT
ejpam-5293	22	12	x	x	X
ejpam-5293	22	13	→	→	SYM
ejpam-5293	22	14	x	x	PART
ejpam-5293	22	15	,	,	PUNCT
ejpam-5293	22	16	and	and	CCONJ
ejpam-5293	22	17	fixed	fix	VERB
ejpam-5293	22	18	an	an	DET
ejpam-5293	22	19	initial	initial	ADJ
ejpam-5293	22	20	condition	condition	NOUN
ejpam-5293	22	21	x0	x0	PROPN
ejpam-5293	22	22	∈	∈	PROPN
ejpam-5293	22	23	x	x	AUX
ejpam-5293	22	24	,	,	PUNCT
ejpam-5293	22	25	it	it	PRON
ejpam-5293	22	26	is	be	AUX
ejpam-5293	22	27	crucial	crucial	ADJ
ejpam-5293	22	28	to	to	PART
ejpam-5293	22	29	identify	identify	VERB
ejpam-5293	22	30	those	those	DET
ejpam-5293	22	31	x	x	SYM
ejpam-5293	22	32	∈	∈	PROPN
ejpam-5293	22	33	x	x	PUNCT
ejpam-5293	22	34	which	which	DET
ejpam-5293	22	35	evolution	evolution	NOUN
ejpam-5293	22	36	under	under	ADP
ejpam-5293	22	37	the	the	DET
ejpam-5293	22	38	iterates	iterate	NOUN
ejpam-5293	22	39	of	of	ADP
ejpam-5293	22	40	f	f	PROPN
ejpam-5293	22	41	follows	follow	VERB
ejpam-5293	22	42	sufficiently	sufficiently	ADV
ejpam-5293	22	43	close	close	ADJ
ejpam-5293	22	44	that	that	PRON
ejpam-5293	22	45	of	of	ADP
ejpam-5293	22	46	x0	x0	PROPN
ejpam-5293	22	47	,	,	PUNCT
ejpam-5293	22	48	for	for	ADP
ejpam-5293	22	49	a	a	DET
ejpam-5293	22	50	long	long	ADJ
ejpam-5293	22	51	time	time	NOUN
ejpam-5293	22	52	;	;	PUNCT
ejpam-5293	22	53	also	also	ADV
ejpam-5293	22	54	,	,	PUNCT
ejpam-5293	22	55	to	to	PART
ejpam-5293	22	56	understand	understand	VERB
ejpam-5293	22	57	the	the	DET
ejpam-5293	22	58	asymptotic	asymptotic	ADJ
ejpam-5293	22	59	behavior	behavior	NOUN
ejpam-5293	22	60	of	of	ADP
ejpam-5293	22	61	x	x	PROPN
ejpam-5293	22	62	orbit	orbit	NOUN
ejpam-5293	22	63	relative	relative	ADJ
ejpam-5293	22	64	to	to	ADP
ejpam-5293	22	65	x0	x0	PROPN
ejpam-5293	22	66	orbit	orbit	NOUN
ejpam-5293	22	67	can	can	AUX
ejpam-5293	22	68	be	be	AUX
ejpam-5293	22	69	useful	useful	ADJ
ejpam-5293	22	70	of	of	ADP
ejpam-5293	22	71	this	this	DET
ejpam-5293	22	72	lemma	lemma	PROPN
ejpam-5293	22	73	.	.	PUNCT
ejpam-5293	23	1	besides	besides	SCONJ
ejpam-5293	23	2	presenting	present	VERB
ejpam-5293	23	3	a	a	DET
ejpam-5293	23	4	detailed	detailed	ADJ
ejpam-5293	23	5	proof	proof	NOUN
ejpam-5293	23	6	of	of	ADP
ejpam-5293	23	7	the	the	DET
ejpam-5293	23	8	acl	acl	PROPN
ejpam-5293	23	9	for	for	ADP
ejpam-5293	23	10	hyperbolic	hyperbolic	ADJ
ejpam-5293	23	11	diffeomorphisms	diffeomorphism	NOUN
ejpam-5293	23	12	,	,	PUNCT
ejpam-5293	23	13	an	an	DET
ejpam-5293	23	14	inequality	inequality	NOUN
ejpam-5293	23	15	that	that	PRON
ejpam-5293	23	16	quantitatively	quantitatively	ADV
ejpam-5293	23	17	estimates	estimate	VERB
ejpam-5293	23	18	how	how	SCONJ
ejpam-5293	23	19	the	the	DET
ejpam-5293	23	20	constructed	construct	VERB
ejpam-5293	23	21	periodic	periodic	ADJ
ejpam-5293	23	22	orbit	orbit	NOUN
ejpam-5293	23	23	differs	differ	VERB
ejpam-5293	23	24	from	from	ADP
ejpam-5293	23	25	the	the	DET
ejpam-5293	23	26	initial	initial	ADJ
ejpam-5293	23	27	orbit	orbit	NOUN
ejpam-5293	23	28	is	be	AUX
ejpam-5293	23	29	here	here	ADV
ejpam-5293	23	30	proved	prove	VERB
ejpam-5293	23	31	.	.	PUNCT
ejpam-5293	24	1	this	this	DET
ejpam-5293	24	2	inequality	inequality	NOUN
ejpam-5293	24	3	is	be	AUX
ejpam-5293	24	4	crucial	crucial	ADJ
ejpam-5293	24	5	in	in	ADP
ejpam-5293	24	6	the	the	DET
ejpam-5293	24	7	livschitz	livschitz	NOUN
ejpam-5293	24	8	theorem	theorem	NOUN
ejpam-5293	24	9	for	for	ADP
ejpam-5293	24	10	hyperbolic	hyperbolic	ADJ
ejpam-5293	24	11	diffeomorphisms	diffeomorphism	NOUN
ejpam-5293	24	12	proof	proof	NOUN
ejpam-5293	24	13	.	.	PUNCT
ejpam-5293	25	1	the	the	DET
ejpam-5293	25	2	livschitz	livschitz	PROPN
ejpam-5293	25	3	theorem	theorem	NOUN
ejpam-5293	25	4	is	be	AUX
ejpam-5293	25	5	an	an	DET
ejpam-5293	25	6	essential	essential	ADJ
ejpam-5293	25	7	tool	tool	NOUN
ejpam-5293	25	8	for	for	ADP
ejpam-5293	25	9	obtaining	obtain	VERB
ejpam-5293	25	10	global	global	ADJ
ejpam-5293	25	11	data	datum	NOUN
ejpam-5293	25	12	of	of	ADP
ejpam-5293	25	13	a	a	DET
ejpam-5293	25	14	cohomological	cohomological	ADJ
ejpam-5293	25	15	nature	nature	NOUN
ejpam-5293	25	16	from	from	ADP
ejpam-5293	25	17	periodic	periodic	ADJ
ejpam-5293	25	18	data	datum	NOUN
ejpam-5293	25	19	.	.	PUNCT
ejpam-5293	26	1	indeed	indeed	ADV
ejpam-5293	26	2	,	,	PUNCT
ejpam-5293	26	3	in	in	ADP
ejpam-5293	26	4	the	the	DET
ejpam-5293	26	5	dynamical	dynamical	ADJ
ejpam-5293	26	6	systems	system	NOUN
ejpam-5293	26	7	theory	theory	NOUN
ejpam-5293	26	8	,	,	PUNCT
ejpam-5293	26	9	several	several	ADJ
ejpam-5293	26	10	main	main	ADJ
ejpam-5293	26	11	problems	problem	NOUN
ejpam-5293	26	12	can	can	AUX
ejpam-5293	26	13	be	be	AUX
ejpam-5293	26	14	reduced	reduce	VERB
ejpam-5293	26	15	to	to	ADP
ejpam-5293	26	16	solving	solve	VERB
ejpam-5293	26	17	the	the	DET
ejpam-5293	26	18	so	so	ADV
ejpam-5293	26	19	-	-	PUNCT
ejpam-5293	26	20	called	call	VERB
ejpam-5293	26	21	cohomological	cohomological	ADJ
ejpam-5293	26	22	equations	equation	NOUN
ejpam-5293	26	23	φ	φ	X
ejpam-5293	26	24	=	=	SYM
ejpam-5293	27	1	φ	φ	PROPN
ejpam-5293	27	2	◦	◦	NOUN
ejpam-5293	27	3	f	f	PROPN
ejpam-5293	28	1	−	−	PROPN
ejpam-5293	28	2	φ	φ	PROPN
ejpam-5293	28	3	,	,	PUNCT
ejpam-5293	28	4	where	where	SCONJ
ejpam-5293	28	5	f	f	NOUN
ejpam-5293	28	6	:	:	PUNCT
ejpam-5293	28	7	x	x	X
ejpam-5293	28	8	→	→	PUNCT
ejpam-5293	28	9	x	x	X
ejpam-5293	28	10	is	be	AUX
ejpam-5293	28	11	a	a	DET
ejpam-5293	28	12	dynamical	dynamical	ADJ
ejpam-5293	28	13	system	system	NOUN
ejpam-5293	28	14	and	and	CCONJ
ejpam-5293	28	15	φ	φ	NOUN
ejpam-5293	28	16	:	:	PUNCT
ejpam-5293	28	17	x	x	X
ejpam-5293	28	18	→	→	SYM
ejpam-5293	28	19	r	r	NOUN
ejpam-5293	28	20	is	be	AUX
ejpam-5293	28	21	a	a	DET
ejpam-5293	28	22	function	function	NOUN
ejpam-5293	28	23	,	,	PUNCT
ejpam-5293	28	24	both	both	PRON
ejpam-5293	28	25	known	know	VERB
ejpam-5293	28	26	,	,	PUNCT
ejpam-5293	28	27	and	and	CCONJ
ejpam-5293	28	28	φ	φ	NUM
ejpam-5293	28	29	:	:	PUNCT
ejpam-5293	28	30	x	x	X
ejpam-5293	28	31	→	→	SYM
ejpam-5293	28	32	r	r	NOUN
ejpam-5293	28	33	is	be	AUX
ejpam-5293	28	34	an	an	DET
ejpam-5293	28	35	unknown	unknown	ADJ
ejpam-5293	28	36	function	function	NOUN
ejpam-5293	28	37	.	.	PUNCT
ejpam-5293	29	1	the	the	DET
ejpam-5293	29	2	study	study	NOUN
ejpam-5293	29	3	of	of	ADP
ejpam-5293	29	4	these	these	DET
ejpam-5293	29	5	equations	equation	NOUN
ejpam-5293	29	6	is	be	AUX
ejpam-5293	29	7	related	relate	VERB
ejpam-5293	29	8	,	,	PUNCT
ejpam-5293	29	9	in	in	ADP
ejpam-5293	29	10	particular	particular	ADJ
ejpam-5293	29	11	,	,	PUNCT
ejpam-5293	29	12	to	to	ADP
ejpam-5293	29	13	the	the	DET
ejpam-5293	29	14	existence	existence	NOUN
ejpam-5293	29	15	of	of	ADP
ejpam-5293	29	16	absolutely	absolutely	ADV
ejpam-5293	29	17	continuous	continuous	ADJ
ejpam-5293	29	18	measures	measure	NOUN
ejpam-5293	29	19	for	for	ADP
ejpam-5293	29	20	expansive	expansive	ADJ
ejpam-5293	29	21	circle	circle	NOUN
ejpam-5293	29	22	maps	map	NOUN
ejpam-5293	29	23	and	and	CCONJ
ejpam-5293	29	24	the	the	DET
ejpam-5293	29	25	topological	topological	ADJ
ejpam-5293	29	26	stability	stability	NOUN
ejpam-5293	29	27	of	of	ADP
ejpam-5293	29	28	hyperbolic	hyperbolic	ADJ
ejpam-5293	29	29	torus	torus	NOUN
ejpam-5293	29	30	automorphisms	automorphism	NOUN
ejpam-5293	30	1	[	[	X
ejpam-5293	30	2	7	7	NUM
ejpam-5293	30	3	]	]	PUNCT
ejpam-5293	30	4	.	.	PUNCT
ejpam-5293	31	1	such	such	ADJ
ejpam-5293	31	2	equations	equation	NOUN
ejpam-5293	31	3	also	also	ADV
ejpam-5293	31	4	arise	arise	VERB
ejpam-5293	31	5	naturally	naturally	ADV
ejpam-5293	31	6	in	in	ADP
ejpam-5293	31	7	celestial	celestial	ADJ
ejpam-5293	31	8	mechanics	mechanic	NOUN
ejpam-5293	31	9	and	and	CCONJ
ejpam-5293	31	10	statistical	statistical	ADJ
ejpam-5293	31	11	mechanics	mechanic	NOUN
ejpam-5293	31	12	(	(	PUNCT
ejpam-5293	31	13	see	see	VERB
ejpam-5293	31	14	,	,	PUNCT
ejpam-5293	31	15	for	for	ADP
ejpam-5293	31	16	instance	instance	NOUN
ejpam-5293	31	17	,	,	PUNCT
ejpam-5293	31	18	[	[	X
ejpam-5293	31	19	2	2	NUM
ejpam-5293	31	20	]	]	PUNCT
ejpam-5293	31	21	)	)	PUNCT
ejpam-5293	31	22	.	.	PUNCT
ejpam-5293	32	1	given	give	VERB
ejpam-5293	32	2	a	a	DET
ejpam-5293	32	3	hyperbolic	hyperbolic	ADJ
ejpam-5293	32	4	dynamical	dynamical	ADJ
ejpam-5293	32	5	system	system	NOUN
ejpam-5293	32	6	,	,	PUNCT
ejpam-5293	32	7	the	the	DET
ejpam-5293	32	8	livschitz	livschitz	NOUN
ejpam-5293	32	9	theorem	theorem	NOUN
ejpam-5293	32	10	provides	provide	VERB
ejpam-5293	32	11	a	a	DET
ejpam-5293	32	12	necessary	necessary	ADJ
ejpam-5293	32	13	and	and	CCONJ
ejpam-5293	32	14	sufficient	sufficient	ADJ
ejpam-5293	32	15	condition	condition	NOUN
ejpam-5293	32	16	,	,	PUNCT
ejpam-5293	32	17	based	base	VERB
ejpam-5293	32	18	only	only	ADV
ejpam-5293	32	19	on	on	ADP
ejpam-5293	32	20	the	the	DET
ejpam-5293	32	21	data	datum	NOUN
ejpam-5293	32	22	given	give	VERB
ejpam-5293	32	23	by	by	ADP
ejpam-5293	32	24	periodic	periodic	ADJ
ejpam-5293	32	25	orbits	orbit	NOUN
ejpam-5293	32	26	,	,	PUNCT
ejpam-5293	32	27	for	for	ADP
ejpam-5293	32	28	the	the	DET
ejpam-5293	32	29	existence	existence	NOUN
ejpam-5293	32	30	of	of	ADP
ejpam-5293	32	31	hölder	hölder	NOUN
ejpam-5293	32	32	solutions	solution	NOUN
ejpam-5293	32	33	of	of	ADP
ejpam-5293	32	34	the	the	DET
ejpam-5293	32	35	cohomological	cohomological	ADJ
ejpam-5293	32	36	equations	equation	NOUN
ejpam-5293	32	37	.	.	PUNCT
ejpam-5293	33	1	acl	acl	PROPN
ejpam-5293	33	2	is	be	AUX
ejpam-5293	33	3	a	a	DET
ejpam-5293	33	4	key	key	ADJ
ejpam-5293	33	5	component	component	NOUN
ejpam-5293	33	6	in	in	ADP
ejpam-5293	33	7	the	the	DET
ejpam-5293	33	8	proof	proof	NOUN
ejpam-5293	33	9	of	of	ADP
ejpam-5293	33	10	the	the	DET
ejpam-5293	33	11	livschitz	livschitz	NOUN
ejpam-5293	33	12	theorem	theorem	NOUN
ejpam-5293	33	13	,	,	PUNCT
ejpam-5293	33	14	as	as	SCONJ
ejpam-5293	33	15	it	it	PRON
ejpam-5293	33	16	provides	provide	VERB
ejpam-5293	33	17	the	the	DET
ejpam-5293	33	18	necessary	necessary	ADJ
ejpam-5293	33	19	link	link	NOUN
ejpam-5293	33	20	between	between	ADP
ejpam-5293	33	21	the	the	DET
ejpam-5293	33	22	behavior	behavior	NOUN
ejpam-5293	33	23	along	along	ADP
ejpam-5293	33	24	periodic	periodic	ADJ
ejpam-5293	33	25	orbits	orbit	NOUN
ejpam-5293	33	26	and	and	CCONJ
ejpam-5293	33	27	the	the	DET
ejpam-5293	33	28	existence	existence	NOUN
ejpam-5293	33	29	of	of	ADP
ejpam-5293	33	30	solutions	solution	NOUN
ejpam-5293	33	31	to	to	ADP
ejpam-5293	33	32	cohomological	cohomological	ADJ
ejpam-5293	33	33	equations	equation	NOUN
ejpam-5293	33	34	with	with	ADP
ejpam-5293	33	35	adequate	adequate	ADJ
ejpam-5293	33	36	regularity	regularity	NOUN
ejpam-5293	33	37	,	,	PUNCT
ejpam-5293	33	38	as	as	SCONJ
ejpam-5293	33	39	illustrated	illustrate	VERB
ejpam-5293	33	40	below	below	ADV
ejpam-5293	33	41	.	.	PUNCT
ejpam-5293	34	1	this	this	DET
ejpam-5293	34	2	article	article	NOUN
ejpam-5293	34	3	aims	aim	VERB
ejpam-5293	34	4	to	to	PART
ejpam-5293	34	5	present	present	VERB
ejpam-5293	34	6	a	a	DET
ejpam-5293	34	7	proof	proof	NOUN
ejpam-5293	34	8	of	of	ADP
ejpam-5293	34	9	acl	acl	PROPN
ejpam-5293	34	10	oriented	orient	VERB
ejpam-5293	34	11	towards	towards	ADP
ejpam-5293	34	12	the	the	DET
ejpam-5293	34	13	study	study	NOUN
ejpam-5293	34	14	of	of	ADP
ejpam-5293	34	15	cohomology	cohomology	NOUN
ejpam-5293	34	16	in	in	ADP
ejpam-5293	34	17	discrete	discrete	ADJ
ejpam-5293	34	18	dynamical	dynamical	ADJ
ejpam-5293	34	19	systems	system	NOUN
ejpam-5293	34	20	;	;	PUNCT
ejpam-5293	34	21	in	in	ADP
ejpam-5293	34	22	this	this	DET
ejpam-5293	34	23	way	way	NOUN
ejpam-5293	34	24	,	,	PUNCT
ejpam-5293	34	25	it	it	PRON
ejpam-5293	34	26	provides	provide	VERB
ejpam-5293	34	27	a	a	DET
ejpam-5293	34	28	self	self	NOUN
ejpam-5293	34	29	-	-	PUNCT
ejpam-5293	34	30	contained	contain	VERB
ejpam-5293	34	31	approach	approach	NOUN
ejpam-5293	34	32	to	to	ADP
ejpam-5293	34	33	the	the	DET
ejpam-5293	34	34	livschitz	livschitz	NOUN
ejpam-5293	34	35	theorem	theorem	NOUN
ejpam-5293	34	36	,	,	PUNCT
ejpam-5293	34	37	which	which	DET
ejpam-5293	34	38	proof	proof	NOUN
ejpam-5293	34	39	is	be	AUX
ejpam-5293	34	40	presented	present	VERB
ejpam-5293	34	41	for	for	ADP
ejpam-5293	34	42	pedagogical	pedagogical	ADJ
ejpam-5293	34	43	purposes	purpose	NOUN
ejpam-5293	34	44	also	also	ADV
ejpam-5293	34	45	.	.	PUNCT
ejpam-5293	35	1	as	as	ADV
ejpam-5293	35	2	far	far	ADV
ejpam-5293	35	3	as	as	SCONJ
ejpam-5293	35	4	we	we	PRON
ejpam-5293	35	5	know	know	VERB
ejpam-5293	35	6	,	,	PUNCT
ejpam-5293	35	7	there	there	PRON
ejpam-5293	35	8	is	be	VERB
ejpam-5293	35	9	no	no	DET
ejpam-5293	35	10	detailed	detailed	ADJ
ejpam-5293	35	11	treatment	treatment	NOUN
ejpam-5293	35	12	of	of	ADP
ejpam-5293	35	13	acl	acl	PROPN
ejpam-5293	35	14	in	in	ADP
ejpam-5293	35	15	the	the	DET
ejpam-5293	35	16	literature	literature	NOUN
ejpam-5293	35	17	,	,	PUNCT
ejpam-5293	35	18	pragmatically	pragmatically	ADV
ejpam-5293	35	19	oriented	orient	VERB
ejpam-5293	35	20	to	to	ADP
ejpam-5293	35	21	the	the	DET
ejpam-5293	35	22	cohomological	cohomological	ADJ
ejpam-5293	35	23	context	context	NOUN
ejpam-5293	35	24	,	,	PUNCT
ejpam-5293	35	25	except	except	SCONJ
ejpam-5293	35	26	for	for	ADP
ejpam-5293	35	27	hyperbolic	hyperbolic	ADJ
ejpam-5293	35	28	flows	flow	NOUN
ejpam-5293	35	29	and	and	CCONJ
ejpam-5293	35	30	the	the	DET
ejpam-5293	35	31	generalization	generalization	NOUN
ejpam-5293	35	32	to	to	ADP
ejpam-5293	35	33	a	a	DET
ejpam-5293	35	34	class	class	NOUN
ejpam-5293	35	35	of	of	ADP
ejpam-5293	35	36	suspension	suspension	NOUN
ejpam-5293	35	37	flows	flow	NOUN
ejpam-5293	35	38	in	in	ADP
ejpam-5293	35	39	the	the	DET
ejpam-5293	35	40	article	article	NOUN
ejpam-5293	35	41	[	[	X
ejpam-5293	35	42	10	10	NUM
ejpam-5293	35	43	]	]	PUNCT
ejpam-5293	35	44	.	.	PUNCT
ejpam-5293	36	1	the	the	DET
ejpam-5293	36	2	novelty	novelty	NOUN
ejpam-5293	36	3	of	of	ADP
ejpam-5293	36	4	this	this	DET
ejpam-5293	36	5	research	research	NOUN
ejpam-5293	36	6	lies	lie	VERB
ejpam-5293	36	7	in	in	ADP
ejpam-5293	36	8	the	the	DET
ejpam-5293	36	9	comprehensive	comprehensive	PROPN
ejpam-5293	36	10	r.	r.	PROPN
ejpam-5293	36	11	d.	d.	PROPN
ejpam-5293	36	12	laureano	laureano	PROPN
ejpam-5293	36	13	/	/	SYM
ejpam-5293	36	14	eur	eur	PROPN
ejpam-5293	36	15	.	.	PUNCT
ejpam-5293	37	1	j.	j.	PROPN
ejpam-5293	37	2	pure	pure	PROPN
ejpam-5293	37	3	appl	appl	PROPN
ejpam-5293	37	4	.	.	PROPN
ejpam-5293	37	5	math	math	PROPN
ejpam-5293	37	6	,	,	PUNCT
ejpam-5293	37	7	17	17	NUM
ejpam-5293	37	8	(	(	PUNCT
ejpam-5293	37	9	3	3	NUM
ejpam-5293	37	10	)	)	PUNCT
ejpam-5293	37	11	(	(	PUNCT
ejpam-5293	37	12	2024	2024	NUM
ejpam-5293	37	13	)	)	PUNCT
ejpam-5293	37	14	,	,	PUNCT
ejpam-5293	37	15	1403	1403	NUM
ejpam-5293	37	16	-	-	SYM
ejpam-5293	37	17	1416	1416	NUM
ejpam-5293	37	18	1405	1405	NUM
ejpam-5293	37	19	treatment	treatment	NOUN
ejpam-5293	37	20	of	of	ADP
ejpam-5293	37	21	the	the	DET
ejpam-5293	37	22	livschitz	livschitz	NOUN
ejpam-5293	37	23	theorem	theorem	VERB
ejpam-5293	37	24	in	in	ADP
ejpam-5293	37	25	discrete	discrete	ADJ
ejpam-5293	37	26	time	time	NOUN
ejpam-5293	37	27	,	,	PUNCT
ejpam-5293	37	28	building	build	VERB
ejpam-5293	37	29	upon	upon	SCONJ
ejpam-5293	37	30	the	the	DET
ejpam-5293	37	31	fundamental	fundamental	ADJ
ejpam-5293	37	32	relationship	relationship	NOUN
ejpam-5293	37	33	between	between	ADP
ejpam-5293	37	34	the	the	DET
ejpam-5293	37	35	existence	existence	NOUN
ejpam-5293	37	36	of	of	ADP
ejpam-5293	37	37	solutions	solution	NOUN
ejpam-5293	37	38	to	to	ADP
ejpam-5293	37	39	cohomological	cohomological	ADJ
ejpam-5293	37	40	equations	equation	NOUN
ejpam-5293	37	41	and	and	CCONJ
ejpam-5293	37	42	the	the	DET
ejpam-5293	37	43	behavior	behavior	NOUN
ejpam-5293	37	44	of	of	ADP
ejpam-5293	37	45	cocycles	cocycle	NOUN
ejpam-5293	37	46	along	along	ADP
ejpam-5293	37	47	periodic	periodic	ADJ
ejpam-5293	37	48	orbits	orbit	NOUN
ejpam-5293	37	49	.	.	PUNCT
ejpam-5293	38	1	it	it	PRON
ejpam-5293	38	2	extends	extend	VERB
ejpam-5293	38	3	the	the	DET
ejpam-5293	38	4	livschitz	livschitz	NOUN
ejpam-5293	38	5	theorem	theorem	VERB
ejpam-5293	38	6	to	to	ADP
ejpam-5293	38	7	a	a	DET
ejpam-5293	38	8	broader	broad	ADJ
ejpam-5293	38	9	class	class	NOUN
ejpam-5293	38	10	of	of	ADP
ejpam-5293	38	11	dynamical	dynamical	ADJ
ejpam-5293	38	12	systems	system	NOUN
ejpam-5293	38	13	,	,	PUNCT
ejpam-5293	38	14	providing	provide	VERB
ejpam-5293	38	15	a	a	DET
ejpam-5293	38	16	unified	unified	ADJ
ejpam-5293	38	17	framework	framework	NOUN
ejpam-5293	38	18	for	for	ADP
ejpam-5293	38	19	analyzing	analyze	VERB
ejpam-5293	38	20	the	the	DET
ejpam-5293	38	21	regularity	regularity	NOUN
ejpam-5293	38	22	of	of	ADP
ejpam-5293	38	23	solutions	solution	NOUN
ejpam-5293	38	24	to	to	ADP
ejpam-5293	38	25	cohomological	cohomological	ADJ
ejpam-5293	38	26	equations	equation	NOUN
ejpam-5293	38	27	.	.	PUNCT
ejpam-5293	39	1	for	for	ADP
ejpam-5293	39	2	a	a	DET
ejpam-5293	39	3	broader	broad	ADJ
ejpam-5293	39	4	knowledge	knowledge	NOUN
ejpam-5293	39	5	of	of	ADP
ejpam-5293	39	6	the	the	DET
ejpam-5293	39	7	acl	acl	PROPN
ejpam-5293	39	8	and	and	CCONJ
ejpam-5293	39	9	the	the	DET
ejpam-5293	39	10	livschitz	livschitz	NOUN
ejpam-5293	39	11	theorem	theorem	NOUN
ejpam-5293	39	12	,	,	PUNCT
ejpam-5293	39	13	article	article	NOUN
ejpam-5293	39	14	[	[	X
ejpam-5293	39	15	10	10	NUM
ejpam-5293	39	16	]	]	PUNCT
ejpam-5293	39	17	can	can	AUX
ejpam-5293	39	18	be	be	AUX
ejpam-5293	39	19	consulted	consult	VERB
ejpam-5293	39	20	for	for	ADP
ejpam-5293	39	21	development	development	NOUN
ejpam-5293	39	22	of	of	ADP
ejpam-5293	39	23	the	the	DET
ejpam-5293	39	24	cohomology	cohomology	NOUN
ejpam-5293	39	25	in	in	ADP
ejpam-5293	39	26	continuous	continuous	ADJ
ejpam-5293	39	27	time	time	NOUN
ejpam-5293	39	28	and	and	CCONJ
ejpam-5293	39	29	proofs	proof	NOUN
ejpam-5293	39	30	of	of	ADP
ejpam-5293	39	31	the	the	DET
ejpam-5293	39	32	livschitz	livschitz	NOUN
ejpam-5293	39	33	theorem	theorem	NOUN
ejpam-5293	39	34	for	for	ADP
ejpam-5293	39	35	hyperbolic	hyperbolic	ADJ
ejpam-5293	39	36	flows	flow	NOUN
ejpam-5293	39	37	and	and	CCONJ
ejpam-5293	39	38	also	also	ADV
ejpam-5293	39	39	for	for	ADP
ejpam-5293	39	40	suspension	suspension	NOUN
ejpam-5293	39	41	flows	flow	NOUN
ejpam-5293	39	42	are	be	AUX
ejpam-5293	39	43	presented	present	VERB
ejpam-5293	39	44	,	,	PUNCT
ejpam-5293	39	45	concerning	concern	VERB
ejpam-5293	39	46	[	[	X
ejpam-5293	39	47	1	1	NUM
ejpam-5293	39	48	,	,	PUNCT
ejpam-5293	39	49	3–5	3–5	NUM
ejpam-5293	39	50	,	,	PUNCT
ejpam-5293	39	51	8	8	NUM
ejpam-5293	39	52	,	,	PUNCT
ejpam-5293	39	53	9	9	NUM
ejpam-5293	39	54	,	,	PUNCT
ejpam-5293	39	55	15	15	NUM
ejpam-5293	39	56	,	,	PUNCT
ejpam-5293	39	57	17	17	NUM
ejpam-5293	39	58	,	,	PUNCT
ejpam-5293	39	59	18	18	NUM
ejpam-5293	39	60	]	]	PUNCT
ejpam-5293	39	61	.	.	PUNCT
ejpam-5293	40	1	the	the	DET
ejpam-5293	40	2	livschitz	livschitz	PROPN
ejpam-5293	40	3	theorem	theorem	NOUN
ejpam-5293	40	4	and	and	CCONJ
ejpam-5293	40	5	its	its	PRON
ejpam-5293	40	6	connection	connection	NOUN
ejpam-5293	40	7	to	to	ADP
ejpam-5293	40	8	the	the	DET
ejpam-5293	40	9	acl	acl	PROPN
ejpam-5293	40	10	have	have	VERB
ejpam-5293	40	11	implications	implication	NOUN
ejpam-5293	40	12	in	in	ADP
ejpam-5293	40	13	various	various	ADJ
ejpam-5293	40	14	fields	field	NOUN
ejpam-5293	40	15	,	,	PUNCT
ejpam-5293	40	16	such	such	ADJ
ejpam-5293	40	17	as	as	ADP
ejpam-5293	40	18	the	the	DET
ejpam-5293	40	19	study	study	NOUN
ejpam-5293	40	20	of	of	ADP
ejpam-5293	40	21	transport	transport	NOUN
ejpam-5293	40	22	properties	property	NOUN
ejpam-5293	40	23	in	in	ADP
ejpam-5293	40	24	dynamical	dynamical	ADJ
ejpam-5293	40	25	systems	system	NOUN
ejpam-5293	40	26	,	,	PUNCT
ejpam-5293	40	27	the	the	DET
ejpam-5293	40	28	analysis	analysis	NOUN
ejpam-5293	40	29	of	of	ADP
ejpam-5293	40	30	markov	markov	NOUN
ejpam-5293	40	31	chains	chain	NOUN
ejpam-5293	40	32	,	,	PUNCT
ejpam-5293	40	33	and	and	CCONJ
ejpam-5293	40	34	the	the	DET
ejpam-5293	40	35	study	study	NOUN
ejpam-5293	40	36	of	of	ADP
ejpam-5293	40	37	spectral	spectral	ADJ
ejpam-5293	40	38	properties	property	NOUN
ejpam-5293	40	39	of	of	ADP
ejpam-5293	40	40	operators	operator	NOUN
ejpam-5293	40	41	associated	associate	VERB
ejpam-5293	40	42	with	with	ADP
ejpam-5293	40	43	dynamical	dynamical	ADJ
ejpam-5293	40	44	systems	system	NOUN
ejpam-5293	40	45	.	.	PUNCT
ejpam-5293	41	1	furthermore	furthermore	ADV
ejpam-5293	41	2	,	,	PUNCT
ejpam-5293	41	3	the	the	DET
ejpam-5293	41	4	techniques	technique	NOUN
ejpam-5293	41	5	developed	develop	VERB
ejpam-5293	41	6	in	in	ADP
ejpam-5293	41	7	this	this	DET
ejpam-5293	41	8	research	research	NOUN
ejpam-5293	41	9	can	can	AUX
ejpam-5293	41	10	be	be	AUX
ejpam-5293	41	11	leveraged	leverage	VERB
ejpam-5293	41	12	to	to	PART
ejpam-5293	41	13	study	study	VERB
ejpam-5293	41	14	the	the	DET
ejpam-5293	41	15	behavior	behavior	NOUN
ejpam-5293	41	16	of	of	ADP
ejpam-5293	41	17	numerical	numerical	ADJ
ejpam-5293	41	18	schemes	scheme	NOUN
ejpam-5293	41	19	for	for	ADP
ejpam-5293	41	20	simulating	simulate	VERB
ejpam-5293	41	21	wave	wave	NOUN
ejpam-5293	41	22	phenomena	phenomenon	NOUN
ejpam-5293	41	23	,	,	PUNCT
ejpam-5293	41	24	such	such	ADJ
ejpam-5293	41	25	as	as	ADP
ejpam-5293	41	26	the	the	DET
ejpam-5293	41	27	kuramotosivashinsky	kuramotosivashinsky	PROPN
ejpam-5293	41	28	equation	equation	NOUN
ejpam-5293	41	29	and	and	CCONJ
ejpam-5293	41	30	fourth	fourth	ADJ
ejpam-5293	41	31	-	-	PUNCT
ejpam-5293	41	32	order	order	NOUN
ejpam-5293	41	33	reaction	reaction	NOUN
ejpam-5293	41	34	-	-	PUNCT
ejpam-5293	41	35	diffusion	diffusion	NOUN
ejpam-5293	41	36	equations	equation	NOUN
ejpam-5293	41	37	[	[	X
ejpam-5293	41	38	13	13	NUM
ejpam-5293	41	39	,	,	PUNCT
ejpam-5293	41	40	14	14	NUM
ejpam-5293	41	41	]	]	PUNCT
ejpam-5293	41	42	.	.	PUNCT
ejpam-5293	42	1	we	we	PRON
ejpam-5293	42	2	introduce	introduce	VERB
ejpam-5293	42	3	fundamental	fundamental	ADJ
ejpam-5293	42	4	notions	notion	NOUN
ejpam-5293	42	5	for	for	ADP
ejpam-5293	42	6	the	the	DET
ejpam-5293	42	7	cohomology	cohomology	NOUN
ejpam-5293	42	8	study	study	NOUN
ejpam-5293	42	9	in	in	ADP
ejpam-5293	42	10	discrete	discrete	ADJ
ejpam-5293	42	11	dynamical	dynamical	ADJ
ejpam-5293	42	12	systems	system	NOUN
ejpam-5293	42	13	(	(	PUNCT
ejpam-5293	42	14	section	section	NOUN
ejpam-5293	42	15	2	2	NUM
ejpam-5293	42	16	)	)	PUNCT
ejpam-5293	42	17	.	.	PUNCT
ejpam-5293	43	1	in	in	ADP
ejpam-5293	43	2	particular	particular	ADJ
ejpam-5293	43	3	,	,	PUNCT
ejpam-5293	43	4	we	we	PRON
ejpam-5293	43	5	introduce	introduce	VERB
ejpam-5293	43	6	the	the	DET
ejpam-5293	43	7	concepts	concept	NOUN
ejpam-5293	43	8	of	of	ADP
ejpam-5293	43	9	cocycle	cocycle	NOUN
ejpam-5293	43	10	,	,	PUNCT
ejpam-5293	43	11	coboundary	coboundary	NOUN
ejpam-5293	43	12	and	and	CCONJ
ejpam-5293	43	13	cohomology	cohomology	NOUN
ejpam-5293	43	14	between	between	ADP
ejpam-5293	43	15	cocycles	cocycle	NOUN
ejpam-5293	43	16	in	in	ADP
ejpam-5293	43	17	discrete	discrete	ADJ
ejpam-5293	43	18	time	time	NOUN
ejpam-5293	43	19	.	.	PUNCT
ejpam-5293	44	1	we	we	PRON
ejpam-5293	44	2	present	present	VERB
ejpam-5293	44	3	cohomological	cohomological	ADJ
ejpam-5293	44	4	equations	equation	NOUN
ejpam-5293	44	5	and	and	CCONJ
ejpam-5293	44	6	emphasize	emphasize	VERB
ejpam-5293	44	7	the	the	DET
ejpam-5293	44	8	fundamental	fundamental	ADJ
ejpam-5293	44	9	relationship	relationship	NOUN
ejpam-5293	44	10	between	between	ADP
ejpam-5293	44	11	the	the	DET
ejpam-5293	44	12	existence	existence	NOUN
ejpam-5293	44	13	of	of	ADP
ejpam-5293	44	14	solutions	solution	NOUN
ejpam-5293	44	15	of	of	ADP
ejpam-5293	44	16	these	these	DET
ejpam-5293	44	17	equations	equation	NOUN
ejpam-5293	44	18	and	and	CCONJ
ejpam-5293	44	19	the	the	DET
ejpam-5293	44	20	behavior	behavior	NOUN
ejpam-5293	44	21	of	of	ADP
ejpam-5293	44	22	the	the	DET
ejpam-5293	44	23	cocycles	cocycle	NOUN
ejpam-5293	44	24	along	along	ADP
ejpam-5293	44	25	periodic	periodic	ADJ
ejpam-5293	44	26	orbits	orbit	NOUN
ejpam-5293	44	27	.	.	PUNCT
ejpam-5293	45	1	intending	intend	VERB
ejpam-5293	45	2	to	to	PART
ejpam-5293	45	3	present	present	VERB
ejpam-5293	45	4	a	a	DET
ejpam-5293	45	5	detailed	detailed	ADJ
ejpam-5293	45	6	proof	proof	NOUN
ejpam-5293	45	7	of	of	ADP
ejpam-5293	45	8	the	the	DET
ejpam-5293	45	9	livschitz	livschitz	NOUN
ejpam-5293	45	10	theorem	theorem	VERB
ejpam-5293	45	11	in	in	ADP
ejpam-5293	45	12	a	a	DET
ejpam-5293	45	13	version	version	NOUN
ejpam-5293	45	14	for	for	ADP
ejpam-5293	45	15	hyperbolic	hyperbolic	ADJ
ejpam-5293	45	16	diffeomorphisms	diffeomorphism	NOUN
ejpam-5293	45	17	,	,	PUNCT
ejpam-5293	45	18	we	we	PRON
ejpam-5293	45	19	begin	begin	VERB
ejpam-5293	45	20	section	section	NOUN
ejpam-5293	45	21	3	3	NUM
ejpam-5293	45	22	by	by	ADP
ejpam-5293	45	23	outlining	outline	VERB
ejpam-5293	45	24	the	the	DET
ejpam-5293	45	25	proof	proof	NOUN
ejpam-5293	45	26	of	of	ADP
ejpam-5293	45	27	acl	acl	PROPN
ejpam-5293	45	28	for	for	ADP
ejpam-5293	45	29	diffeomorphisms	diffeomorphism	NOUN
ejpam-5293	45	30	(	(	PUNCT
ejpam-5293	45	31	subsection	subsection	NOUN
ejpam-5293	45	32	3.1	3.1	NUM
ejpam-5293	45	33	)	)	PUNCT
ejpam-5293	45	34	,	,	PUNCT
ejpam-5293	45	35	with	with	ADP
ejpam-5293	45	36	emphasis	emphasis	NOUN
ejpam-5293	45	37	on	on	ADP
ejpam-5293	45	38	the	the	DET
ejpam-5293	45	39	statement	statement	NOUN
ejpam-5293	45	40	of	of	ADP
ejpam-5293	45	41	the	the	DET
ejpam-5293	45	42	inequality	inequality	NOUN
ejpam-5293	45	43	that	that	PRON
ejpam-5293	45	44	quantitatively	quantitatively	ADV
ejpam-5293	45	45	estimates	estimate	VERB
ejpam-5293	45	46	distances	distance	NOUN
ejpam-5293	45	47	between	between	ADP
ejpam-5293	45	48	constructed	construct	VERB
ejpam-5293	45	49	periodic	periodic	ADJ
ejpam-5293	45	50	orbit	orbit	NOUN
ejpam-5293	45	51	and	and	CCONJ
ejpam-5293	45	52	the	the	DET
ejpam-5293	45	53	initial	initial	ADJ
ejpam-5293	45	54	orbit	orbit	NOUN
ejpam-5293	45	55	.	.	PUNCT
ejpam-5293	46	1	the	the	DET
ejpam-5293	46	2	statement	statement	NOUN
ejpam-5293	46	3	of	of	ADP
ejpam-5293	46	4	that	that	DET
ejpam-5293	46	5	distance	distance	NOUN
ejpam-5293	46	6	control	control	NOUN
ejpam-5293	46	7	estimate	estimate	NOUN
ejpam-5293	46	8	is	be	AUX
ejpam-5293	46	9	crucial	crucial	ADJ
ejpam-5293	46	10	for	for	SCONJ
ejpam-5293	46	11	the	the	DET
ejpam-5293	46	12	livschitz	livschitz	NOUN
ejpam-5293	46	13	theorem	theorem	VERB
ejpam-5293	46	14	’s	’s	PART
ejpam-5293	46	15	proof	proof	NOUN
ejpam-5293	46	16	(	(	PUNCT
ejpam-5293	46	17	subsection	subsection	NOUN
ejpam-5293	46	18	3.2	3.2	NUM
ejpam-5293	46	19	)	)	PUNCT
ejpam-5293	46	20	.	.	PUNCT
ejpam-5293	47	1	except	except	SCONJ
ejpam-5293	47	2	for	for	ADP
ejpam-5293	47	3	the	the	DET
ejpam-5293	47	4	statement	statement	NOUN
ejpam-5293	47	5	of	of	ADP
ejpam-5293	47	6	that	that	DET
ejpam-5293	47	7	inequality	inequality	NOUN
ejpam-5293	47	8	as	as	ADP
ejpam-5293	47	9	a	a	DET
ejpam-5293	47	10	distance	distance	NOUN
ejpam-5293	47	11	control	control	NOUN
ejpam-5293	47	12	estimate	estimate	NOUN
ejpam-5293	47	13	,	,	PUNCT
ejpam-5293	47	14	the	the	DET
ejpam-5293	47	15	proofs	proof	NOUN
ejpam-5293	47	16	presented	present	VERB
ejpam-5293	47	17	here	here	ADV
ejpam-5293	47	18	closely	closely	ADV
ejpam-5293	47	19	follow	follow	VERB
ejpam-5293	47	20	the	the	DET
ejpam-5293	47	21	suggestions	suggestion	NOUN
ejpam-5293	47	22	of	of	ADP
ejpam-5293	47	23	katok	katok	NOUN
ejpam-5293	47	24	and	and	CCONJ
ejpam-5293	47	25	hasselblatt	hasselblatt	NOUN
ejpam-5293	47	26	in	in	ADP
ejpam-5293	47	27	[	[	X
ejpam-5293	47	28	6	6	NUM
ejpam-5293	47	29	]	]	PUNCT
ejpam-5293	47	30	.	.	PUNCT
ejpam-5293	48	1	all	all	DET
ejpam-5293	48	2	the	the	DET
ejpam-5293	48	3	proofs	proof	NOUN
ejpam-5293	48	4	are	be	AUX
ejpam-5293	48	5	given	give	VERB
ejpam-5293	48	6	in	in	ADP
ejpam-5293	48	7	great	great	ADJ
ejpam-5293	48	8	detail	detail	NOUN
ejpam-5293	48	9	and	and	CCONJ
ejpam-5293	48	10	connected	connect	VERB
ejpam-5293	48	11	to	to	ADP
ejpam-5293	48	12	the	the	DET
ejpam-5293	48	13	cohomology	cohomology	NOUN
ejpam-5293	48	14	theory	theory	NOUN
ejpam-5293	48	15	,	,	PUNCT
ejpam-5293	48	16	with	with	ADP
ejpam-5293	48	17	an	an	DET
ejpam-5293	48	18	additional	additional	ADJ
ejpam-5293	48	19	pedagogical	pedagogical	ADJ
ejpam-5293	48	20	nature	nature	NOUN
ejpam-5293	48	21	.	.	PUNCT
ejpam-5293	49	1	we	we	PRON
ejpam-5293	49	2	finalize	finalize	VERB
ejpam-5293	49	3	presenting	present	VERB
ejpam-5293	49	4	some	some	DET
ejpam-5293	49	5	conclusions	conclusion	NOUN
ejpam-5293	49	6	and	and	CCONJ
ejpam-5293	49	7	comments	comment	NOUN
ejpam-5293	49	8	(	(	PUNCT
ejpam-5293	49	9	section	section	NOUN
ejpam-5293	49	10	4	4	NUM
ejpam-5293	49	11	)	)	PUNCT
ejpam-5293	49	12	.	.	PUNCT
ejpam-5293	50	1	2	2	X
ejpam-5293	50	2	.	.	X
ejpam-5293	50	3	cocycles	cocycle	NOUN
ejpam-5293	50	4	and	and	CCONJ
ejpam-5293	50	5	cohomology	cohomology	NOUN
ejpam-5293	50	6	in	in	ADP
ejpam-5293	50	7	discrete	discrete	ADJ
ejpam-5293	50	8	time	time	NOUN
ejpam-5293	50	9	let	let	VERB
ejpam-5293	50	10	f	f	X
ejpam-5293	50	11	:	:	PUNCT
ejpam-5293	50	12	z×x	z×x	NOUN
ejpam-5293	50	13	→	→	PUNCT
ejpam-5293	50	14	x	x	X
ejpam-5293	50	15	be	be	AUX
ejpam-5293	50	16	a	a	DET
ejpam-5293	50	17	dynamical	dynamical	ADJ
ejpam-5293	50	18	system	system	NOUN
ejpam-5293	50	19	with	with	ADP
ejpam-5293	50	20	phase	phase	NOUN
ejpam-5293	50	21	space	space	NOUN
ejpam-5293	50	22	x	x	PUNCT
ejpam-5293	50	23	and	and	CCONJ
ejpam-5293	50	24	discrete	discrete	ADJ
ejpam-5293	50	25	time	time	NOUN
ejpam-5293	50	26	.	.	PUNCT
ejpam-5293	51	1	so	so	ADV
ejpam-5293	51	2	,	,	PUNCT
ejpam-5293	51	3	they	they	PRON
ejpam-5293	51	4	are	be	AUX
ejpam-5293	51	5	valid	valid	ADJ
ejpam-5293	51	6	the	the	DET
ejpam-5293	51	7	group	group	NOUN
ejpam-5293	51	8	properties	property	NOUN
ejpam-5293	51	9	f(m+	f(m+	DET
ejpam-5293	51	10	n	n	CCONJ
ejpam-5293	51	11	,	,	PUNCT
ejpam-5293	51	12	x	x	X
ejpam-5293	51	13	)	)	PUNCT
ejpam-5293	51	14	=	=	SYM
ejpam-5293	51	15	f(m	f(m	PROPN
ejpam-5293	51	16	,	,	PUNCT
ejpam-5293	51	17	f(n	f(n	PROPN
ejpam-5293	51	18	,	,	PUNCT
ejpam-5293	51	19	x	x	NOUN
ejpam-5293	51	20	)	)	PUNCT
ejpam-5293	51	21	)	)	PUNCT
ejpam-5293	51	22	f(0	f(0	NOUN
ejpam-5293	51	23	,	,	PUNCT
ejpam-5293	51	24	x	x	NOUN
ejpam-5293	51	25	)	)	PUNCT
ejpam-5293	51	26	=	=	SYM
ejpam-5293	52	1	x	x	NOUN
ejpam-5293	52	2	,	,	PUNCT
ejpam-5293	52	3	for	for	ADP
ejpam-5293	52	4	each	each	DET
ejpam-5293	52	5	x	x	SYM
ejpam-5293	52	6	∈	∈	PROPN
ejpam-5293	52	7	x	x	X
ejpam-5293	52	8	and	and	CCONJ
ejpam-5293	52	9	n	n	CCONJ
ejpam-5293	52	10	,	,	PUNCT
ejpam-5293	52	11	m	m	PROPN
ejpam-5293	52	12	∈	∈	PROPN
ejpam-5293	52	13	z.	z.	NOUN
ejpam-5293	52	14	given	give	VERB
ejpam-5293	52	15	n	n	PRON
ejpam-5293	52	16	∈	∈	PROPN
ejpam-5293	52	17	z	z	NOUN
ejpam-5293	52	18	,	,	PUNCT
ejpam-5293	52	19	we	we	PRON
ejpam-5293	52	20	define	define	VERB
ejpam-5293	52	21	the	the	DET
ejpam-5293	52	22	map	map	NOUN
ejpam-5293	52	23	f(n	f(n	PROPN
ejpam-5293	52	24	)	)	PUNCT
ejpam-5293	52	25	:	:	PUNCT
ejpam-5293	53	1	x	x	X
ejpam-5293	53	2	→	→	SYM
ejpam-5293	53	3	x	x	SYM
ejpam-5293	53	4	by	by	ADP
ejpam-5293	53	5	f(n)x	f(n)x	PROPN
ejpam-5293	53	6	=	=	SYM
ejpam-5293	53	7	f(n	f(n	PROPN
ejpam-5293	53	8	,	,	PUNCT
ejpam-5293	53	9	x	x	X
ejpam-5293	53	10	)	)	PUNCT
ejpam-5293	53	11	through	through	ADP
ejpam-5293	53	12	the	the	DET
ejpam-5293	53	13	dynamical	dynamical	ADJ
ejpam-5293	53	14	system	system	NOUN
ejpam-5293	53	15	f	f	PROPN
ejpam-5293	53	16	.	.	PUNCT
ejpam-5293	54	1	we	we	PRON
ejpam-5293	54	2	designate	designate	VERB
ejpam-5293	54	3	by	by	ADP
ejpam-5293	54	4	cocycle	cocycle	PROPN
ejpam-5293	54	5	over	over	ADP
ejpam-5293	54	6	f	f	PROPN
ejpam-5293	54	7	each	each	DET
ejpam-5293	54	8	function	function	VERB
ejpam-5293	54	9	α	α	NOUN
ejpam-5293	54	10	:	:	PUNCT
ejpam-5293	55	1	z	z	NOUN
ejpam-5293	55	2	×	×	NOUN
ejpam-5293	55	3	x	x	INTJ
ejpam-5293	55	4	→	→	SYM
ejpam-5293	55	5	r	r	NOUN
ejpam-5293	55	6	verifying	verify	VERB
ejpam-5293	55	7	the	the	DET
ejpam-5293	55	8	property	property	NOUN
ejpam-5293	55	9	α(m+	α(m+	NOUN
ejpam-5293	55	10	n	n	CCONJ
ejpam-5293	55	11	,	,	PUNCT
ejpam-5293	55	12	x	x	NOUN
ejpam-5293	55	13	)	)	PUNCT
ejpam-5293	55	14	=	=	SYM
ejpam-5293	55	15	α(m	α(m	PROPN
ejpam-5293	55	16	,	,	PUNCT
ejpam-5293	55	17	f(n)x	f(n)x	PROPN
ejpam-5293	55	18	)	)	PUNCT
ejpam-5293	56	1	+	+	NUM
ejpam-5293	56	2	α(n	α(n	NOUN
ejpam-5293	56	3	,	,	PUNCT
ejpam-5293	56	4	x	x	PRON
ejpam-5293	56	5	)	)	PUNCT
ejpam-5293	56	6	(	(	PUNCT
ejpam-5293	56	7	1	1	X
ejpam-5293	56	8	)	)	PUNCT
ejpam-5293	56	9	r.	r.	PROPN
ejpam-5293	56	10	d.	d.	PROPN
ejpam-5293	56	11	laureano	laureano	PROPN
ejpam-5293	56	12	/	/	SYM
ejpam-5293	56	13	eur	eur	PROPN
ejpam-5293	56	14	.	.	PUNCT
ejpam-5293	57	1	j.	j.	PROPN
ejpam-5293	57	2	pure	pure	PROPN
ejpam-5293	57	3	appl	appl	PROPN
ejpam-5293	57	4	.	.	PROPN
ejpam-5293	57	5	math	math	PROPN
ejpam-5293	57	6	,	,	PUNCT
ejpam-5293	57	7	17	17	NUM
ejpam-5293	57	8	(	(	PUNCT
ejpam-5293	57	9	3	3	NUM
ejpam-5293	57	10	)	)	PUNCT
ejpam-5293	57	11	(	(	PUNCT
ejpam-5293	57	12	2024	2024	NUM
ejpam-5293	57	13	)	)	PUNCT
ejpam-5293	57	14	,	,	PUNCT
ejpam-5293	57	15	1403	1403	NUM
ejpam-5293	57	16	-	-	SYM
ejpam-5293	57	17	1416	1416	NUM
ejpam-5293	57	18	1406	1406	NUM
ejpam-5293	57	19	whenever	whenever	SCONJ
ejpam-5293	57	20	x	x	SYM
ejpam-5293	57	21	∈	∈	PROPN
ejpam-5293	57	22	x	x	X
ejpam-5293	57	23	and	and	CCONJ
ejpam-5293	57	24	n	n	CCONJ
ejpam-5293	57	25	,	,	PUNCT
ejpam-5293	57	26	m	m	AUX
ejpam-5293	57	27	∈	∈	PROPN
ejpam-5293	57	28	z.	z.	NOUN
ejpam-5293	58	1	the	the	DET
ejpam-5293	58	2	cocycles	cocycle	NOUN
ejpam-5293	58	3	over	over	ADP
ejpam-5293	58	4	f	f	PROPN
ejpam-5293	58	5	constitute	constitute	VERB
ejpam-5293	58	6	a	a	DET
ejpam-5293	58	7	linear	linear	ADJ
ejpam-5293	58	8	space	space	NOUN
ejpam-5293	58	9	.	.	PUNCT
ejpam-5293	59	1	defining	define	VERB
ejpam-5293	59	2	,	,	PUNCT
ejpam-5293	59	3	for	for	ADP
ejpam-5293	59	4	each	each	DET
ejpam-5293	59	5	n	n	PRON
ejpam-5293	59	6	∈	∈	PROPN
ejpam-5293	59	7	z	z	PROPN
ejpam-5293	59	8	,	,	PUNCT
ejpam-5293	59	9	the	the	DET
ejpam-5293	59	10	map	map	NOUN
ejpam-5293	59	11	f̃(n	f̃(n	NOUN
ejpam-5293	59	12	)	)	PUNCT
ejpam-5293	59	13	:	:	PUNCT
ejpam-5293	60	1	x	x	PUNCT
ejpam-5293	60	2	×	×	NOUN
ejpam-5293	60	3	r	r	NOUN
ejpam-5293	60	4	→	→	SYM
ejpam-5293	60	5	x	x	SYM
ejpam-5293	60	6	×	×	NOUN
ejpam-5293	60	7	r	r	NOUN
ejpam-5293	60	8	by	by	ADP
ejpam-5293	60	9	f̃(n)(x	f̃(n)(x	PROPN
ejpam-5293	60	10	,	,	PUNCT
ejpam-5293	60	11	y	y	NOUN
ejpam-5293	60	12	)	)	PUNCT
ejpam-5293	60	13	=	=	SYM
ejpam-5293	60	14	(	(	PUNCT
ejpam-5293	60	15	f(n)x	f(n)x	PROPN
ejpam-5293	60	16	,	,	PUNCT
ejpam-5293	60	17	y	y	PROPN
ejpam-5293	60	18	+	+	CCONJ
ejpam-5293	60	19	α(n	α(n	NOUN
ejpam-5293	60	20	,	,	PUNCT
ejpam-5293	60	21	x	x	NOUN
ejpam-5293	60	22	)	)	PUNCT
ejpam-5293	60	23	)	)	PUNCT
ejpam-5293	60	24	,	,	PUNCT
ejpam-5293	60	25	the	the	DET
ejpam-5293	60	26	property	property	NOUN
ejpam-5293	60	27	(	(	PUNCT
ejpam-5293	60	28	1	1	X
ejpam-5293	60	29	)	)	PUNCT
ejpam-5293	60	30	is	be	AUX
ejpam-5293	60	31	equivalent	equivalent	ADJ
ejpam-5293	60	32	to	to	ADP
ejpam-5293	60	33	f̃(m+	f̃(m+	NOUN
ejpam-5293	60	34	n	n	CCONJ
ejpam-5293	60	35	)	)	PUNCT
ejpam-5293	60	36	=	=	SYM
ejpam-5293	60	37	f̃(m	f̃(m	PROPN
ejpam-5293	60	38	)	)	PUNCT
ejpam-5293	60	39	◦	◦	NOUN
ejpam-5293	60	40	f̃(n	f̃(n	PROPN
ejpam-5293	60	41	)	)	PUNCT
ejpam-5293	60	42	.	.	PUNCT
ejpam-5293	61	1	each	each	DET
ejpam-5293	61	2	function	function	NOUN
ejpam-5293	61	3	φ	φ	X
ejpam-5293	61	4	:	:	PUNCT
ejpam-5293	61	5	x	x	X
ejpam-5293	61	6	→	→	SYM
ejpam-5293	61	7	r	r	NOUN
ejpam-5293	61	8	induces	induce	VERB
ejpam-5293	61	9	a	a	DET
ejpam-5293	61	10	cocycle	cocycle	NOUN
ejpam-5293	61	11	by	by	ADP
ejpam-5293	61	12	defining	define	VERB
ejpam-5293	61	13	α(n	α(n	NOUN
ejpam-5293	61	14	,	,	PUNCT
ejpam-5293	61	15	x	x	PRON
ejpam-5293	61	16	)	)	PUNCT
ejpam-5293	61	17	=	=	SYM
ejpam-5293	61	18	φ(f(n)x)−	φ(f(n)x)−	PROPN
ejpam-5293	61	19	φ(x	φ(x	PROPN
ejpam-5293	61	20	)	)	PUNCT
ejpam-5293	61	21	.	.	PUNCT
ejpam-5293	62	1	(	(	PUNCT
ejpam-5293	62	2	2	2	X
ejpam-5293	62	3	)	)	PUNCT
ejpam-5293	62	4	in	in	ADP
ejpam-5293	62	5	fact	fact	NOUN
ejpam-5293	62	6	,	,	PUNCT
ejpam-5293	62	7	the	the	DET
ejpam-5293	62	8	function	function	NOUN
ejpam-5293	62	9	α	α	PROPN
ejpam-5293	62	10	defined	define	VERB
ejpam-5293	62	11	this	this	DET
ejpam-5293	62	12	way	way	NOUN
ejpam-5293	62	13	satisfies	satisfy	VERB
ejpam-5293	62	14	property	property	NOUN
ejpam-5293	62	15	(	(	PUNCT
ejpam-5293	62	16	1	1	NUM
ejpam-5293	62	17	)	)	PUNCT
ejpam-5293	62	18	since	since	SCONJ
ejpam-5293	62	19	φ(f(m+	φ(f(m+	NOUN
ejpam-5293	62	20	n)x)−	n)x)−	PRON
ejpam-5293	62	21	φ(x	φ(x	NOUN
ejpam-5293	62	22	)	)	PUNCT
ejpam-5293	62	23	=	=	PRON
ejpam-5293	62	24	φ(f(m)(f(n)x))−	φ(f(m)(f(n)x))−	VERB
ejpam-5293	62	25	φ(x	φ(x	NOUN
ejpam-5293	62	26	)	)	PUNCT
ejpam-5293	63	1	=	=	SYM
ejpam-5293	63	2	φ(f(m)f(n)x)−	φ(f(m)f(n)x)−	NOUN
ejpam-5293	63	3	φ(f(n)x	φ(f(n)x	ADV
ejpam-5293	63	4	)	)	PUNCT
ejpam-5293	64	1	+	+	CCONJ
ejpam-5293	64	2	φ(f(n)x)−	φ(f(n)x)−	PROPN
ejpam-5293	64	3	φ(x	φ(x	NOUN
ejpam-5293	64	4	)	)	PUNCT
ejpam-5293	64	5	=	=	SYM
ejpam-5293	65	1	α(m	α(m	PROPN
ejpam-5293	65	2	,	,	PUNCT
ejpam-5293	65	3	f(n)x	f(n)x	PROPN
ejpam-5293	65	4	)	)	PUNCT
ejpam-5293	66	1	+	+	NUM
ejpam-5293	66	2	α(n	α(n	NOUN
ejpam-5293	66	3	,	,	PUNCT
ejpam-5293	66	4	x	x	NOUN
ejpam-5293	66	5	)	)	PUNCT
ejpam-5293	66	6	.	.	PUNCT
ejpam-5293	67	1	the	the	DET
ejpam-5293	67	2	cocycles	cocycle	NOUN
ejpam-5293	67	3	defined	define	VERB
ejpam-5293	67	4	by	by	ADP
ejpam-5293	67	5	(	(	PUNCT
ejpam-5293	67	6	2	2	X
ejpam-5293	67	7	)	)	PUNCT
ejpam-5293	67	8	are	be	AUX
ejpam-5293	67	9	designated	designate	VERB
ejpam-5293	67	10	by	by	ADP
ejpam-5293	67	11	coboundaries	coboundarie	NOUN
ejpam-5293	67	12	.	.	PUNCT
ejpam-5293	68	1	a	a	DET
ejpam-5293	68	2	natural	natural	ADJ
ejpam-5293	68	3	equivalence	equivalence	NOUN
ejpam-5293	68	4	relationship	relationship	NOUN
ejpam-5293	68	5	between	between	ADP
ejpam-5293	68	6	cocycles	cocycle	NOUN
ejpam-5293	68	7	is	be	AUX
ejpam-5293	68	8	the	the	DET
ejpam-5293	68	9	cohomology	cohomology	NOUN
ejpam-5293	68	10	.	.	PUNCT
ejpam-5293	69	1	two	two	NUM
ejpam-5293	69	2	cocycles	cocycle	NOUN
ejpam-5293	69	3	α	α	NOUN
ejpam-5293	69	4	and	and	CCONJ
ejpam-5293	69	5	β	β	X
ejpam-5293	69	6	over	over	ADP
ejpam-5293	69	7	a	a	DET
ejpam-5293	69	8	dynamical	dynamical	ADJ
ejpam-5293	69	9	system	system	NOUN
ejpam-5293	69	10	f	f	X
ejpam-5293	69	11	are	be	AUX
ejpam-5293	69	12	cohomologous	cohomologous	ADJ
ejpam-5293	69	13	if	if	SCONJ
ejpam-5293	69	14	they	they	PRON
ejpam-5293	69	15	differ	differ	VERB
ejpam-5293	69	16	by	by	ADP
ejpam-5293	69	17	a	a	DET
ejpam-5293	69	18	coboundary	coboundary	NOUN
ejpam-5293	69	19	,	,	PUNCT
ejpam-5293	69	20	that	that	ADV
ejpam-5293	69	21	is	is	ADV
ejpam-5293	69	22	,	,	PUNCT
ejpam-5293	69	23	if	if	SCONJ
ejpam-5293	69	24	there	there	PRON
ejpam-5293	69	25	is	be	VERB
ejpam-5293	69	26	a	a	DET
ejpam-5293	69	27	function	function	NOUN
ejpam-5293	69	28	φ	φ	NOUN
ejpam-5293	69	29	:	:	PUNCT
ejpam-5293	69	30	x	x	X
ejpam-5293	69	31	→	→	PUNCT
ejpam-5293	69	32	r	r	NOUN
ejpam-5293	69	33	such	such	ADJ
ejpam-5293	69	34	that	that	SCONJ
ejpam-5293	69	35	α(n	α(n	NOUN
ejpam-5293	69	36	,	,	PUNCT
ejpam-5293	69	37	x)−	x)−	PROPN
ejpam-5293	69	38	β(n	β(n	PROPN
ejpam-5293	69	39	,	,	PUNCT
ejpam-5293	69	40	x	x	X
ejpam-5293	69	41	)	)	PUNCT
ejpam-5293	69	42	=	=	SYM
ejpam-5293	69	43	φ(f(n)x)−	φ(f(n)x)−	PROPN
ejpam-5293	69	44	φ(x	φ(x	PROPN
ejpam-5293	69	45	)	)	PUNCT
ejpam-5293	69	46	.	.	PUNCT
ejpam-5293	70	1	we	we	PRON
ejpam-5293	70	2	note	note	VERB
ejpam-5293	70	3	that	that	SCONJ
ejpam-5293	70	4	a	a	DET
ejpam-5293	70	5	cocycle	cocycle	NOUN
ejpam-5293	70	6	α	α	PROPN
ejpam-5293	70	7	is	be	AUX
ejpam-5293	70	8	a	a	DET
ejpam-5293	70	9	coboundary	coboundary	ADJ
ejpam-5293	70	10	if	if	SCONJ
ejpam-5293	71	1	and	and	CCONJ
ejpam-5293	71	2	only	only	ADV
ejpam-5293	71	3	if	if	SCONJ
ejpam-5293	71	4	α	α	PRON
ejpam-5293	71	5	is	be	AUX
ejpam-5293	71	6	cohomologous	cohomologous	ADJ
ejpam-5293	71	7	to	to	ADP
ejpam-5293	71	8	the	the	DET
ejpam-5293	71	9	trivial	trivial	ADJ
ejpam-5293	71	10	cocycle	cocycle	NOUN
ejpam-5293	71	11	β(n	β(n	PROPN
ejpam-5293	71	12	,	,	PUNCT
ejpam-5293	71	13	x	x	X
ejpam-5293	71	14	)	)	PUNCT
ejpam-5293	71	15	=	=	SYM
ejpam-5293	72	1	0	0	X
ejpam-5293	72	2	.	.	PUNCT
ejpam-5293	73	1	in	in	ADP
ejpam-5293	73	2	this	this	DET
ejpam-5293	73	3	case	case	NOUN
ejpam-5293	73	4	it	it	PRON
ejpam-5293	73	5	is	be	AUX
ejpam-5293	73	6	said	say	VERB
ejpam-5293	73	7	that	that	SCONJ
ejpam-5293	73	8	α	α	PRON
ejpam-5293	73	9	is	be	AUX
ejpam-5293	73	10	cohomologically	cohomologically	ADV
ejpam-5293	73	11	trivial	trivial	ADJ
ejpam-5293	73	12	and	and	CCONJ
ejpam-5293	73	13	a	a	DET
ejpam-5293	73	14	function	function	NOUN
ejpam-5293	73	15	φ	φ	NOUN
ejpam-5293	73	16	satisfying	satisfy	VERB
ejpam-5293	73	17	(	(	PUNCT
ejpam-5293	73	18	2	2	NUM
ejpam-5293	73	19	)	)	PUNCT
ejpam-5293	73	20	is	be	AUX
ejpam-5293	73	21	a	a	DET
ejpam-5293	73	22	trivialization	trivialization	NOUN
ejpam-5293	73	23	of	of	ADP
ejpam-5293	73	24	α	α	NOUN
ejpam-5293	73	25	.	.	PUNCT
ejpam-5293	74	1	also	also	ADV
ejpam-5293	74	2	,	,	PUNCT
ejpam-5293	74	3	for	for	SCONJ
ejpam-5293	74	4	a	a	DET
ejpam-5293	74	5	cocycle	cocycle	NOUN
ejpam-5293	74	6	α	α	NOUN
ejpam-5293	74	7	to	to	PART
ejpam-5293	74	8	be	be	AUX
ejpam-5293	74	9	a	a	DET
ejpam-5293	74	10	coboundary	coboundary	NOUN
ejpam-5293	74	11	it	it	PRON
ejpam-5293	74	12	is	be	AUX
ejpam-5293	74	13	necessary	necessary	ADJ
ejpam-5293	74	14	that	that	SCONJ
ejpam-5293	74	15	α(n	α(n	NOUN
ejpam-5293	74	16	,	,	PUNCT
ejpam-5293	74	17	x	x	X
ejpam-5293	74	18	)	)	PUNCT
ejpam-5293	74	19	=	=	SYM
ejpam-5293	74	20	0	0	NUM
ejpam-5293	74	21	for	for	ADP
ejpam-5293	74	22	all	all	DET
ejpam-5293	74	23	n	n	PRON
ejpam-5293	74	24	∈	∈	PROPN
ejpam-5293	74	25	z	z	NOUN
ejpam-5293	74	26	and	and	CCONJ
ejpam-5293	74	27	x	x	SYM
ejpam-5293	74	28	∈	∈	PROPN
ejpam-5293	74	29	x	x	PUNCT
ejpam-5293	74	30	such	such	ADJ
ejpam-5293	74	31	that	that	PRON
ejpam-5293	74	32	f(n)x	f(n)x	PROPN
ejpam-5293	74	33	=	=	PUNCT
ejpam-5293	74	34	x.	x.	NOUN
ejpam-5293	74	35	equation	equation	NOUN
ejpam-5293	74	36	(	(	PUNCT
ejpam-5293	74	37	2	2	X
ejpam-5293	74	38	)	)	PUNCT
ejpam-5293	74	39	is	be	AUX
ejpam-5293	74	40	said	say	VERB
ejpam-5293	74	41	to	to	PART
ejpam-5293	74	42	be	be	AUX
ejpam-5293	74	43	a	a	DET
ejpam-5293	74	44	cohomological	cohomological	ADJ
ejpam-5293	74	45	equation	equation	NOUN
ejpam-5293	74	46	.	.	PUNCT
ejpam-5293	75	1	each	each	DET
ejpam-5293	75	2	cocycle	cocycle	NOUN
ejpam-5293	75	3	α	α	PROPN
ejpam-5293	75	4	over	over	ADP
ejpam-5293	75	5	a	a	DET
ejpam-5293	75	6	dynamical	dynamical	ADJ
ejpam-5293	75	7	system	system	NOUN
ejpam-5293	75	8	f	f	NOUN
ejpam-5293	75	9	:	:	PUNCT
ejpam-5293	75	10	z	z	NOUN
ejpam-5293	75	11	×	×	NOUN
ejpam-5293	75	12	x	x	INTJ
ejpam-5293	75	13	→	→	PUNCT
ejpam-5293	75	14	x	x	X
ejpam-5293	75	15	is	be	AUX
ejpam-5293	75	16	uniquely	uniquely	ADV
ejpam-5293	75	17	determined	determine	VERB
ejpam-5293	75	18	by	by	ADP
ejpam-5293	75	19	the	the	DET
ejpam-5293	75	20	function	function	NOUN
ejpam-5293	75	21	φ	φ	NOUN
ejpam-5293	75	22	:	:	PUNCT
ejpam-5293	75	23	x	x	X
ejpam-5293	75	24	→	→	SYM
ejpam-5293	75	25	r	r	NOUN
ejpam-5293	75	26	defined	define	VERB
ejpam-5293	75	27	by	by	ADP
ejpam-5293	75	28	φ(x	φ(x	NOUN
ejpam-5293	75	29	)	)	PUNCT
ejpam-5293	75	30	=	=	SYM
ejpam-5293	76	1	α(1	α(1	PROPN
ejpam-5293	76	2	,	,	PUNCT
ejpam-5293	76	3	x	x	NOUN
ejpam-5293	76	4	)	)	PUNCT
ejpam-5293	76	5	.	.	PUNCT
ejpam-5293	77	1	in	in	ADP
ejpam-5293	77	2	fact	fact	NOUN
ejpam-5293	77	3	,	,	PUNCT
ejpam-5293	77	4	it	it	PRON
ejpam-5293	77	5	is	be	AUX
ejpam-5293	77	6	immediate	immediate	ADJ
ejpam-5293	77	7	to	to	PART
ejpam-5293	77	8	verify	verify	VERB
ejpam-5293	77	9	that	that	SCONJ
ejpam-5293	77	10	α(n	α(n	NOUN
ejpam-5293	77	11	,	,	PUNCT
ejpam-5293	77	12	x	x	PRON
ejpam-5293	77	13	)	)	PUNCT
ejpam-5293	77	14	=	=	SYM
ejpam-5293	77	15	{	{	PUNCT
ejpam-5293	77	16	∑n−1	∑n−1	ADP
ejpam-5293	77	17	i=0	i=0	PROPN
ejpam-5293	77	18	φ(f	φ(f	PROPN
ejpam-5293	77	19	ix	ix	PROPN
ejpam-5293	77	20	)	)	PUNCT
ejpam-5293	77	21	if	if	SCONJ
ejpam-5293	77	22	n	n	PROPN
ejpam-5293	77	23	>	>	X
ejpam-5293	77	24	0	0	PUNCT
ejpam-5293	78	1	−	−	NOUN
ejpam-5293	78	2	∑−1	∑−1	NOUN
ejpam-5293	78	3	i	i	PRON
ejpam-5293	78	4	=	=	PROPN
ejpam-5293	78	5	n	n	PROPN
ejpam-5293	78	6	φ(f	φ(f	PROPN
ejpam-5293	78	7	ix	ix	PROPN
ejpam-5293	78	8	)	)	PUNCT
ejpam-5293	78	9	if	if	SCONJ
ejpam-5293	78	10	n	n	PRON
ejpam-5293	78	11	≤	≤	X
ejpam-5293	78	12	0	0	NUM
ejpam-5293	78	13	,	,	PUNCT
ejpam-5293	78	14	(	(	PUNCT
ejpam-5293	78	15	3	3	X
ejpam-5293	78	16	)	)	PUNCT
ejpam-5293	78	17	where	where	SCONJ
ejpam-5293	78	18	f0x	f0x	ADV
ejpam-5293	78	19	=	=	PUNCT
ejpam-5293	78	20	x	x	PROPN
ejpam-5293	78	21	and	and	CCONJ
ejpam-5293	78	22	fx	fx	PROPN
ejpam-5293	78	23	=	=	SYM
ejpam-5293	78	24	f(1	f(1	PROPN
ejpam-5293	78	25	,	,	PUNCT
ejpam-5293	78	26	x	x	NOUN
ejpam-5293	78	27	)	)	PUNCT
ejpam-5293	78	28	.	.	PUNCT
ejpam-5293	79	1	so	so	ADV
ejpam-5293	79	2	,	,	PUNCT
ejpam-5293	79	3	we	we	PRON
ejpam-5293	79	4	can	can	AUX
ejpam-5293	79	5	identify	identify	VERB
ejpam-5293	79	6	the	the	DET
ejpam-5293	79	7	dynamical	dynamical	ADJ
ejpam-5293	79	8	system	system	NOUN
ejpam-5293	79	9	with	with	ADP
ejpam-5293	79	10	the	the	DET
ejpam-5293	79	11	invertible	invertible	ADJ
ejpam-5293	79	12	map	map	NOUN
ejpam-5293	79	13	f	f	X
ejpam-5293	79	14	:	:	PUNCT
ejpam-5293	79	15	x	x	X
ejpam-5293	79	16	→	→	SYM
ejpam-5293	79	17	x	x	SYM
ejpam-5293	79	18	(	(	PUNCT
ejpam-5293	79	19	without	without	ADP
ejpam-5293	79	20	danger	danger	NOUN
ejpam-5293	79	21	of	of	ADP
ejpam-5293	79	22	notation	notation	NOUN
ejpam-5293	79	23	confusion	confusion	NOUN
ejpam-5293	79	24	)	)	PUNCT
ejpam-5293	79	25	being	be	AUX
ejpam-5293	79	26	the	the	DET
ejpam-5293	79	27	inverse	inverse	NOUN
ejpam-5293	79	28	given	give	VERB
ejpam-5293	79	29	by	by	ADP
ejpam-5293	79	30	f−1x	f−1x	ADP
ejpam-5293	79	31	=	=	SYM
ejpam-5293	79	32	f(−1	f(−1	PROPN
ejpam-5293	79	33	,	,	PUNCT
ejpam-5293	79	34	fx	fx	PROPN
ejpam-5293	79	35	)	)	PUNCT
ejpam-5293	79	36	.	.	PUNCT
ejpam-5293	80	1	there	there	PRON
ejpam-5293	80	2	is	be	VERB
ejpam-5293	80	3	then	then	ADV
ejpam-5293	80	4	a	a	DET
ejpam-5293	80	5	one	one	NUM
ejpam-5293	80	6	-	-	PUNCT
ejpam-5293	80	7	to	to	ADP
ejpam-5293	80	8	-	-	PUNCT
ejpam-5293	80	9	one	one	NUM
ejpam-5293	80	10	correspondence	correspondence	NOUN
ejpam-5293	80	11	between	between	ADP
ejpam-5293	80	12	cocycles	cocycle	NOUN
ejpam-5293	80	13	and	and	CCONJ
ejpam-5293	80	14	real	real	ADJ
ejpam-5293	80	15	functions	function	NOUN
ejpam-5293	80	16	defined	define	VERB
ejpam-5293	80	17	on	on	ADP
ejpam-5293	80	18	x.	x.	PROPN
ejpam-5293	80	19	two	two	NUM
ejpam-5293	80	20	function	function	NOUN
ejpam-5293	80	21	φ	φ	PROPN
ejpam-5293	80	22	,	,	PUNCT
ejpam-5293	80	23	ψ	ψ	X
ejpam-5293	80	24	:	:	PUNCT
ejpam-5293	80	25	x	x	X
ejpam-5293	80	26	→	→	SYM
ejpam-5293	80	27	r	r	NOUN
ejpam-5293	80	28	are	be	AUX
ejpam-5293	80	29	called	call	VERB
ejpam-5293	80	30	cohomologous	cohomologous	ADJ
ejpam-5293	80	31	respecting	respect	VERB
ejpam-5293	80	32	to	to	ADP
ejpam-5293	80	33	f	f	PROPN
ejpam-5293	80	34	if	if	SCONJ
ejpam-5293	80	35	φ−ψ	φ−ψ	VERB
ejpam-5293	80	36	=	=	SYM
ejpam-5293	80	37	φ	φ	NUM
ejpam-5293	80	38	◦	◦	NOUN
ejpam-5293	80	39	f−φ	f−φ	NOUN
ejpam-5293	80	40	for	for	ADP
ejpam-5293	80	41	some	some	DET
ejpam-5293	80	42	function	function	NOUN
ejpam-5293	80	43	φ	φ	NOUN
ejpam-5293	80	44	:	:	PUNCT
ejpam-5293	80	45	x	x	X
ejpam-5293	80	46	→	→	SYM
ejpam-5293	80	47	r.	r.	PROPN
ejpam-5293	80	48	we	we	PRON
ejpam-5293	80	49	can	can	AUX
ejpam-5293	80	50	easily	easily	ADV
ejpam-5293	80	51	verify	verify	VERB
ejpam-5293	80	52	that	that	SCONJ
ejpam-5293	80	53	two	two	NUM
ejpam-5293	80	54	functions	function	NOUN
ejpam-5293	80	55	are	be	AUX
ejpam-5293	80	56	cohomologous	cohomologous	ADJ
ejpam-5293	80	57	if	if	SCONJ
ejpam-5293	80	58	and	and	CCONJ
ejpam-5293	80	59	only	only	ADV
ejpam-5293	80	60	if	if	SCONJ
ejpam-5293	80	61	the	the	DET
ejpam-5293	80	62	respective	respective	ADJ
ejpam-5293	80	63	cocycles	cocycle	NOUN
ejpam-5293	80	64	are	be	AUX
ejpam-5293	80	65	cohomologous	cohomologous	ADJ
ejpam-5293	80	66	.	.	PUNCT
ejpam-5293	81	1	furthermore	furthermore	ADV
ejpam-5293	81	2	,	,	PUNCT
ejpam-5293	81	3	a	a	DET
ejpam-5293	81	4	function	function	NOUN
ejpam-5293	81	5	is	be	AUX
ejpam-5293	81	6	called	call	VERB
ejpam-5293	81	7	a	a	DET
ejpam-5293	81	8	coboundary	coboundary	NOUN
ejpam-5293	81	9	if	if	SCONJ
ejpam-5293	81	10	it	it	PRON
ejpam-5293	81	11	is	be	AUX
ejpam-5293	81	12	cohomologous	cohomologous	ADJ
ejpam-5293	81	13	to	to	ADP
ejpam-5293	81	14	the	the	DET
ejpam-5293	81	15	zero	zero	NUM
ejpam-5293	81	16	function	function	NOUN
ejpam-5293	81	17	.	.	PUNCT
ejpam-5293	82	1	given	give	VERB
ejpam-5293	82	2	a	a	DET
ejpam-5293	82	3	function	function	NOUN
ejpam-5293	82	4	φ	φ	NOUN
ejpam-5293	82	5	:	:	PUNCT
ejpam-5293	82	6	x	x	X
ejpam-5293	82	7	→	→	SYM
ejpam-5293	82	8	r	r	NOUN
ejpam-5293	82	9	,	,	PUNCT
ejpam-5293	82	10	let	let	VERB
ejpam-5293	82	11	α	α	PRON
ejpam-5293	82	12	be	be	AUX
ejpam-5293	82	13	the	the	DET
ejpam-5293	82	14	cocycle	cocycle	NOUN
ejpam-5293	82	15	over	over	ADP
ejpam-5293	82	16	f	f	PROPN
ejpam-5293	82	17	defined	define	VERB
ejpam-5293	82	18	by	by	ADP
ejpam-5293	82	19	(	(	PUNCT
ejpam-5293	82	20	3	3	NUM
ejpam-5293	82	21	)	)	PUNCT
ejpam-5293	82	22	.	.	PUNCT
ejpam-5293	83	1	to	to	PART
ejpam-5293	83	2	show	show	VERB
ejpam-5293	83	3	that	that	SCONJ
ejpam-5293	83	4	the	the	DET
ejpam-5293	83	5	equation	equation	NOUN
ejpam-5293	83	6	φ	φ	NOUN
ejpam-5293	83	7	=	=	SYM
ejpam-5293	83	8	φ	φ	PROPN
ejpam-5293	83	9	◦	◦	NOUN
ejpam-5293	83	10	f	f	PROPN
ejpam-5293	83	11	−	−	PROPN
ejpam-5293	83	12	φ	φ	PROPN
ejpam-5293	83	13	,	,	PUNCT
ejpam-5293	83	14	(	(	PUNCT
ejpam-5293	83	15	4	4	X
ejpam-5293	83	16	)	)	PUNCT
ejpam-5293	83	17	also	also	ADV
ejpam-5293	83	18	called	call	VERB
ejpam-5293	83	19	cohomological	cohomological	ADJ
ejpam-5293	83	20	equation	equation	NOUN
ejpam-5293	83	21	,	,	PUNCT
ejpam-5293	83	22	has	have	VERB
ejpam-5293	83	23	a	a	DET
ejpam-5293	83	24	solution	solution	NOUN
ejpam-5293	83	25	is	be	AUX
ejpam-5293	83	26	equivalent	equivalent	ADJ
ejpam-5293	83	27	to	to	PART
ejpam-5293	83	28	show	show	VERB
ejpam-5293	83	29	that	that	SCONJ
ejpam-5293	83	30	the	the	DET
ejpam-5293	83	31	cocycle	cocycle	NOUN
ejpam-5293	83	32	α	α	PROPN
ejpam-5293	83	33	is	be	AUX
ejpam-5293	83	34	a	a	DET
ejpam-5293	83	35	coboundary	coboundary	NOUN
ejpam-5293	83	36	.	.	PUNCT
ejpam-5293	84	1	in	in	ADP
ejpam-5293	84	2	fact	fact	NOUN
ejpam-5293	84	3	,	,	PUNCT
ejpam-5293	84	4	if	if	SCONJ
ejpam-5293	84	5	the	the	DET
ejpam-5293	84	6	cohomological	cohomological	ADJ
ejpam-5293	84	7	equation	equation	NOUN
ejpam-5293	84	8	(	(	PUNCT
ejpam-5293	84	9	4	4	X
ejpam-5293	84	10	)	)	PUNCT
ejpam-5293	84	11	is	be	AUX
ejpam-5293	84	12	satisfied	satisfied	ADJ
ejpam-5293	84	13	then	then	ADV
ejpam-5293	84	14	,	,	PUNCT
ejpam-5293	84	15	for	for	ADP
ejpam-5293	84	16	each	each	DET
ejpam-5293	84	17	n	n	NOUN
ejpam-5293	84	18	>	>	X
ejpam-5293	84	19	0	0	NUM
ejpam-5293	84	20	,	,	PUNCT
ejpam-5293	84	21	we	we	PRON
ejpam-5293	84	22	have	have	VERB
ejpam-5293	84	23	α(n	α(n	NOUN
ejpam-5293	84	24	,	,	PUNCT
ejpam-5293	84	25	x	x	PRON
ejpam-5293	84	26	)	)	PUNCT
ejpam-5293	84	27	=	=	SYM
ejpam-5293	84	28	n−1∑	n−1∑	PROPN
ejpam-5293	84	29	i=0	i=0	PROPN
ejpam-5293	84	30	φ(f	φ(f	PROPN
ejpam-5293	84	31	ix	ix	PROPN
ejpam-5293	84	32	)	)	PUNCT
ejpam-5293	85	1	=	=	SYM
ejpam-5293	85	2	n−1∑	n−1∑	PROPN
ejpam-5293	85	3	i=0	i=0	PROPN
ejpam-5293	86	1	[	[	X
ejpam-5293	86	2	φ(f	φ(f	PROPN
ejpam-5293	86	3	i+1x)−	i+1x)−	PROPN
ejpam-5293	86	4	φ(f	φ(f	PROPN
ejpam-5293	86	5	ix	ix	PROPN
ejpam-5293	86	6	)	)	PUNCT
ejpam-5293	86	7	]	]	PUNCT
ejpam-5293	87	1	=	=	PUNCT
ejpam-5293	87	2	φ(fnx)−	φ(fnx)−	PROPN
ejpam-5293	87	3	φ(x	φ(x	PROPN
ejpam-5293	87	4	)	)	PUNCT
ejpam-5293	87	5	r.	r.	PROPN
ejpam-5293	87	6	d.	d.	PROPN
ejpam-5293	87	7	laureano	laureano	PROPN
ejpam-5293	87	8	/	/	SYM
ejpam-5293	87	9	eur	eur	PROPN
ejpam-5293	87	10	.	.	PUNCT
ejpam-5293	88	1	j.	j.	PROPN
ejpam-5293	88	2	pure	pure	PROPN
ejpam-5293	88	3	appl	appl	PROPN
ejpam-5293	88	4	.	.	PROPN
ejpam-5293	88	5	math	math	PROPN
ejpam-5293	88	6	,	,	PUNCT
ejpam-5293	88	7	17	17	NUM
ejpam-5293	88	8	(	(	PUNCT
ejpam-5293	88	9	3	3	NUM
ejpam-5293	88	10	)	)	PUNCT
ejpam-5293	88	11	(	(	PUNCT
ejpam-5293	88	12	2024	2024	NUM
ejpam-5293	88	13	)	)	PUNCT
ejpam-5293	88	14	,	,	PUNCT
ejpam-5293	88	15	1403	1403	NUM
ejpam-5293	88	16	-	-	SYM
ejpam-5293	88	17	1416	1416	NUM
ejpam-5293	88	18	1407	1407	NUM
ejpam-5293	88	19	(	(	PUNCT
ejpam-5293	88	20	with	with	ADP
ejpam-5293	88	21	similar	similar	ADJ
ejpam-5293	88	22	identities	identity	NOUN
ejpam-5293	88	23	for	for	ADP
ejpam-5293	88	24	n	n	DET
ejpam-5293	88	25	≤	≤	NOUN
ejpam-5293	88	26	0	0	NUM
ejpam-5293	88	27	)	)	PUNCT
ejpam-5293	88	28	and	and	CCONJ
ejpam-5293	88	29	α	α	PRON
ejpam-5293	88	30	is	be	AUX
ejpam-5293	88	31	a	a	DET
ejpam-5293	88	32	coboundary	coboundary	NOUN
ejpam-5293	88	33	.	.	PUNCT
ejpam-5293	89	1	on	on	ADP
ejpam-5293	89	2	the	the	DET
ejpam-5293	89	3	other	other	ADJ
ejpam-5293	89	4	hand	hand	NOUN
ejpam-5293	89	5	,	,	PUNCT
ejpam-5293	89	6	if	if	SCONJ
ejpam-5293	89	7	α	α	PRON
ejpam-5293	89	8	is	be	AUX
ejpam-5293	89	9	a	a	DET
ejpam-5293	89	10	coboundary	coboundary	NOUN
ejpam-5293	89	11	then	then	ADV
ejpam-5293	89	12	there	there	PRON
ejpam-5293	89	13	is	be	VERB
ejpam-5293	89	14	a	a	DET
ejpam-5293	89	15	function	function	NOUN
ejpam-5293	89	16	φ	φ	NOUN
ejpam-5293	89	17	:	:	PUNCT
ejpam-5293	89	18	x	x	X
ejpam-5293	89	19	→	→	PUNCT
ejpam-5293	89	20	r	r	NOUN
ejpam-5293	89	21	such	such	ADJ
ejpam-5293	89	22	that	that	SCONJ
ejpam-5293	89	23	α(n	α(n	NOUN
ejpam-5293	89	24	,	,	PUNCT
ejpam-5293	89	25	x	x	X
ejpam-5293	89	26	)	)	PUNCT
ejpam-5293	89	27	=	=	SYM
ejpam-5293	89	28	φ(fnx	φ(fnx	PROPN
ejpam-5293	89	29	)	)	PUNCT
ejpam-5293	89	30	−	−	ADP
ejpam-5293	89	31	φ(x	φ(x	NOUN
ejpam-5293	89	32	)	)	PUNCT
ejpam-5293	89	33	.	.	PUNCT
ejpam-5293	90	1	making	make	VERB
ejpam-5293	90	2	n	n	NOUN
ejpam-5293	90	3	=	=	SYM
ejpam-5293	90	4	1	1	NUM
ejpam-5293	90	5	we	we	PRON
ejpam-5293	90	6	conclude	conclude	VERB
ejpam-5293	90	7	that	that	SCONJ
ejpam-5293	90	8	the	the	DET
ejpam-5293	90	9	cohomological	cohomological	ADJ
ejpam-5293	90	10	equation	equation	NOUN
ejpam-5293	90	11	(	(	PUNCT
ejpam-5293	90	12	4	4	X
ejpam-5293	90	13	)	)	PUNCT
ejpam-5293	90	14	is	be	AUX
ejpam-5293	90	15	satisfied	satisfy	VERB
ejpam-5293	90	16	by	by	ADP
ejpam-5293	90	17	φ	φ	PROPN
ejpam-5293	90	18	.	.	PUNCT
ejpam-5293	91	1	suppose	suppose	VERB
ejpam-5293	91	2	now	now	ADV
ejpam-5293	91	3	that	that	SCONJ
ejpam-5293	91	4	the	the	DET
ejpam-5293	91	5	cohomological	cohomological	ADJ
ejpam-5293	91	6	equation	equation	NOUN
ejpam-5293	91	7	(	(	PUNCT
ejpam-5293	91	8	4	4	X
ejpam-5293	91	9	)	)	PUNCT
ejpam-5293	91	10	has	have	VERB
ejpam-5293	91	11	a	a	DET
ejpam-5293	91	12	solution	solution	NOUN
ejpam-5293	91	13	.	.	PUNCT
ejpam-5293	92	1	if	if	SCONJ
ejpam-5293	92	2	x	x	PRON
ejpam-5293	92	3	is	be	AUX
ejpam-5293	92	4	a	a	DET
ejpam-5293	92	5	m	m	ADJ
ejpam-5293	92	6	-	-	ADJ
ejpam-5293	92	7	periodic	periodic	ADJ
ejpam-5293	92	8	point	point	NOUN
ejpam-5293	92	9	of	of	ADP
ejpam-5293	92	10	the	the	DET
ejpam-5293	92	11	dynamical	dynamical	ADJ
ejpam-5293	92	12	system	system	NOUN
ejpam-5293	92	13	f	f	PROPN
ejpam-5293	92	14	,	,	PUNCT
ejpam-5293	92	15	fmx	fmx	PROPN
ejpam-5293	92	16	=	=	SYM
ejpam-5293	92	17	x	x	NOUN
ejpam-5293	92	18	,	,	PUNCT
ejpam-5293	92	19	then	then	ADV
ejpam-5293	92	20	m−1∑	m−1∑	PROPN
ejpam-5293	92	21	i=0	i=0	PROPN
ejpam-5293	92	22	φ(f	φ(f	PROPN
ejpam-5293	92	23	ix	ix	PROPN
ejpam-5293	92	24	)	)	PUNCT
ejpam-5293	92	25	=	=	SYM
ejpam-5293	92	26	α	α	PROPN
ejpam-5293	92	27	(	(	PUNCT
ejpam-5293	92	28	m	m	PROPN
ejpam-5293	92	29	,	,	PUNCT
ejpam-5293	92	30	x	x	NOUN
ejpam-5293	92	31	)	)	PUNCT
ejpam-5293	92	32	=	=	SYM
ejpam-5293	92	33	φ	φ	PROPN
ejpam-5293	92	34	(	(	PUNCT
ejpam-5293	92	35	fmx)−	fmx)−	PROPN
ejpam-5293	92	36	φ	φ	PROPN
ejpam-5293	92	37	(	(	PUNCT
ejpam-5293	92	38	x	x	NOUN
ejpam-5293	92	39	)	)	PUNCT
ejpam-5293	92	40	=	=	SYM
ejpam-5293	92	41	0	0	X
ejpam-5293	92	42	.	.	PUNCT
ejpam-5293	93	1	therefore	therefore	ADV
ejpam-5293	93	2	,	,	PUNCT
ejpam-5293	93	3	it	it	PRON
ejpam-5293	93	4	is	be	AUX
ejpam-5293	93	5	necessary	necessary	ADJ
ejpam-5293	93	6	that	that	SCONJ
ejpam-5293	93	7	∑m−1	∑m−1	ADJ
ejpam-5293	93	8	i=0	i=0	PROPN
ejpam-5293	93	9	φ(f	φ(f	PROPN
ejpam-5293	93	10	ix	ix	PROPN
ejpam-5293	93	11	)	)	PUNCT
ejpam-5293	93	12	=	=	SYM
ejpam-5293	93	13	0	0	NUM
ejpam-5293	93	14	for	for	ADP
ejpam-5293	93	15	all	all	DET
ejpam-5293	93	16	m	m	ADJ
ejpam-5293	93	17	-	-	ADJ
ejpam-5293	93	18	periodic	periodic	ADJ
ejpam-5293	93	19	point	point	NOUN
ejpam-5293	93	20	x	x	PUNCT
ejpam-5293	93	21	so	so	SCONJ
ejpam-5293	93	22	that	that	SCONJ
ejpam-5293	93	23	there	there	PRON
ejpam-5293	93	24	is	be	VERB
ejpam-5293	93	25	a	a	DET
ejpam-5293	93	26	solution	solution	NOUN
ejpam-5293	93	27	φ	φ	NOUN
ejpam-5293	93	28	to	to	ADP
ejpam-5293	93	29	the	the	DET
ejpam-5293	93	30	cohomological	cohomological	ADJ
ejpam-5293	93	31	equation	equation	NOUN
ejpam-5293	93	32	(	(	PUNCT
ejpam-5293	93	33	4	4	NUM
ejpam-5293	93	34	)	)	PUNCT
ejpam-5293	93	35	.	.	PUNCT
ejpam-5293	94	1	if	if	SCONJ
ejpam-5293	94	2	it	it	PRON
ejpam-5293	94	3	is	be	AUX
ejpam-5293	94	4	not	not	PART
ejpam-5293	94	5	required	require	VERB
ejpam-5293	94	6	any	any	DET
ejpam-5293	94	7	additional	additional	ADJ
ejpam-5293	94	8	property	property	NOUN
ejpam-5293	94	9	to	to	ADP
ejpam-5293	94	10	a	a	DET
ejpam-5293	94	11	solution	solution	NOUN
ejpam-5293	94	12	of	of	ADP
ejpam-5293	94	13	the	the	DET
ejpam-5293	94	14	cohomological	cohomological	ADJ
ejpam-5293	94	15	equation	equation	NOUN
ejpam-5293	94	16	then	then	ADV
ejpam-5293	94	17	there	there	PRON
ejpam-5293	94	18	is	be	VERB
ejpam-5293	94	19	no	no	DET
ejpam-5293	94	20	difficulty	difficulty	NOUN
ejpam-5293	94	21	in	in	ADP
ejpam-5293	94	22	showing	show	VERB
ejpam-5293	94	23	their	their	PRON
ejpam-5293	94	24	existence	existence	NOUN
ejpam-5293	94	25	,	,	PUNCT
ejpam-5293	94	26	provided	provide	VERB
ejpam-5293	94	27	that	that	SCONJ
ejpam-5293	94	28	∑m−1	∑m−1	NOUN
ejpam-5293	94	29	i=0	i=0	PROPN
ejpam-5293	94	30	φ(f	φ(f	PROPN
ejpam-5293	94	31	ix	ix	PROPN
ejpam-5293	94	32	)	)	PUNCT
ejpam-5293	95	1	=	=	SYM
ejpam-5293	95	2	0	0	NUM
ejpam-5293	95	3	for	for	ADP
ejpam-5293	95	4	each	each	DET
ejpam-5293	95	5	m	m	ADJ
ejpam-5293	95	6	-	-	ADJ
ejpam-5293	95	7	periodic	periodic	ADJ
ejpam-5293	95	8	point	point	NOUN
ejpam-5293	95	9	x.	x.	NOUN
ejpam-5293	95	10	indeed	indeed	ADV
ejpam-5293	95	11	,	,	PUNCT
ejpam-5293	95	12	we	we	PRON
ejpam-5293	95	13	can	can	AUX
ejpam-5293	95	14	pick	pick	VERB
ejpam-5293	95	15	up	up	ADP
ejpam-5293	95	16	one	one	NUM
ejpam-5293	95	17	point	point	NOUN
ejpam-5293	95	18	x	x	X
ejpam-5293	95	19	from	from	ADP
ejpam-5293	95	20	each	each	DET
ejpam-5293	95	21	orbit	orbit	NOUN
ejpam-5293	95	22	of	of	ADP
ejpam-5293	95	23	f	f	PROPN
ejpam-5293	95	24	,	,	PUNCT
ejpam-5293	95	25	arbitrarily	arbitrarily	ADV
ejpam-5293	95	26	choose	choose	VERB
ejpam-5293	95	27	φ	φ	PROPN
ejpam-5293	95	28	(	(	PUNCT
ejpam-5293	95	29	x	x	X
ejpam-5293	95	30	)	)	PUNCT
ejpam-5293	95	31	∈	∈	PROPN
ejpam-5293	95	32	r	r	NOUN
ejpam-5293	95	33	and	and	CCONJ
ejpam-5293	95	34	then	then	ADV
ejpam-5293	95	35	define	define	VERB
ejpam-5293	95	36	φ	φ	PROPN
ejpam-5293	95	37	over	over	ADP
ejpam-5293	95	38	the	the	DET
ejpam-5293	95	39	points	point	NOUN
ejpam-5293	95	40	of	of	ADP
ejpam-5293	95	41	each	each	DET
ejpam-5293	95	42	orbit	orbit	NOUN
ejpam-5293	95	43	by	by	ADP
ejpam-5293	95	44	φ	φ	PROPN
ejpam-5293	95	45	(	(	PUNCT
ejpam-5293	95	46	fnx	fnx	PROPN
ejpam-5293	95	47	)	)	PUNCT
ejpam-5293	96	1	=	=	SYM
ejpam-5293	96	2	φ	φ	X
ejpam-5293	96	3	(	(	PUNCT
ejpam-5293	96	4	x	x	NOUN
ejpam-5293	96	5	)	)	PUNCT
ejpam-5293	96	6	+	+	CCONJ
ejpam-5293	96	7	n−1∑	n−1∑	PROPN
ejpam-5293	96	8	i=0	i=0	PROPN
ejpam-5293	96	9	φ(f	φ(f	PROPN
ejpam-5293	96	10	ix	ix	PROPN
ejpam-5293	96	11	)	)	PUNCT
ejpam-5293	96	12	.	.	PUNCT
ejpam-5293	97	1	however	however	ADV
ejpam-5293	97	2	,	,	PUNCT
ejpam-5293	97	3	if	if	SCONJ
ejpam-5293	97	4	there	there	PRON
ejpam-5293	97	5	is	be	VERB
ejpam-5293	97	6	some	some	DET
ejpam-5293	97	7	additional	additional	ADJ
ejpam-5293	97	8	structure	structure	NOUN
ejpam-5293	97	9	in	in	ADP
ejpam-5293	97	10	the	the	DET
ejpam-5293	97	11	phase	phase	NOUN
ejpam-5293	97	12	space	space	NOUN
ejpam-5293	97	13	x	x	PUNCT
ejpam-5293	97	14	which	which	PRON
ejpam-5293	97	15	we	we	PRON
ejpam-5293	97	16	intend	intend	VERB
ejpam-5293	97	17	to	to	PART
ejpam-5293	97	18	maintain	maintain	VERB
ejpam-5293	97	19	,	,	PUNCT
ejpam-5293	97	20	this	this	DET
ejpam-5293	97	21	procedure	procedure	NOUN
ejpam-5293	97	22	may	may	AUX
ejpam-5293	97	23	be	be	AUX
ejpam-5293	97	24	unsatisfactory	unsatisfactory	ADJ
ejpam-5293	97	25	.	.	PUNCT
ejpam-5293	98	1	for	for	ADP
ejpam-5293	98	2	example	example	NOUN
ejpam-5293	98	3	,	,	PUNCT
ejpam-5293	98	4	in	in	ADP
ejpam-5293	98	5	the	the	DET
ejpam-5293	98	6	case	case	NOUN
ejpam-5293	98	7	of	of	ADP
ejpam-5293	98	8	irrational	irrational	ADJ
ejpam-5293	98	9	rotation	rotation	NOUN
ejpam-5293	98	10	of	of	ADP
ejpam-5293	98	11	the	the	DET
ejpam-5293	98	12	circle	circle	NOUN
ejpam-5293	98	13	,	,	PUNCT
ejpam-5293	98	14	this	this	DET
ejpam-5293	98	15	construction	construction	NOUN
ejpam-5293	98	16	necessarily	necessarily	ADV
ejpam-5293	98	17	start	start	VERB
ejpam-5293	98	18	from	from	ADP
ejpam-5293	98	19	a	a	DET
ejpam-5293	98	20	collection	collection	NOUN
ejpam-5293	98	21	of	of	ADP
ejpam-5293	98	22	non	non	ADJ
ejpam-5293	98	23	-	-	ADJ
ejpam-5293	98	24	measurable	measurable	ADJ
ejpam-5293	98	25	points	point	NOUN
ejpam-5293	98	26	and	and	CCONJ
ejpam-5293	98	27	so	so	ADV
ejpam-5293	98	28	,	,	PUNCT
ejpam-5293	98	29	in	in	ADP
ejpam-5293	98	30	general	general	ADJ
ejpam-5293	98	31	,	,	PUNCT
ejpam-5293	98	32	we	we	PRON
ejpam-5293	98	33	obtain	obtain	VERB
ejpam-5293	98	34	a	a	DET
ejpam-5293	98	35	non	non	ADJ
ejpam-5293	98	36	-	-	ADJ
ejpam-5293	98	37	measurable	measurable	ADJ
ejpam-5293	98	38	solution	solution	NOUN
ejpam-5293	98	39	of	of	ADP
ejpam-5293	98	40	the	the	DET
ejpam-5293	98	41	cohomological	cohomological	ADJ
ejpam-5293	98	42	equation	equation	NOUN
ejpam-5293	98	43	.	.	PUNCT
ejpam-5293	99	1	3	3	X
ejpam-5293	99	2	.	.	X
ejpam-5293	99	3	livschitz	livschitz	PROPN
ejpam-5293	99	4	theorem	theorem	NOUN
ejpam-5293	99	5	for	for	ADP
ejpam-5293	99	6	hyperbolic	hyperbolic	ADJ
ejpam-5293	99	7	diffeomorphisms	diffeomorphism	NOUN
ejpam-5293	99	8	let	let	VERB
ejpam-5293	99	9	m	m	PRON
ejpam-5293	99	10	be	be	AUX
ejpam-5293	99	11	a	a	DET
ejpam-5293	99	12	riemannian	riemannian	ADJ
ejpam-5293	99	13	manifold	manifold	NOUN
ejpam-5293	99	14	,	,	PUNCT
ejpam-5293	99	15	with	with	ADP
ejpam-5293	99	16	norm	norm	NOUN
ejpam-5293	99	17	∥·∥x	∥·∥x	NOUN
ejpam-5293	99	18	and	and	CCONJ
ejpam-5293	99	19	inner	inner	ADJ
ejpam-5293	99	20	product	product	NOUN
ejpam-5293	99	21	⟨	⟨	VERB
ejpam-5293	99	22	·	·	PUNCT
ejpam-5293	99	23	,	,	PUNCT
ejpam-5293	99	24	·	·	PUNCT
ejpam-5293	99	25	⟩x	⟩x	PROPN
ejpam-5293	99	26	in	in	ADP
ejpam-5293	99	27	the	the	DET
ejpam-5293	99	28	tangent	tangent	NOUN
ejpam-5293	99	29	space	space	NOUN
ejpam-5293	99	30	txm	txm	PROPN
ejpam-5293	99	31	of	of	ADP
ejpam-5293	99	32	each	each	DET
ejpam-5293	99	33	point	point	NOUN
ejpam-5293	99	34	x	x	PUNCT
ejpam-5293	99	35	∈m	∈m	NOUN
ejpam-5293	99	36	.	.	PUNCT
ejpam-5293	100	1	in	in	ADP
ejpam-5293	100	2	what	what	PRON
ejpam-5293	100	3	follows	follow	VERB
ejpam-5293	100	4	we	we	PRON
ejpam-5293	100	5	will	will	AUX
ejpam-5293	100	6	write	write	VERB
ejpam-5293	100	7	only	only	ADV
ejpam-5293	100	8	∥·∥	∥·∥	PROPN
ejpam-5293	100	9	and	and	CCONJ
ejpam-5293	100	10	⟨	⟨	NOUN
ejpam-5293	100	11	·	·	NUM
ejpam-5293	100	12	,	,	PUNCT
ejpam-5293	100	13	·	·	PUNCT
ejpam-5293	100	14	⟩	⟩	NOUN
ejpam-5293	100	15	without	without	ADP
ejpam-5293	100	16	reference	reference	NOUN
ejpam-5293	100	17	to	to	ADP
ejpam-5293	100	18	the	the	DET
ejpam-5293	100	19	point	point	NOUN
ejpam-5293	100	20	x.	x.	NOUN
ejpam-5293	100	21	a	a	DET
ejpam-5293	100	22	distance	distance	NOUN
ejpam-5293	100	23	d	d	NOUN
ejpam-5293	100	24	is	be	AUX
ejpam-5293	100	25	defined	define	VERB
ejpam-5293	100	26	in	in	ADP
ejpam-5293	100	27	m	m	PROPN
ejpam-5293	100	28	by	by	ADP
ejpam-5293	100	29	d(x	d(x	PROPN
ejpam-5293	100	30	,	,	PUNCT
ejpam-5293	100	31	y	y	NOUN
ejpam-5293	101	1	)	)	PUNCT
ejpam-5293	101	2	=	=	SYM
ejpam-5293	101	3	inf	inf	PROPN
ejpam-5293	101	4	γ	γ	X
ejpam-5293	101	5	∫	∫	PROPN
ejpam-5293	101	6	1	1	NUM
ejpam-5293	101	7	0	0	NUM
ejpam-5293	101	8	∥γ′(t)∥	∥γ′(t)∥	PRON
ejpam-5293	102	1	dt	dt	X
ejpam-5293	102	2	,	,	PUNCT
ejpam-5293	102	3	where	where	SCONJ
ejpam-5293	102	4	the	the	DET
ejpam-5293	102	5	infimum	infimum	NOUN
ejpam-5293	102	6	is	be	AUX
ejpam-5293	102	7	taken	take	VERB
ejpam-5293	102	8	over	over	ADP
ejpam-5293	102	9	all	all	DET
ejpam-5293	102	10	differentiable	differentiable	ADJ
ejpam-5293	102	11	curves	curve	NOUN
ejpam-5293	102	12	γ	γ	NOUN
ejpam-5293	102	13	:	:	PUNCT
ejpam-5293	103	1	[	[	X
ejpam-5293	103	2	0	0	NUM
ejpam-5293	103	3	,	,	PUNCT
ejpam-5293	103	4	1	1	NUM
ejpam-5293	103	5	]	]	PUNCT
ejpam-5293	103	6	→m	→m	PUNCT
ejpam-5293	103	7	such	such	ADJ
ejpam-5293	103	8	that	that	DET
ejpam-5293	103	9	γ(0	γ(0	NOUN
ejpam-5293	103	10	)	)	PUNCT
ejpam-5293	103	11	=	=	SYM
ejpam-5293	103	12	x	x	PROPN
ejpam-5293	103	13	and	and	CCONJ
ejpam-5293	103	14	γ(1	γ(1	PROPN
ejpam-5293	103	15	)	)	PUNCT
ejpam-5293	103	16	=	=	VERB
ejpam-5293	104	1	y.	y.	NOUN
ejpam-5293	104	2	let	let	VERB
ejpam-5293	104	3	f	f	NOUN
ejpam-5293	104	4	:	:	PUNCT
ejpam-5293	104	5	m	m	VERB
ejpam-5293	104	6	→	→	NOUN
ejpam-5293	104	7	m	m	AUX
ejpam-5293	104	8	be	be	AUX
ejpam-5293	104	9	a	a	DET
ejpam-5293	104	10	diffeomorphism	diffeomorphism	NOUN
ejpam-5293	104	11	and	and	CCONJ
ejpam-5293	104	12	λ	λ	X
ejpam-5293	104	13	⊂	⊂	PROPN
ejpam-5293	104	14	m	m	VERB
ejpam-5293	104	15	an	an	DET
ejpam-5293	104	16	f	f	PROPN
ejpam-5293	104	17	-invariant	-invariant	PROPN
ejpam-5293	104	18	set	set	NOUN
ejpam-5293	104	19	,	,	PUNCT
ejpam-5293	104	20	fλ	fλ	NOUN
ejpam-5293	104	21	=	=	SYM
ejpam-5293	104	22	λ	λ	PROPN
ejpam-5293	104	23	.	.	PUNCT
ejpam-5293	105	1	the	the	DET
ejpam-5293	105	2	map	map	NOUN
ejpam-5293	105	3	f	f	PROPN
ejpam-5293	105	4	|λ	|λ	ADV
ejpam-5293	105	5	is	be	AUX
ejpam-5293	105	6	topologically	topologically	ADV
ejpam-5293	105	7	transitive	transitive	ADJ
ejpam-5293	105	8	if	if	SCONJ
ejpam-5293	105	9	there	there	PRON
ejpam-5293	105	10	is	be	VERB
ejpam-5293	105	11	x0	x0	PROPN
ejpam-5293	105	12	∈m	∈m	NOUN
ejpam-5293	105	13	whose	whose	DET
ejpam-5293	105	14	orbit	orbit	NOUN
ejpam-5293	105	15	{	{	PUNCT
ejpam-5293	105	16	fnx0	fnx0	NOUN
ejpam-5293	105	17	:	:	PUNCT
ejpam-5293	105	18	n	n	X
ejpam-5293	105	19	∈	∈	PROPN
ejpam-5293	105	20	z	z	X
ejpam-5293	105	21	}	}	PUNCT
ejpam-5293	105	22	is	be	AUX
ejpam-5293	105	23	dense	dense	ADJ
ejpam-5293	105	24	in	in	ADP
ejpam-5293	105	25	λ	λ	X
ejpam-5293	105	26	.	.	PUNCT
ejpam-5293	106	1	if	if	SCONJ
ejpam-5293	106	2	there	there	PRON
ejpam-5293	106	3	is	be	VERB
ejpam-5293	106	4	an	an	DET
ejpam-5293	106	5	open	open	ADJ
ejpam-5293	106	6	neighborhood	neighborhood	NOUN
ejpam-5293	106	7	v	v	NOUN
ejpam-5293	106	8	of	of	ADP
ejpam-5293	106	9	λ	λ	NOUN
ejpam-5293	106	10	such	such	ADJ
ejpam-5293	106	11	that	that	SCONJ
ejpam-5293	106	12	λ	λ	NOUN
ejpam-5293	106	13	=	=	SYM
ejpam-5293	106	14	⋂	⋂	PROPN
ejpam-5293	106	15	n∈z	n∈z	PRON
ejpam-5293	106	16	f	f	PROPN
ejpam-5293	106	17	nv	nv	PROPN
ejpam-5293	106	18	,	,	PUNCT
ejpam-5293	106	19	then	then	ADV
ejpam-5293	106	20	λ	λ	PROPN
ejpam-5293	106	21	is	be	AUX
ejpam-5293	106	22	locally	locally	ADV
ejpam-5293	106	23	maximal	maximal	ADJ
ejpam-5293	106	24	for	for	ADP
ejpam-5293	106	25	f	f	PROPN
ejpam-5293	106	26	.	.	PUNCT
ejpam-5293	107	1	an	an	DET
ejpam-5293	107	2	f	f	PROPN
ejpam-5293	107	3	-invariant	-invariant	PROPN
ejpam-5293	107	4	set	set	VERB
ejpam-5293	107	5	λ	λ	X
ejpam-5293	107	6	⊂m	⊂m	PROPN
ejpam-5293	107	7	is	be	AUX
ejpam-5293	107	8	hyperbolic	hyperbolic	ADJ
ejpam-5293	107	9	for	for	ADP
ejpam-5293	107	10	f	f	PROPN
ejpam-5293	107	11	if	if	SCONJ
ejpam-5293	107	12	:	:	PUNCT
ejpam-5293	107	13	•	•	ADP
ejpam-5293	107	14	the	the	DET
ejpam-5293	107	15	tangent	tangent	NOUN
ejpam-5293	107	16	space	space	NOUN
ejpam-5293	107	17	restricted	restrict	VERB
ejpam-5293	107	18	to	to	ADP
ejpam-5293	107	19	λ	λ	PROPN
ejpam-5293	107	20	can	can	AUX
ejpam-5293	107	21	be	be	AUX
ejpam-5293	107	22	written	write	VERB
ejpam-5293	107	23	as	as	ADP
ejpam-5293	107	24	a	a	DET
ejpam-5293	107	25	continuous	continuous	ADJ
ejpam-5293	107	26	direct	direct	ADJ
ejpam-5293	107	27	sum	sum	NOUN
ejpam-5293	107	28	of	of	ADP
ejpam-5293	107	29	df	df	NOUN
ejpam-5293	107	30	invariant	invariant	ADJ
ejpam-5293	107	31	bundles	bundle	NOUN
ejpam-5293	107	32	,	,	PUNCT
ejpam-5293	107	33	that	that	ADV
ejpam-5293	107	34	is	is	ADV
ejpam-5293	107	35	,	,	PUNCT
ejpam-5293	107	36	for	for	ADP
ejpam-5293	107	37	each	each	DET
ejpam-5293	107	38	x	x	SYM
ejpam-5293	107	39	∈	∈	PROPN
ejpam-5293	107	40	λ	λ	NOUN
ejpam-5293	107	41	there	there	PRON
ejpam-5293	107	42	is	be	VERB
ejpam-5293	107	43	a	a	DET
ejpam-5293	107	44	decomposition	decomposition	NOUN
ejpam-5293	107	45	of	of	ADP
ejpam-5293	107	46	the	the	DET
ejpam-5293	107	47	tangent	tangent	ADJ
ejpam-5293	107	48	space	space	NOUN
ejpam-5293	107	49	in	in	ADP
ejpam-5293	107	50	the	the	DET
ejpam-5293	107	51	stable	stable	ADJ
ejpam-5293	107	52	and	and	CCONJ
ejpam-5293	107	53	unstable	unstable	ADJ
ejpam-5293	107	54	subspaces	subspace	NOUN
ejpam-5293	107	55	,	,	PUNCT
ejpam-5293	107	56	txm	txm	PROPN
ejpam-5293	107	57	=	=	PROPN
ejpam-5293	107	58	es(x)⊕	es(x)⊕	PROPN
ejpam-5293	107	59	eu(x	eu(x	ADV
ejpam-5293	107	60	)	)	PUNCT
ejpam-5293	107	61	,	,	PUNCT
ejpam-5293	107	62	r.	r.	PROPN
ejpam-5293	107	63	d.	d.	PROPN
ejpam-5293	107	64	laureano	laureano	PROPN
ejpam-5293	107	65	/	/	SYM
ejpam-5293	107	66	eur	eur	PROPN
ejpam-5293	107	67	.	.	PUNCT
ejpam-5293	108	1	j.	j.	PROPN
ejpam-5293	108	2	pure	pure	PROPN
ejpam-5293	108	3	appl	appl	PROPN
ejpam-5293	108	4	.	.	PROPN
ejpam-5293	108	5	math	math	PROPN
ejpam-5293	108	6	,	,	PUNCT
ejpam-5293	108	7	17	17	NUM
ejpam-5293	108	8	(	(	PUNCT
ejpam-5293	108	9	3	3	NUM
ejpam-5293	108	10	)	)	PUNCT
ejpam-5293	108	11	(	(	PUNCT
ejpam-5293	108	12	2024	2024	NUM
ejpam-5293	108	13	)	)	PUNCT
ejpam-5293	108	14	,	,	PUNCT
ejpam-5293	108	15	1403	1403	NUM
ejpam-5293	108	16	-	-	SYM
ejpam-5293	108	17	1416	1416	NUM
ejpam-5293	108	18	1408	1408	NUM
ejpam-5293	108	19	that	that	PRON
ejpam-5293	108	20	varies	vary	VERB
ejpam-5293	108	21	continuously	continuously	ADV
ejpam-5293	108	22	with	with	ADP
ejpam-5293	108	23	x	x	PUNCT
ejpam-5293	108	24	and	and	CCONJ
ejpam-5293	108	25	verifies	verifie	NOUN
ejpam-5293	108	26	the	the	DET
ejpam-5293	108	27	equalities	equality	NOUN
ejpam-5293	108	28	dxfe	dxfe	PROPN
ejpam-5293	108	29	s(x	s(x	PROPN
ejpam-5293	108	30	)	)	PUNCT
ejpam-5293	108	31	=	=	SYM
ejpam-5293	108	32	es(fx	es(fx	PROPN
ejpam-5293	108	33	)	)	PUNCT
ejpam-5293	108	34	and	and	CCONJ
ejpam-5293	108	35	dxfe	dxfe	VERB
ejpam-5293	108	36	u(x	u(x	NOUN
ejpam-5293	108	37	)	)	PUNCT
ejpam-5293	108	38	=	=	SYM
ejpam-5293	108	39	eu(fx	eu(fx	NOUN
ejpam-5293	108	40	)	)	PUNCT
ejpam-5293	108	41	;	;	PUNCT
ejpam-5293	108	42	•	•	X
ejpam-5293	108	43	there	there	PRON
ejpam-5293	108	44	are	be	VERB
ejpam-5293	108	45	constants	constant	NOUN
ejpam-5293	108	46	c	c	NOUN
ejpam-5293	108	47	>	>	X
ejpam-5293	108	48	0	0	PUNCT
ejpam-5293	109	1	and	and	CCONJ
ejpam-5293	109	2	τ	τ	PROPN
ejpam-5293	109	3	∈	∈	PROPN
ejpam-5293	109	4	(	(	PUNCT
ejpam-5293	109	5	0	0	NUM
ejpam-5293	109	6	,	,	PUNCT
ejpam-5293	109	7	1	1	NUM
ejpam-5293	109	8	)	)	PUNCT
ejpam-5293	109	9	such	such	ADJ
ejpam-5293	109	10	that	that	SCONJ
ejpam-5293	109	11	,	,	PUNCT
ejpam-5293	109	12	for	for	ADP
ejpam-5293	109	13	all	all	DET
ejpam-5293	109	14	x	x	SYM
ejpam-5293	109	15	∈	∈	PROPN
ejpam-5293	109	16	λ	λ	NOUN
ejpam-5293	109	17	and	and	CCONJ
ejpam-5293	109	18	n	n	CCONJ
ejpam-5293	109	19	∈	∈	PROPN
ejpam-5293	109	20	n	n	CCONJ
ejpam-5293	109	21	,	,	PUNCT
ejpam-5293	109	22	we	we	PRON
ejpam-5293	109	23	have	have	VERB
ejpam-5293	109	24	∥dxfnv∥	∥dxfnv∥	NUM
ejpam-5293	109	25	≤	≤	NUM
ejpam-5293	109	26	cτn	cτn	NOUN
ejpam-5293	109	27	∥v∥	∥v∥	VERB
ejpam-5293	109	28	for	for	ADP
ejpam-5293	109	29	v	v	PROPN
ejpam-5293	109	30	∈	∈	PROPN
ejpam-5293	109	31	es(x	es(x	NOUN
ejpam-5293	109	32	)	)	PUNCT
ejpam-5293	109	33	,	,	PUNCT
ejpam-5293	109	34	and	and	CCONJ
ejpam-5293	109	35	∥dxf−nv∥	∥dxf−nv∥	PROPN
ejpam-5293	109	36	≤	≤	NUM
ejpam-5293	109	37	cτn	cτn	NOUN
ejpam-5293	109	38	∥v∥	∥v∥	VERB
ejpam-5293	109	39	for	for	ADP
ejpam-5293	109	40	v	v	NOUN
ejpam-5293	109	41	∈	∈	NOUN
ejpam-5293	109	42	eu(x	eu(x	ADV
ejpam-5293	109	43	)	)	PUNCT
ejpam-5293	109	44	.	.	PUNCT
ejpam-5293	110	1	given	give	VERB
ejpam-5293	110	2	f	f	PROPN
ejpam-5293	110	3	:	:	PUNCT
ejpam-5293	110	4	m	m	VERB
ejpam-5293	110	5	→	→	SYM
ejpam-5293	110	6	m	m	X
ejpam-5293	110	7	,	,	PUNCT
ejpam-5293	110	8	consider	consider	VERB
ejpam-5293	110	9	the	the	DET
ejpam-5293	110	10	function	function	NOUN
ejpam-5293	110	11	φ	φ	NOUN
ejpam-5293	110	12	:	:	PUNCT
ejpam-5293	110	13	m	m	AUX
ejpam-5293	110	14	→	→	SYM
ejpam-5293	110	15	r	r	NOUN
ejpam-5293	110	16	and	and	CCONJ
ejpam-5293	110	17	the	the	DET
ejpam-5293	110	18	cohomological	cohomological	ADJ
ejpam-5293	110	19	equation	equation	NOUN
ejpam-5293	110	20	(	(	PUNCT
ejpam-5293	110	21	4	4	NUM
ejpam-5293	110	22	)	)	PUNCT
ejpam-5293	110	23	.	.	PUNCT
ejpam-5293	111	1	as	as	SCONJ
ejpam-5293	111	2	presented	present	VERB
ejpam-5293	111	3	in	in	ADP
ejpam-5293	111	4	section	section	NOUN
ejpam-5293	111	5	2	2	NUM
ejpam-5293	111	6	,	,	PUNCT
ejpam-5293	111	7	if	if	SCONJ
ejpam-5293	111	8	equation	equation	NOUN
ejpam-5293	111	9	(	(	PUNCT
ejpam-5293	111	10	4	4	X
ejpam-5293	111	11	)	)	PUNCT
ejpam-5293	111	12	has	have	VERB
ejpam-5293	111	13	a	a	DET
ejpam-5293	111	14	solution	solution	NOUN
ejpam-5293	111	15	then	then	ADV
ejpam-5293	111	16	∑m−1	∑m−1	NOUN
ejpam-5293	111	17	i=0	i=0	PROPN
ejpam-5293	111	18	φ(f	φ(f	PROPN
ejpam-5293	111	19	ix	ix	PROPN
ejpam-5293	111	20	)	)	PUNCT
ejpam-5293	112	1	=	=	SYM
ejpam-5293	112	2	0	0	PUNCT
ejpam-5293	113	1	whenever	whenever	SCONJ
ejpam-5293	113	2	x	x	PRON
ejpam-5293	113	3	is	be	AUX
ejpam-5293	113	4	a	a	DET
ejpam-5293	113	5	m	m	ADJ
ejpam-5293	113	6	-	-	ADJ
ejpam-5293	113	7	periodic	periodic	ADJ
ejpam-5293	113	8	point	point	NOUN
ejpam-5293	113	9	of	of	ADP
ejpam-5293	113	10	f	f	PROPN
ejpam-5293	113	11	,	,	PUNCT
ejpam-5293	113	12	fmx	fmx	PROPN
ejpam-5293	113	13	=	=	PUNCT
ejpam-5293	113	14	x.	x.	NOUN
ejpam-5293	113	15	in	in	ADP
ejpam-5293	113	16	addition	addition	NOUN
ejpam-5293	113	17	,	,	PUNCT
ejpam-5293	113	18	we	we	PRON
ejpam-5293	113	19	have	have	AUX
ejpam-5293	113	20	shown	show	VERB
ejpam-5293	113	21	that	that	SCONJ
ejpam-5293	113	22	this	this	PRON
ejpam-5293	113	23	is	be	AUX
ejpam-5293	113	24	a	a	DET
ejpam-5293	113	25	necessary	necessary	ADJ
ejpam-5293	113	26	and	and	CCONJ
ejpam-5293	113	27	sufficient	sufficient	ADJ
ejpam-5293	113	28	for	for	ADP
ejpam-5293	113	29	the	the	DET
ejpam-5293	113	30	existence	existence	NOUN
ejpam-5293	113	31	of	of	ADP
ejpam-5293	113	32	solutions	solution	NOUN
ejpam-5293	113	33	of	of	ADP
ejpam-5293	113	34	the	the	DET
ejpam-5293	113	35	cohomological	cohomological	ADJ
ejpam-5293	113	36	equation	equation	NOUN
ejpam-5293	113	37	(	(	PUNCT
ejpam-5293	113	38	4	4	NUM
ejpam-5293	113	39	)	)	PUNCT
ejpam-5293	113	40	.	.	PUNCT
ejpam-5293	114	1	however	however	ADV
ejpam-5293	114	2	,	,	PUNCT
ejpam-5293	114	3	the	the	DET
ejpam-5293	114	4	solutions	solution	NOUN
ejpam-5293	114	5	can	can	AUX
ejpam-5293	114	6	be	be	AUX
ejpam-5293	114	7	discontinuous	discontinuous	ADJ
ejpam-5293	114	8	or	or	CCONJ
ejpam-5293	114	9	even	even	ADV
ejpam-5293	114	10	not	not	PART
ejpam-5293	114	11	measurable	measurable	ADJ
ejpam-5293	114	12	.	.	PUNCT
ejpam-5293	115	1	naturally	naturally	ADV
ejpam-5293	115	2	arises	arise	VERB
ejpam-5293	115	3	the	the	DET
ejpam-5293	115	4	question	question	NOUN
ejpam-5293	115	5	of	of	ADP
ejpam-5293	115	6	how	how	SCONJ
ejpam-5293	115	7	to	to	PART
ejpam-5293	115	8	ensure	ensure	VERB
ejpam-5293	115	9	the	the	DET
ejpam-5293	115	10	existence	existence	NOUN
ejpam-5293	115	11	of	of	ADP
ejpam-5293	115	12	continuous	continuous	ADJ
ejpam-5293	115	13	solutions	solution	NOUN
ejpam-5293	115	14	or	or	CCONJ
ejpam-5293	115	15	even	even	ADV
ejpam-5293	115	16	with	with	ADP
ejpam-5293	115	17	some	some	DET
ejpam-5293	115	18	additional	additional	ADJ
ejpam-5293	115	19	regularity	regularity	NOUN
ejpam-5293	115	20	.	.	PUNCT
ejpam-5293	116	1	the	the	DET
ejpam-5293	116	2	livschitz	livschitz	PROPN
ejpam-5293	116	3	theorem	theorem	VERB
ejpam-5293	116	4	formulated	formulate	VERB
ejpam-5293	116	5	below	below	ADP
ejpam-5293	116	6	answers	answer	NOUN
ejpam-5293	116	7	this	this	DET
ejpam-5293	116	8	question	question	NOUN
ejpam-5293	116	9	in	in	ADP
ejpam-5293	116	10	the	the	DET
ejpam-5293	116	11	context	context	NOUN
ejpam-5293	116	12	of	of	ADP
ejpam-5293	116	13	hyperbolic	hyperbolic	ADJ
ejpam-5293	116	14	dynamics	dynamic	NOUN
ejpam-5293	116	15	.	.	PUNCT
ejpam-5293	117	1	theorem	theorem	NOUN
ejpam-5293	117	2	1	1	NUM
ejpam-5293	117	3	.	.	PUNCT
ejpam-5293	118	1	(	(	PUNCT
ejpam-5293	118	2	livschitz	livschitz	PROPN
ejpam-5293	118	3	theorem	theorem	NOUN
ejpam-5293	118	4	for	for	ADP
ejpam-5293	118	5	hyperbolic	hyperbolic	ADJ
ejpam-5293	118	6	diffeomorphisms	diffeomorphism	NOUN
ejpam-5293	118	7	)	)	PUNCT
ejpam-5293	118	8	let	let	VERB
ejpam-5293	118	9	f	f	PRON
ejpam-5293	118	10	:	:	PUNCT
ejpam-5293	118	11	m	m	AUX
ejpam-5293	118	12	→m	→m	PUNCT
ejpam-5293	118	13	be	be	AUX
ejpam-5293	118	14	a	a	DET
ejpam-5293	118	15	c1	c1	NOUN
ejpam-5293	118	16	diffeomorphism	diffeomorphism	NOUN
ejpam-5293	118	17	defined	define	VERB
ejpam-5293	118	18	on	on	ADP
ejpam-5293	118	19	a	a	DET
ejpam-5293	118	20	riemannian	riemannian	ADJ
ejpam-5293	118	21	manifold	manifold	NOUN
ejpam-5293	118	22	m	m	NOUN
ejpam-5293	118	23	.	.	PUNCT
ejpam-5293	119	1	let	let	VERB
ejpam-5293	119	2	λ	λ	PROPN
ejpam-5293	119	3	⊂	⊂	PROPN
ejpam-5293	119	4	m	m	AUX
ejpam-5293	119	5	be	be	AUX
ejpam-5293	119	6	a	a	DET
ejpam-5293	119	7	compact	compact	ADJ
ejpam-5293	119	8	invariant	invariant	ADJ
ejpam-5293	119	9	hyperbolic	hyperbolic	ADJ
ejpam-5293	119	10	set	set	VERB
ejpam-5293	119	11	locally	locally	ADV
ejpam-5293	119	12	maximal	maximal	ADJ
ejpam-5293	119	13	with	with	ADP
ejpam-5293	119	14	f	f	PROPN
ejpam-5293	119	15	|λ	|λ	ADV
ejpam-5293	119	16	topologically	topologically	ADV
ejpam-5293	119	17	transitive	transitive	ADJ
ejpam-5293	119	18	.	.	PUNCT
ejpam-5293	120	1	suppose	suppose	VERB
ejpam-5293	120	2	that	that	SCONJ
ejpam-5293	120	3	φ	φ	NOUN
ejpam-5293	120	4	:	:	PUNCT
ejpam-5293	120	5	λ	λ	X
ejpam-5293	120	6	→	→	SYM
ejpam-5293	120	7	r	r	NOUN
ejpam-5293	120	8	is	be	AUX
ejpam-5293	120	9	a	a	DET
ejpam-5293	120	10	hölder	hölder	NOUN
ejpam-5293	120	11	function	function	NOUN
ejpam-5293	120	12	such	such	ADJ
ejpam-5293	120	13	that	that	SCONJ
ejpam-5293	120	14	m−1∑	m−1∑	PROPN
ejpam-5293	120	15	i=0	i=0	PROPN
ejpam-5293	120	16	φ(f	φ(f	PROPN
ejpam-5293	120	17	ix	ix	PROPN
ejpam-5293	120	18	)	)	PUNCT
ejpam-5293	121	1	=	=	SYM
ejpam-5293	121	2	0	0	PUNCT
ejpam-5293	121	3	whenever	whenever	SCONJ
ejpam-5293	121	4	fm(x	fm(x	PRON
ejpam-5293	121	5	)	)	PUNCT
ejpam-5293	121	6	=	=	PUNCT
ejpam-5293	122	1	x.	x.	NOUN
ejpam-5293	122	2	then	then	ADV
ejpam-5293	122	3	there	there	PRON
ejpam-5293	122	4	is	be	VERB
ejpam-5293	122	5	a	a	DET
ejpam-5293	122	6	hölder	hölder	NOUN
ejpam-5293	122	7	function	function	NOUN
ejpam-5293	122	8	φ	φ	NOUN
ejpam-5293	122	9	:	:	PUNCT
ejpam-5293	123	1	λ	λ	X
ejpam-5293	123	2	→	→	SYM
ejpam-5293	123	3	r	r	NOUN
ejpam-5293	123	4	,	,	PUNCT
ejpam-5293	123	5	with	with	ADP
ejpam-5293	123	6	at	at	ADP
ejpam-5293	123	7	least	least	ADJ
ejpam-5293	123	8	the	the	DET
ejpam-5293	123	9	same	same	ADJ
ejpam-5293	123	10	hölder	hölder	NOUN
ejpam-5293	123	11	exponent	exponent	NOUN
ejpam-5293	123	12	as	as	ADP
ejpam-5293	123	13	φ	φ	NUM
ejpam-5293	123	14	,	,	PUNCT
ejpam-5293	123	15	and	and	CCONJ
ejpam-5293	123	16	unique	unique	VERB
ejpam-5293	123	17	up	up	ADP
ejpam-5293	123	18	to	to	ADP
ejpam-5293	123	19	an	an	DET
ejpam-5293	123	20	additive	additive	ADJ
ejpam-5293	123	21	constant	constant	ADJ
ejpam-5293	123	22	,	,	PUNCT
ejpam-5293	123	23	such	such	ADJ
ejpam-5293	123	24	that	that	SCONJ
ejpam-5293	123	25	φ	φ	PROPN
ejpam-5293	123	26	=	=	SYM
ejpam-5293	123	27	φ	φ	PROPN
ejpam-5293	123	28	◦	◦	NOUN
ejpam-5293	123	29	f	f	PROPN
ejpam-5293	124	1	−	−	PROPN
ejpam-5293	124	2	φ	φ	PROPN
ejpam-5293	124	3	.	.	PUNCT
ejpam-5293	125	1	given	give	VERB
ejpam-5293	125	2	the	the	DET
ejpam-5293	125	3	relationship	relationship	NOUN
ejpam-5293	125	4	exposed	expose	VERB
ejpam-5293	125	5	in	in	ADP
ejpam-5293	125	6	section	section	NOUN
ejpam-5293	125	7	2	2	NUM
ejpam-5293	125	8	between	between	ADP
ejpam-5293	125	9	solving	solve	VERB
ejpam-5293	125	10	cohomological	cohomological	ADJ
ejpam-5293	125	11	equations	equation	NOUN
ejpam-5293	125	12	and	and	CCONJ
ejpam-5293	125	13	obtaining	obtain	VERB
ejpam-5293	125	14	coboundaries	coboundarie	NOUN
ejpam-5293	125	15	,	,	PUNCT
ejpam-5293	125	16	we	we	PRON
ejpam-5293	125	17	can	can	AUX
ejpam-5293	125	18	interpret	interpret	VERB
ejpam-5293	125	19	the	the	DET
ejpam-5293	125	20	theorem	theorem	NOUN
ejpam-5293	125	21	1	1	NUM
ejpam-5293	125	22	as	as	SCONJ
ejpam-5293	125	23	follows	follow	VERB
ejpam-5293	125	24	:	:	PUNCT
ejpam-5293	125	25	for	for	ADP
ejpam-5293	125	26	hyperbolic	hyperbolic	ADJ
ejpam-5293	125	27	dynamics	dynamic	NOUN
ejpam-5293	125	28	and	and	CCONJ
ejpam-5293	125	29	hölder	hölder	NOUN
ejpam-5293	125	30	functions	function	NOUN
ejpam-5293	125	31	,	,	PUNCT
ejpam-5293	125	32	the	the	DET
ejpam-5293	125	33	periodic	periodic	ADJ
ejpam-5293	125	34	data	datum	NOUN
ejpam-5293	125	35	are	be	AUX
ejpam-5293	125	36	necessary	necessary	ADJ
ejpam-5293	125	37	and	and	CCONJ
ejpam-5293	125	38	sufficient	sufficient	ADJ
ejpam-5293	125	39	to	to	PART
ejpam-5293	125	40	identify	identify	VERB
ejpam-5293	125	41	hölder	hölder	NOUN
ejpam-5293	125	42	coboundaries	coboundarie	NOUN
ejpam-5293	125	43	.	.	PUNCT
ejpam-5293	126	1	note	note	VERB
ejpam-5293	126	2	that	that	SCONJ
ejpam-5293	126	3	a	a	DET
ejpam-5293	126	4	function	function	NOUN
ejpam-5293	126	5	φ	φ	NOUN
ejpam-5293	126	6	:	:	PUNCT
ejpam-5293	126	7	m	m	VERB
ejpam-5293	126	8	→	→	SYM
ejpam-5293	126	9	r	r	NOUN
ejpam-5293	126	10	is	be	AUX
ejpam-5293	126	11	called	call	VERB
ejpam-5293	126	12	hölder	hölder	NOUN
ejpam-5293	126	13	with	with	ADP
ejpam-5293	126	14	exponent	exponent	PROPN
ejpam-5293	126	15	θ	θ	PROPN
ejpam-5293	126	16	,	,	PUNCT
ejpam-5293	126	17	0	0	NUM
ejpam-5293	126	18	<	<	X
ejpam-5293	126	19	θ	θ	X
ejpam-5293	126	20	≤	≤	NUM
ejpam-5293	126	21	1	1	NUM
ejpam-5293	126	22	,	,	PUNCT
ejpam-5293	126	23	if	if	SCONJ
ejpam-5293	126	24	there	there	PRON
ejpam-5293	126	25	is	be	VERB
ejpam-5293	126	26	k	k	PROPN
ejpam-5293	126	27	>	>	X
ejpam-5293	126	28	0	0	NUM
ejpam-5293	126	29	such	such	ADJ
ejpam-5293	126	30	that	that	SCONJ
ejpam-5293	126	31	|φ(x)−	|φ(x)−	NOUN
ejpam-5293	126	32	φ(y)|	φ(y)|	ADV
ejpam-5293	126	33	≤	≤	NOUN
ejpam-5293	126	34	kd(x	kd(x	PUNCT
ejpam-5293	126	35	,	,	PUNCT
ejpam-5293	126	36	y)θ	y)θ	X
ejpam-5293	126	37	for	for	ADP
ejpam-5293	126	38	all	all	DET
ejpam-5293	126	39	x	x	NOUN
ejpam-5293	126	40	,	,	PUNCT
ejpam-5293	126	41	y	y	PROPN
ejpam-5293	126	42	∈m	∈m	NOUN
ejpam-5293	126	43	.	.	PUNCT
ejpam-5293	127	1	while	while	SCONJ
ejpam-5293	127	2	closely	closely	ADV
ejpam-5293	127	3	following	follow	VERB
ejpam-5293	127	4	the	the	DET
ejpam-5293	127	5	suggestions	suggestion	NOUN
ejpam-5293	127	6	of	of	ADP
ejpam-5293	127	7	katok	katok	NOUN
ejpam-5293	127	8	and	and	CCONJ
ejpam-5293	127	9	hasselblatt	hasselblatt	NOUN
ejpam-5293	128	1	[	[	X
ejpam-5293	128	2	6	6	NUM
ejpam-5293	128	3	]	]	PUNCT
ejpam-5293	128	4	,	,	PUNCT
ejpam-5293	128	5	the	the	DET
ejpam-5293	128	6	proof	proof	NOUN
ejpam-5293	128	7	of	of	ADP
ejpam-5293	128	8	the	the	DET
ejpam-5293	128	9	theorem	theorem	NOUN
ejpam-5293	128	10	1	1	NUM
ejpam-5293	128	11	here	here	ADV
ejpam-5293	128	12	presented	present	VERB
ejpam-5293	128	13	is	be	AUX
ejpam-5293	128	14	pragmatically	pragmatically	ADV
ejpam-5293	128	15	oriented	orient	VERB
ejpam-5293	128	16	to	to	ADP
ejpam-5293	128	17	the	the	DET
ejpam-5293	128	18	study	study	NOUN
ejpam-5293	128	19	of	of	ADP
ejpam-5293	128	20	cohomology	cohomology	NOUN
ejpam-5293	128	21	in	in	ADP
ejpam-5293	128	22	dynamical	dynamical	ADJ
ejpam-5293	128	23	systems	system	NOUN
ejpam-5293	128	24	,	,	PUNCT
ejpam-5293	128	25	and	and	CCONJ
ejpam-5293	128	26	consists	consist	VERB
ejpam-5293	128	27	of	of	ADP
ejpam-5293	128	28	the	the	DET
ejpam-5293	128	29	following	follow	VERB
ejpam-5293	128	30	steps	step	NOUN
ejpam-5293	128	31	:	:	PUNCT
ejpam-5293	128	32	1	1	X
ejpam-5293	128	33	)	)	PUNCT
ejpam-5293	128	34	the	the	DET
ejpam-5293	128	35	function	function	NOUN
ejpam-5293	128	36	φ	φ	PROPN
ejpam-5293	128	37	is	be	AUX
ejpam-5293	128	38	determined	determine	VERB
ejpam-5293	128	39	along	along	ADP
ejpam-5293	128	40	a	a	DET
ejpam-5293	128	41	dense	dense	ADJ
ejpam-5293	128	42	orbit	orbit	NOUN
ejpam-5293	128	43	,	,	PUNCT
ejpam-5293	128	44	guaranteed	guarantee	VERB
ejpam-5293	128	45	by	by	ADP
ejpam-5293	128	46	the	the	DET
ejpam-5293	128	47	existence	existence	NOUN
ejpam-5293	128	48	of	of	ADP
ejpam-5293	128	49	topological	topological	ADJ
ejpam-5293	128	50	transitivity	transitivity	NOUN
ejpam-5293	128	51	of	of	ADP
ejpam-5293	128	52	f	f	PROPN
ejpam-5293	128	53	in	in	ADP
ejpam-5293	128	54	λ	λ	PROPN
ejpam-5293	128	55	,	,	PUNCT
ejpam-5293	128	56	by	by	ADP
ejpam-5293	128	57	choosing	choose	VERB
ejpam-5293	128	58	an	an	DET
ejpam-5293	128	59	arbitrary	arbitrary	ADJ
ejpam-5293	128	60	value	value	NOUN
ejpam-5293	128	61	in	in	ADP
ejpam-5293	128	62	one	one	NUM
ejpam-5293	128	63	of	of	ADP
ejpam-5293	128	64	the	the	DET
ejpam-5293	128	65	orbit	orbit	NOUN
ejpam-5293	128	66	points	point	NOUN
ejpam-5293	128	67	;	;	PUNCT
ejpam-5293	129	1	r.	r.	PROPN
ejpam-5293	129	2	d.	d.	PROPN
ejpam-5293	129	3	laureano	laureano	PROPN
ejpam-5293	129	4	/	/	SYM
ejpam-5293	129	5	eur	eur	PROPN
ejpam-5293	129	6	.	.	PUNCT
ejpam-5293	130	1	j.	j.	PROPN
ejpam-5293	130	2	pure	pure	PROPN
ejpam-5293	130	3	appl	appl	PROPN
ejpam-5293	130	4	.	.	PROPN
ejpam-5293	130	5	math	math	PROPN
ejpam-5293	130	6	,	,	PUNCT
ejpam-5293	130	7	17	17	NUM
ejpam-5293	130	8	(	(	PUNCT
ejpam-5293	130	9	3	3	NUM
ejpam-5293	130	10	)	)	PUNCT
ejpam-5293	130	11	(	(	PUNCT
ejpam-5293	130	12	2024	2024	NUM
ejpam-5293	130	13	)	)	PUNCT
ejpam-5293	130	14	,	,	PUNCT
ejpam-5293	130	15	1403	1403	NUM
ejpam-5293	130	16	-	-	SYM
ejpam-5293	130	17	1416	1416	NUM
ejpam-5293	130	18	1409	1409	NUM
ejpam-5293	130	19	2	2	NUM
ejpam-5293	130	20	)	)	PUNCT
ejpam-5293	130	21	the	the	DET
ejpam-5293	130	22	hölder	hölder	NOUN
ejpam-5293	130	23	regularity	regularity	NOUN
ejpam-5293	130	24	of	of	ADP
ejpam-5293	130	25	φ	φ	PROPN
ejpam-5293	130	26	is	be	AUX
ejpam-5293	130	27	then	then	ADV
ejpam-5293	130	28	used	use	VERB
ejpam-5293	130	29	to	to	PART
ejpam-5293	130	30	ensure	ensure	VERB
ejpam-5293	130	31	the	the	DET
ejpam-5293	130	32	hölder	hölder	NOUN
ejpam-5293	130	33	regularity	regularity	NOUN
ejpam-5293	130	34	of	of	ADP
ejpam-5293	130	35	φ	φ	PROPN
ejpam-5293	130	36	while	while	SCONJ
ejpam-5293	130	37	φ	φ	PROPN
ejpam-5293	130	38	is	be	AUX
ejpam-5293	130	39	extended	extend	VERB
ejpam-5293	130	40	to	to	ADP
ejpam-5293	130	41	the	the	DET
ejpam-5293	130	42	whole	whole	ADJ
ejpam-5293	130	43	set	set	NOUN
ejpam-5293	130	44	λ	λ	PROPN
ejpam-5293	130	45	.	.	PUNCT
ejpam-5293	131	1	the	the	DET
ejpam-5293	131	2	acl	acl	PROPN
ejpam-5293	131	3	for	for	ADP
ejpam-5293	131	4	diffeomorphism	diffeomorphism	NOUN
ejpam-5293	131	5	is	be	AUX
ejpam-5293	131	6	crucial	crucial	ADJ
ejpam-5293	131	7	for	for	ADP
ejpam-5293	131	8	the	the	DET
ejpam-5293	131	9	first	first	ADJ
ejpam-5293	131	10	part	part	NOUN
ejpam-5293	131	11	of	of	ADP
ejpam-5293	131	12	the	the	DET
ejpam-5293	131	13	proof	proof	NOUN
ejpam-5293	131	14	.	.	PUNCT
ejpam-5293	132	1	for	for	ADP
ejpam-5293	132	2	diffeomorphisms	diffeomorphism	NOUN
ejpam-5293	132	3	with	with	ADP
ejpam-5293	132	4	hyperbolic	hyperbolic	ADJ
ejpam-5293	132	5	sets	set	NOUN
ejpam-5293	132	6	,	,	PUNCT
ejpam-5293	132	7	it	it	PRON
ejpam-5293	132	8	ensures	ensure	VERB
ejpam-5293	132	9	that	that	SCONJ
ejpam-5293	132	10	there	there	PRON
ejpam-5293	132	11	are	be	VERB
ejpam-5293	132	12	always	always	ADV
ejpam-5293	132	13	periodic	periodic	ADJ
ejpam-5293	132	14	orbits	orbit	NOUN
ejpam-5293	132	15	in	in	ADP
ejpam-5293	132	16	the	the	DET
ejpam-5293	132	17	neighborhood	neighborhood	NOUN
ejpam-5293	132	18	of	of	ADP
ejpam-5293	132	19	orbits	orbit	NOUN
ejpam-5293	132	20	that	that	PRON
ejpam-5293	132	21	turn	turn	VERB
ejpam-5293	132	22	close	close	ADJ
ejpam-5293	132	23	enough	enough	ADV
ejpam-5293	132	24	of	of	ADP
ejpam-5293	132	25	themselves	themselves	PRON
ejpam-5293	132	26	.	.	PUNCT
ejpam-5293	133	1	as	as	ADP
ejpam-5293	133	2	a	a	DET
ejpam-5293	133	3	consequence	consequence	NOUN
ejpam-5293	133	4	,	,	PUNCT
ejpam-5293	133	5	we	we	PRON
ejpam-5293	133	6	obtain	obtain	VERB
ejpam-5293	133	7	an	an	DET
ejpam-5293	133	8	control	control	NOUN
ejpam-5293	133	9	estimate	estimate	NOUN
ejpam-5293	133	10	to	to	ADP
ejpam-5293	133	11	the	the	DET
ejpam-5293	133	12	distance	distance	NOUN
ejpam-5293	133	13	between	between	ADP
ejpam-5293	133	14	the	the	DET
ejpam-5293	133	15	corresponding	corresponding	ADJ
ejpam-5293	133	16	points	point	NOUN
ejpam-5293	133	17	in	in	ADP
ejpam-5293	133	18	the	the	DET
ejpam-5293	133	19	initial	initial	ADJ
ejpam-5293	133	20	orbit	orbit	NOUN
ejpam-5293	133	21	and	and	CCONJ
ejpam-5293	133	22	the	the	DET
ejpam-5293	133	23	periodic	periodic	ADJ
ejpam-5293	133	24	orbit	orbit	NOUN
ejpam-5293	133	25	(	(	PUNCT
ejpam-5293	133	26	regarding	regard	VERB
ejpam-5293	133	27	this	this	DET
ejpam-5293	133	28	see	see	NOUN
ejpam-5293	133	29	for	for	ADP
ejpam-5293	133	30	instance	instance	NOUN
ejpam-5293	133	31	[	[	X
ejpam-5293	133	32	5	5	NUM
ejpam-5293	133	33	]	]	NUM
ejpam-5293	133	34	)	)	PUNCT
ejpam-5293	133	35	.	.	PUNCT
ejpam-5293	134	1	3.1	3.1	NUM
ejpam-5293	134	2	.	.	PUNCT
ejpam-5293	134	3	proof	proof	NOUN
ejpam-5293	134	4	of	of	ADP
ejpam-5293	134	5	the	the	DET
ejpam-5293	134	6	anosov	anosov	NOUN
ejpam-5293	134	7	closing	close	VERB
ejpam-5293	134	8	lemma	lemma	PROPN
ejpam-5293	134	9	for	for	ADP
ejpam-5293	134	10	diffeomorphisms	diffeomorphism	NOUN
ejpam-5293	134	11	:	:	PUNCT
ejpam-5293	134	12	distance	distance	NOUN
ejpam-5293	134	13	control	control	NOUN
ejpam-5293	134	14	inequality	inequality	NOUN
ejpam-5293	134	15	since	since	SCONJ
ejpam-5293	134	16	it	it	PRON
ejpam-5293	134	17	is	be	AUX
ejpam-5293	134	18	involved	involve	VERB
ejpam-5293	134	19	in	in	ADP
ejpam-5293	134	20	many	many	ADJ
ejpam-5293	134	21	details	detail	NOUN
ejpam-5293	134	22	of	of	ADP
ejpam-5293	134	23	the	the	DET
ejpam-5293	134	24	acl	acl	PROPN
ejpam-5293	134	25	proof	proof	NOUN
ejpam-5293	134	26	,	,	PUNCT
ejpam-5293	134	27	we	we	PRON
ejpam-5293	134	28	first	first	ADV
ejpam-5293	134	29	present	present	VERB
ejpam-5293	134	30	the	the	DET
ejpam-5293	134	31	hadamardperron	hadamardperron	PROPN
ejpam-5293	134	32	theorem	theorem	NOUN
ejpam-5293	134	33	in	in	ADP
ejpam-5293	134	34	the	the	DET
ejpam-5293	134	35	context	context	NOUN
ejpam-5293	134	36	of	of	ADP
ejpam-5293	134	37	hyperbolic	hyperbolic	ADJ
ejpam-5293	134	38	sets	set	NOUN
ejpam-5293	134	39	.	.	PUNCT
ejpam-5293	135	1	theorem	theorem	NOUN
ejpam-5293	135	2	2	2	NUM
ejpam-5293	135	3	.	.	PUNCT
ejpam-5293	135	4	(	(	PUNCT
ejpam-5293	135	5	hadamard	hadamard	ADJ
ejpam-5293	135	6	–	–	PUNCT
ejpam-5293	135	7	perron	perron	PROPN
ejpam-5293	135	8	theorem	theorem	VERB
ejpam-5293	135	9	for	for	ADP
ejpam-5293	135	10	hyperbolic	hyperbolic	ADJ
ejpam-5293	135	11	diffeomorphisms	diffeomorphism	NOUN
ejpam-5293	135	12	)	)	PUNCT
ejpam-5293	135	13	let	let	VERB
ejpam-5293	135	14	m	m	PRON
ejpam-5293	135	15	be	be	AUX
ejpam-5293	135	16	a	a	DET
ejpam-5293	135	17	riemannian	riemannian	ADJ
ejpam-5293	135	18	manifold	manifold	NOUN
ejpam-5293	135	19	,	,	PUNCT
ejpam-5293	135	20	f	f	X
ejpam-5293	135	21	:	:	PUNCT
ejpam-5293	135	22	m	m	VERB
ejpam-5293	135	23	→	→	SYM
ejpam-5293	135	24	m	m	VERB
ejpam-5293	135	25	a	a	DET
ejpam-5293	135	26	c1	c1	NOUN
ejpam-5293	135	27	diffeomorphism	diffeomorphism	NOUN
ejpam-5293	135	28	and	and	CCONJ
ejpam-5293	135	29	λ	λ	X
ejpam-5293	135	30	⊂	⊂	PROPN
ejpam-5293	135	31	m	m	VERB
ejpam-5293	135	32	a	a	DET
ejpam-5293	135	33	compact	compact	ADJ
ejpam-5293	135	34	hyperbolic	hyperbolic	ADJ
ejpam-5293	135	35	set	set	NOUN
ejpam-5293	135	36	.	.	PUNCT
ejpam-5293	136	1	then	then	ADV
ejpam-5293	136	2	,	,	PUNCT
ejpam-5293	136	3	for	for	ADP
ejpam-5293	136	4	each	each	DET
ejpam-5293	136	5	x	x	SYM
ejpam-5293	136	6	∈	∈	PROPN
ejpam-5293	136	7	λ	λ	PROPN
ejpam-5293	136	8	,	,	PUNCT
ejpam-5293	136	9	there	there	PRON
ejpam-5293	136	10	are	be	VERB
ejpam-5293	136	11	stable	stable	ADJ
ejpam-5293	136	12	and	and	CCONJ
ejpam-5293	136	13	unstable	unstable	ADJ
ejpam-5293	136	14	local	local	ADJ
ejpam-5293	136	15	embedded	embed	VERB
ejpam-5293	136	16	c1	c1	PROPN
ejpam-5293	136	17	manifolds	manifold	NOUN
ejpam-5293	136	18	,	,	PUNCT
ejpam-5293	136	19	respectively	respectively	ADV
ejpam-5293	136	20	w	w	NOUN
ejpam-5293	136	21	s(x	s(x	PROPN
ejpam-5293	136	22	)	)	PUNCT
ejpam-5293	136	23	and	and	CCONJ
ejpam-5293	136	24	w	w	ADP
ejpam-5293	136	25	u(x	u(x	NOUN
ejpam-5293	136	26	)	)	PUNCT
ejpam-5293	136	27	,	,	PUNCT
ejpam-5293	136	28	such	such	ADJ
ejpam-5293	136	29	that	that	SCONJ
ejpam-5293	136	30	:	:	PUNCT
ejpam-5293	136	31	i.	i.	PROPN
ejpam-5293	136	32	txw	txw	PROPN
ejpam-5293	136	33	s(x	s(x	PROPN
ejpam-5293	136	34	)	)	PUNCT
ejpam-5293	136	35	=	=	SYM
ejpam-5293	136	36	es(x	es(x	X
ejpam-5293	136	37	)	)	PUNCT
ejpam-5293	136	38	and	and	CCONJ
ejpam-5293	136	39	txw	txw	NOUN
ejpam-5293	136	40	u(x	u(x	PROPN
ejpam-5293	136	41	)	)	PUNCT
ejpam-5293	136	42	=	=	PUNCT
ejpam-5293	136	43	eu(x	eu(x	NOUN
ejpam-5293	136	44	)	)	PUNCT
ejpam-5293	136	45	;	;	PUNCT
ejpam-5293	137	1	ii	ii	X
ejpam-5293	137	2	.	.	PUNCT
ejpam-5293	138	1	f(w	f(w	PROPN
ejpam-5293	138	2	s(x	s(x	PROPN
ejpam-5293	138	3	)	)	PUNCT
ejpam-5293	138	4	)	)	PUNCT
ejpam-5293	139	1	⊂w	⊂w	PROPN
ejpam-5293	139	2	s(fx	s(fx	ADJ
ejpam-5293	139	3	)	)	PUNCT
ejpam-5293	139	4	and	and	CCONJ
ejpam-5293	139	5	f−1(w	f−1(w	ADV
ejpam-5293	139	6	u(x	u(x	PROPN
ejpam-5293	139	7	)	)	PUNCT
ejpam-5293	139	8	)	)	PUNCT
ejpam-5293	140	1	⊂w	⊂w	PROPN
ejpam-5293	140	2	u(f−1x	u(f−1x	PROPN
ejpam-5293	140	3	)	)	PUNCT
ejpam-5293	140	4	;	;	PUNCT
ejpam-5293	140	5	iii	iii	X
ejpam-5293	140	6	.	.	NOUN
ejpam-5293	141	1	for	for	ADP
ejpam-5293	141	2	each	each	DET
ejpam-5293	141	3	δ	δ	PROPN
ejpam-5293	141	4	>	>	X
ejpam-5293	141	5	0	0	PUNCT
ejpam-5293	142	1	there	there	PRON
ejpam-5293	142	2	is	be	VERB
ejpam-5293	142	3	d	d	NOUN
ejpam-5293	142	4	=	=	SYM
ejpam-5293	142	5	d(δ	d(δ	PROPN
ejpam-5293	142	6	)	)	PUNCT
ejpam-5293	142	7	>	>	X
ejpam-5293	142	8	0	0	NUM
ejpam-5293	142	9	such	such	ADJ
ejpam-5293	142	10	that	that	SCONJ
ejpam-5293	142	11	,	,	PUNCT
ejpam-5293	142	12	for	for	ADP
ejpam-5293	142	13	each	each	DET
ejpam-5293	142	14	n	n	PRON
ejpam-5293	142	15	∈	∈	PROPN
ejpam-5293	142	16	n	n	CCONJ
ejpam-5293	142	17	,	,	PUNCT
ejpam-5293	142	18	we	we	PRON
ejpam-5293	142	19	have	have	VERB
ejpam-5293	142	20	d(fnx	d(fnx	PROPN
ejpam-5293	142	21	,	,	PUNCT
ejpam-5293	142	22	fny	fny	NOUN
ejpam-5293	142	23	)	)	PUNCT
ejpam-5293	142	24	≤	≤	NOUN
ejpam-5293	142	25	d(τ+δ)nd(x	d(τ+δ)nd(x	NOUN
ejpam-5293	142	26	,	,	PUNCT
ejpam-5293	142	27	y	y	NOUN
ejpam-5293	142	28	)	)	PUNCT
ejpam-5293	142	29	for	for	ADP
ejpam-5293	142	30	y	y	PROPN
ejpam-5293	142	31	∈w	∈w	PROPN
ejpam-5293	142	32	s(x	s(x	NOUN
ejpam-5293	142	33	)	)	PUNCT
ejpam-5293	142	34	,	,	PUNCT
ejpam-5293	142	35	and	and	CCONJ
ejpam-5293	142	36	d(f−nx	d(f−nx	PROPN
ejpam-5293	142	37	,	,	PUNCT
ejpam-5293	142	38	f−ny	f−ny	NOUN
ejpam-5293	142	39	)	)	PUNCT
ejpam-5293	142	40	≤	≤	NOUN
ejpam-5293	142	41	d(τ+δ)nd(x	d(τ+δ)nd(x	NOUN
ejpam-5293	142	42	,	,	PUNCT
ejpam-5293	142	43	y	y	NOUN
ejpam-5293	142	44	)	)	PUNCT
ejpam-5293	142	45	for	for	ADP
ejpam-5293	142	46	y	y	PROPN
ejpam-5293	142	47	∈w	∈w	PROPN
ejpam-5293	142	48	u(x	u(x	NOUN
ejpam-5293	142	49	)	)	PUNCT
ejpam-5293	142	50	;	;	PUNCT
ejpam-5293	143	1	iv	iv	X
ejpam-5293	143	2	.	.	PUNCT
ejpam-5293	144	1	there	there	PRON
ejpam-5293	144	2	are	be	VERB
ejpam-5293	144	3	β	β	X
ejpam-5293	144	4	>	>	X
ejpam-5293	144	5	0	0	PUNCT
ejpam-5293	144	6	and	and	CCONJ
ejpam-5293	144	7	an	an	DET
ejpam-5293	144	8	unique	unique	ADJ
ejpam-5293	144	9	family	family	NOUN
ejpam-5293	144	10	ux	ux	ADP
ejpam-5293	144	11	of	of	ADP
ejpam-5293	144	12	neighborhoods	neighborhood	NOUN
ejpam-5293	144	13	containing	contain	VERB
ejpam-5293	144	14	the	the	DET
ejpam-5293	144	15	ball	ball	NOUN
ejpam-5293	144	16	around	around	ADP
ejpam-5293	144	17	x	x	PUNCT
ejpam-5293	144	18	∈	∈	PROPN
ejpam-5293	144	19	λ	λ	NOUN
ejpam-5293	144	20	of	of	ADP
ejpam-5293	144	21	radius	radius	NOUN
ejpam-5293	144	22	β	β	PROPN
ejpam-5293	144	23	such	such	ADJ
ejpam-5293	144	24	that	that	DET
ejpam-5293	144	25	w	w	PROPN
ejpam-5293	144	26	s(x	s(x	PROPN
ejpam-5293	144	27	)	)	PUNCT
ejpam-5293	145	1	=	=	PRON
ejpam-5293	145	2	{	{	PUNCT
ejpam-5293	145	3	y	y	PROPN
ejpam-5293	145	4	∈m	∈m	NOUN
ejpam-5293	145	5	:	:	PUNCT
ejpam-5293	145	6	fny	fny	PROPN
ejpam-5293	145	7	∈	∈	PROPN
ejpam-5293	145	8	ufnx	ufnx	NOUN
ejpam-5293	145	9	for	for	ADP
ejpam-5293	145	10	n	n	PRON
ejpam-5293	145	11	∈	∈	PROPN
ejpam-5293	145	12	n	n	CCONJ
ejpam-5293	145	13	}	}	PUNCT
ejpam-5293	145	14	w	w	ADJ
ejpam-5293	145	15	u(x	u(x	NOUN
ejpam-5293	145	16	)	)	PUNCT
ejpam-5293	145	17	=	=	PRON
ejpam-5293	145	18	{	{	PUNCT
ejpam-5293	145	19	y	y	PROPN
ejpam-5293	145	20	∈m	∈m	NOUN
ejpam-5293	145	21	:	:	PUNCT
ejpam-5293	145	22	f−ny	f−ny	PROPN
ejpam-5293	145	23	∈	∈	PROPN
ejpam-5293	145	24	uf−nx	uf−nx	NOUN
ejpam-5293	145	25	for	for	ADP
ejpam-5293	145	26	n	n	PRON
ejpam-5293	145	27	∈	∈	PROPN
ejpam-5293	145	28	n	n	CCONJ
ejpam-5293	145	29	}	}	PUNCT
ejpam-5293	145	30	the	the	DET
ejpam-5293	145	31	proof	proof	NOUN
ejpam-5293	145	32	of	of	ADP
ejpam-5293	145	33	the	the	DET
ejpam-5293	145	34	theorem	theorem	ADJ
ejpam-5293	145	35	2	2	NUM
ejpam-5293	145	36	presents	present	VERB
ejpam-5293	145	37	a	a	DET
ejpam-5293	145	38	methodology	methodology	NOUN
ejpam-5293	145	39	that	that	PRON
ejpam-5293	145	40	plays	play	VERB
ejpam-5293	145	41	a	a	DET
ejpam-5293	145	42	central	central	ADJ
ejpam-5293	145	43	role	role	NOUN
ejpam-5293	145	44	in	in	ADP
ejpam-5293	145	45	hyperbolic	hyperbolic	ADJ
ejpam-5293	145	46	dynamical	dynamical	ADJ
ejpam-5293	145	47	systems	system	NOUN
ejpam-5293	145	48	theory	theory	NOUN
ejpam-5293	145	49	(	(	PUNCT
ejpam-5293	145	50	see	see	VERB
ejpam-5293	145	51	[	[	X
ejpam-5293	145	52	6	6	NUM
ejpam-5293	145	53	]	]	NUM
ejpam-5293	145	54	)	)	PUNCT
ejpam-5293	145	55	.	.	PUNCT
ejpam-5293	146	1	it	it	PRON
ejpam-5293	146	2	involves	involve	VERB
ejpam-5293	146	3	the	the	DET
ejpam-5293	146	4	use	use	NOUN
ejpam-5293	146	5	of	of	ADP
ejpam-5293	146	6	the	the	DET
ejpam-5293	146	7	contraction	contraction	NOUN
ejpam-5293	146	8	mapping	mapping	NOUN
ejpam-5293	146	9	principle	principle	NOUN
ejpam-5293	146	10	in	in	ADP
ejpam-5293	146	11	appropriately	appropriately	ADV
ejpam-5293	146	12	constructed	construct	VERB
ejpam-5293	146	13	functional	functional	ADJ
ejpam-5293	146	14	spaces	space	NOUN
ejpam-5293	146	15	.	.	PUNCT
ejpam-5293	147	1	it	it	PRON
ejpam-5293	147	2	follows	follow	VERB
ejpam-5293	147	3	from	from	ADP
ejpam-5293	147	4	properties	property	NOUN
ejpam-5293	147	5	iii	iii	PROPN
ejpam-5293	147	6	.	.	PUNCT
ejpam-5293	148	1	and	and	CCONJ
ejpam-5293	148	2	iv	iv	X
ejpam-5293	148	3	.	.	PUNCT
ejpam-5293	149	1	that	that	SCONJ
ejpam-5293	149	2	given	give	VERB
ejpam-5293	149	3	any	any	DET
ejpam-5293	149	4	two	two	NUM
ejpam-5293	149	5	stable	stable	ADJ
ejpam-5293	149	6	local	local	ADJ
ejpam-5293	149	7	manifolds	manifold	NOUN
ejpam-5293	149	8	w	w	PROPN
ejpam-5293	149	9	s	s	PROPN
ejpam-5293	149	10	1	1	NUM
ejpam-5293	149	11	(	(	PUNCT
ejpam-5293	149	12	x	x	NOUN
ejpam-5293	149	13	)	)	PUNCT
ejpam-5293	149	14	and	and	CCONJ
ejpam-5293	149	15	w	w	PROPN
ejpam-5293	149	16	s	s	ADJ
ejpam-5293	149	17	2	2	NUM
ejpam-5293	149	18	(	(	PUNCT
ejpam-5293	149	19	x	x	NOUN
ejpam-5293	149	20	)	)	PUNCT
ejpam-5293	149	21	of	of	ADP
ejpam-5293	149	22	x	x	PUNCT
ejpam-5293	149	23	satisfying	satisfy	VERB
ejpam-5293	149	24	the	the	DET
ejpam-5293	149	25	properties	property	NOUN
ejpam-5293	149	26	of	of	ADP
ejpam-5293	149	27	hadamard	hadamard	ADJ
ejpam-5293	149	28	-	-	PUNCT
ejpam-5293	149	29	perron	perron	NOUN
ejpam-5293	149	30	theorem	theorem	VERB
ejpam-5293	149	31	,	,	PUNCT
ejpam-5293	149	32	their	their	PRON
ejpam-5293	149	33	intersection	intersection	NOUN
ejpam-5293	149	34	contains	contain	VERB
ejpam-5293	149	35	an	an	DET
ejpam-5293	149	36	open	open	ADJ
ejpam-5293	149	37	neighborhood	neighborhood	NOUN
ejpam-5293	149	38	of	of	ADP
ejpam-5293	149	39	x	x	PUNCT
ejpam-5293	149	40	in	in	ADP
ejpam-5293	149	41	each	each	PRON
ejpam-5293	149	42	of	of	ADP
ejpam-5293	149	43	them	they	PRON
ejpam-5293	149	44	.	.	PUNCT
ejpam-5293	150	1	thus	thus	ADV
ejpam-5293	150	2	it	it	PRON
ejpam-5293	150	3	can	can	AUX
ejpam-5293	150	4	be	be	AUX
ejpam-5293	150	5	concluded	conclude	VERB
ejpam-5293	150	6	that	that	SCONJ
ejpam-5293	150	7	on	on	ADP
ejpam-5293	150	8	a	a	DET
ejpam-5293	150	9	certain	certain	ADJ
ejpam-5293	150	10	n	n	PRON
ejpam-5293	150	11	≥	≥	NOUN
ejpam-5293	150	12	0	0	NUM
ejpam-5293	150	13	we	we	PRON
ejpam-5293	150	14	have	have	VERB
ejpam-5293	150	15	fn(w	fn(w	ADV
ejpam-5293	150	16	s	s	PART
ejpam-5293	150	17	1	1	NUM
ejpam-5293	150	18	(	(	PUNCT
ejpam-5293	150	19	f	f	PROPN
ejpam-5293	150	20	−nx	−nx	PROPN
ejpam-5293	150	21	)	)	PUNCT
ejpam-5293	150	22	)	)	PUNCT
ejpam-5293	151	1	⊂	⊂	PROPN
ejpam-5293	152	1	w	w	PROPN
ejpam-5293	152	2	s	s	PROPN
ejpam-5293	152	3	2	2	NUM
ejpam-5293	152	4	(	(	PUNCT
ejpam-5293	152	5	x	x	NOUN
ejpam-5293	152	6	)	)	PUNCT
ejpam-5293	152	7	and	and	CCONJ
ejpam-5293	152	8	fn(w	fn(w	ADV
ejpam-5293	152	9	s	s	PART
ejpam-5293	152	10	2	2	NUM
ejpam-5293	152	11	(	(	PUNCT
ejpam-5293	152	12	f	f	PROPN
ejpam-5293	152	13	−nx	−nx	PROPN
ejpam-5293	152	14	)	)	PUNCT
ejpam-5293	152	15	)	)	PUNCT
ejpam-5293	153	1	⊂	⊂	PROPN
ejpam-5293	154	1	w	w	PROPN
ejpam-5293	154	2	s	s	PROPN
ejpam-5293	154	3	1	1	NUM
ejpam-5293	154	4	(	(	PUNCT
ejpam-5293	154	5	x	x	NOUN
ejpam-5293	154	6	)	)	PUNCT
ejpam-5293	154	7	.	.	PUNCT
ejpam-5293	155	1	such	such	DET
ejpam-5293	155	2	a	a	DET
ejpam-5293	155	3	number	number	NOUN
ejpam-5293	155	4	n	n	NUM
ejpam-5293	155	5	can	can	AUX
ejpam-5293	155	6	be	be	AUX
ejpam-5293	155	7	chosen	choose	VERB
ejpam-5293	155	8	uniformly	uniformly	ADV
ejpam-5293	155	9	for	for	ADP
ejpam-5293	155	10	all	all	DET
ejpam-5293	155	11	x	x	SYM
ejpam-5293	155	12	∈	∈	PROPN
ejpam-5293	155	13	λ	λ	PROPN
ejpam-5293	155	14	.	.	PUNCT
ejpam-5293	156	1	the	the	DET
ejpam-5293	156	2	same	same	ADJ
ejpam-5293	156	3	holds	hold	VERB
ejpam-5293	156	4	for	for	ADP
ejpam-5293	156	5	unstable	unstable	ADJ
ejpam-5293	156	6	r.	r.	PROPN
ejpam-5293	156	7	d.	d.	PROPN
ejpam-5293	156	8	laureano	laureano	PROPN
ejpam-5293	156	9	/	/	SYM
ejpam-5293	156	10	eur	eur	PROPN
ejpam-5293	156	11	.	.	PUNCT
ejpam-5293	157	1	j.	j.	PROPN
ejpam-5293	157	2	pure	pure	PROPN
ejpam-5293	157	3	appl	appl	PROPN
ejpam-5293	157	4	.	.	PROPN
ejpam-5293	157	5	math	math	PROPN
ejpam-5293	157	6	,	,	PUNCT
ejpam-5293	157	7	17	17	NUM
ejpam-5293	157	8	(	(	PUNCT
ejpam-5293	157	9	3	3	NUM
ejpam-5293	157	10	)	)	PUNCT
ejpam-5293	157	11	(	(	PUNCT
ejpam-5293	157	12	2024	2024	NUM
ejpam-5293	157	13	)	)	PUNCT
ejpam-5293	157	14	,	,	PUNCT
ejpam-5293	157	15	1403	1403	NUM
ejpam-5293	157	16	-	-	SYM
ejpam-5293	157	17	1416	1416	NUM
ejpam-5293	157	18	1410	1410	NUM
ejpam-5293	157	19	local	local	ADJ
ejpam-5293	157	20	manifolds	manifold	NOUN
ejpam-5293	157	21	with	with	ADP
ejpam-5293	157	22	n	n	NOUN
ejpam-5293	157	23	replaced	replace	VERB
ejpam-5293	157	24	by	by	ADP
ejpam-5293	157	25	−n	−n	NOUN
ejpam-5293	157	26	.	.	PUNCT
ejpam-5293	158	1	this	this	PRON
ejpam-5293	158	2	implies	imply	VERB
ejpam-5293	158	3	that	that	SCONJ
ejpam-5293	158	4	the	the	DET
ejpam-5293	158	5	stable	stable	ADJ
ejpam-5293	158	6	and	and	CCONJ
ejpam-5293	158	7	unstable	unstable	ADJ
ejpam-5293	158	8	global	global	ADJ
ejpam-5293	158	9	manifolds	manifold	NOUN
ejpam-5293	158	10	given	give	VERB
ejpam-5293	158	11	by	by	ADP
ejpam-5293	158	12	w̃	w̃	PROPN
ejpam-5293	158	13	s(x	s(x	PROPN
ejpam-5293	158	14	)	)	PUNCT
ejpam-5293	158	15	=	=	SYM
ejpam-5293	158	16	∞⋃	∞⋃	PROPN
ejpam-5293	158	17	n=0	n=0	PROPN
ejpam-5293	158	18	f−n(w	f−n(w	PROPN
ejpam-5293	158	19	s(fnx	s(fnx	PROPN
ejpam-5293	158	20	)	)	PUNCT
ejpam-5293	158	21	)	)	PUNCT
ejpam-5293	159	1	and	and	CCONJ
ejpam-5293	159	2	w̃	w̃	PROPN
ejpam-5293	159	3	u(x	u(x	PROPN
ejpam-5293	159	4	)	)	PUNCT
ejpam-5293	159	5	=	=	SYM
ejpam-5293	159	6	∞⋃	∞⋃	PROPN
ejpam-5293	159	7	n=0	n=0	PUNCT
ejpam-5293	159	8	fn(w	fn(w	X
ejpam-5293	159	9	u(f−nx	u(f−nx	NOUN
ejpam-5293	159	10	)	)	PUNCT
ejpam-5293	159	11	)	)	PUNCT
ejpam-5293	159	12	are	be	AUX
ejpam-5293	159	13	independent	independent	ADJ
ejpam-5293	159	14	of	of	ADP
ejpam-5293	159	15	a	a	DET
ejpam-5293	159	16	particular	particular	ADJ
ejpam-5293	159	17	choice	choice	NOUN
ejpam-5293	159	18	of	of	ADP
ejpam-5293	159	19	stable	stable	ADJ
ejpam-5293	159	20	and	and	CCONJ
ejpam-5293	159	21	unstable	unstable	ADJ
ejpam-5293	159	22	local	local	ADJ
ejpam-5293	159	23	manifolds	manifold	NOUN
ejpam-5293	159	24	and	and	CCONJ
ejpam-5293	159	25	can	can	AUX
ejpam-5293	159	26	be	be	AUX
ejpam-5293	159	27	topologically	topologically	ADV
ejpam-5293	159	28	characterized	characterize	VERB
ejpam-5293	159	29	by	by	ADP
ejpam-5293	159	30	the	the	DET
ejpam-5293	159	31	sets	set	NOUN
ejpam-5293	159	32	w̃	w̃	PROPN
ejpam-5293	159	33	s(x	s(x	PROPN
ejpam-5293	159	34	)	)	PUNCT
ejpam-5293	159	35	=	=	PRON
ejpam-5293	160	1	{	{	PUNCT
ejpam-5293	160	2	y	y	PROPN
ejpam-5293	160	3	∈m	∈m	NOUN
ejpam-5293	160	4	:	:	PUNCT
ejpam-5293	160	5	d(fnx	d(fnx	NOUN
ejpam-5293	160	6	,	,	PUNCT
ejpam-5293	160	7	fny	fny	NOUN
ejpam-5293	160	8	)	)	PUNCT
ejpam-5293	160	9	→	→	SYM
ejpam-5293	160	10	0	0	NUM
ejpam-5293	160	11	when	when	SCONJ
ejpam-5293	160	12	n→	n→	PROPN
ejpam-5293	160	13	+	+	ADJ
ejpam-5293	160	14	∞	∞	NOUN
ejpam-5293	160	15	}	}	PUNCT
ejpam-5293	160	16	,	,	PUNCT
ejpam-5293	160	17	w̃	w̃	PROPN
ejpam-5293	160	18	u(x	u(x	PROPN
ejpam-5293	160	19	)	)	PUNCT
ejpam-5293	160	20	=	=	SYM
ejpam-5293	160	21	{	{	PUNCT
ejpam-5293	160	22	y	y	PROPN
ejpam-5293	160	23	∈m	∈m	NOUN
ejpam-5293	160	24	:	:	PUNCT
ejpam-5293	161	1	d(fnx	d(fnx	NOUN
ejpam-5293	161	2	,	,	PUNCT
ejpam-5293	161	3	fny	fny	NOUN
ejpam-5293	161	4	)	)	PUNCT
ejpam-5293	161	5	→	→	SYM
ejpam-5293	161	6	0	0	NUM
ejpam-5293	161	7	when	when	SCONJ
ejpam-5293	161	8	n→	n→	PROPN
ejpam-5293	161	9	−∞	−∞	NOUN
ejpam-5293	161	10	}	}	PUNCT
ejpam-5293	161	11	.	.	PUNCT
ejpam-5293	162	1	the	the	DET
ejpam-5293	162	2	balls	ball	NOUN
ejpam-5293	162	3	with	with	ADP
ejpam-5293	162	4	radius	radius	NOUN
ejpam-5293	162	5	ε	ε	PROPN
ejpam-5293	162	6	and	and	CCONJ
ejpam-5293	162	7	center	center	NOUN
ejpam-5293	162	8	x	x	SYM
ejpam-5293	162	9	belonging	belong	VERB
ejpam-5293	162	10	to	to	ADP
ejpam-5293	162	11	w̃	w̃	PROPN
ejpam-5293	162	12	s(x	s(x	PROPN
ejpam-5293	162	13	)	)	PUNCT
ejpam-5293	162	14	and	and	CCONJ
ejpam-5293	162	15	w̃	w̃	PROPN
ejpam-5293	162	16	u(x	u(x	PROPN
ejpam-5293	162	17	)	)	PUNCT
ejpam-5293	162	18	are	be	AUX
ejpam-5293	162	19	denoted	denote	VERB
ejpam-5293	162	20	byw	byw	PROPN
ejpam-5293	162	21	s	s	PROPN
ejpam-5293	162	22	ε	ε	PROPN
ejpam-5293	162	23	(	(	PUNCT
ejpam-5293	162	24	x	x	NOUN
ejpam-5293	162	25	)	)	PUNCT
ejpam-5293	162	26	and	and	CCONJ
ejpam-5293	162	27	w	w	PART
ejpam-5293	162	28	u	u	PROPN
ejpam-5293	162	29	ε	ε	PROPN
ejpam-5293	162	30	(	(	PUNCT
ejpam-5293	162	31	x	x	NOUN
ejpam-5293	162	32	)	)	PUNCT
ejpam-5293	162	33	,	,	PUNCT
ejpam-5293	162	34	respectively	respectively	ADV
ejpam-5293	162	35	.	.	PUNCT
ejpam-5293	163	1	now	now	ADV
ejpam-5293	163	2	,	,	PUNCT
ejpam-5293	163	3	we	we	PRON
ejpam-5293	163	4	have	have	VERB
ejpam-5293	163	5	all	all	DET
ejpam-5293	163	6	the	the	DET
ejpam-5293	163	7	elements	element	NOUN
ejpam-5293	163	8	and	and	CCONJ
ejpam-5293	163	9	notation	notation	NOUN
ejpam-5293	163	10	to	to	PART
ejpam-5293	163	11	write	write	VERB
ejpam-5293	163	12	the	the	DET
ejpam-5293	163	13	acl	acl	PROPN
ejpam-5293	163	14	for	for	ADP
ejpam-5293	163	15	hyperbolic	hyperbolic	ADJ
ejpam-5293	163	16	diffeomorphisms	diffeomorphism	NOUN
ejpam-5293	163	17	and	and	CCONJ
ejpam-5293	163	18	proceed	proceed	VERB
ejpam-5293	163	19	to	to	ADP
ejpam-5293	163	20	its	its	PRON
ejpam-5293	163	21	detailed	detailed	ADJ
ejpam-5293	163	22	proof	proof	NOUN
ejpam-5293	163	23	.	.	PUNCT
ejpam-5293	164	1	lemma	lemma	PROPN
ejpam-5293	164	2	1	1	NUM
ejpam-5293	164	3	.	.	PUNCT
ejpam-5293	165	1	(	(	PUNCT
ejpam-5293	165	2	acl	acl	PROPN
ejpam-5293	165	3	for	for	ADP
ejpam-5293	165	4	hyperbolic	hyperbolic	ADJ
ejpam-5293	165	5	diffeomorphisms	diffeomorphism	NOUN
ejpam-5293	165	6	)	)	PUNCT
ejpam-5293	165	7	given	give	VERB
ejpam-5293	165	8	a	a	DET
ejpam-5293	165	9	riemannian	riemannian	ADJ
ejpam-5293	165	10	manifold	manifold	NOUN
ejpam-5293	165	11	m	m	NOUN
ejpam-5293	165	12	,	,	PUNCT
ejpam-5293	165	13	let	let	VERB
ejpam-5293	165	14	λ	λ	PROPN
ejpam-5293	165	15	⊂	⊂	PROPN
ejpam-5293	165	16	m	m	AUX
ejpam-5293	165	17	be	be	AUX
ejpam-5293	165	18	a	a	DET
ejpam-5293	165	19	compact	compact	ADJ
ejpam-5293	165	20	hyperbolic	hyperbolic	NOUN
ejpam-5293	165	21	set	set	VERB
ejpam-5293	165	22	locally	locally	ADV
ejpam-5293	165	23	maximal	maximal	ADJ
ejpam-5293	165	24	for	for	ADP
ejpam-5293	165	25	the	the	DET
ejpam-5293	165	26	c1	c1	PROPN
ejpam-5293	165	27	diffeomorphism	diffeomorphism	NOUN
ejpam-5293	166	1	f	f	X
ejpam-5293	166	2	:	:	PUNCT
ejpam-5293	166	3	m	m	VERB
ejpam-5293	166	4	→	→	NOUN
ejpam-5293	166	5	m	m	PROPN
ejpam-5293	166	6	.	.	PUNCT
ejpam-5293	167	1	then	then	ADV
ejpam-5293	167	2	,	,	PUNCT
ejpam-5293	167	3	for	for	ADP
ejpam-5293	167	4	all	all	DET
ejpam-5293	167	5	λ	λ	X
ejpam-5293	167	6	∈	∈	PROPN
ejpam-5293	167	7	(	(	PUNCT
ejpam-5293	167	8	0	0	NUM
ejpam-5293	167	9	,	,	PUNCT
ejpam-5293	167	10	1	1	NUM
ejpam-5293	167	11	)	)	PUNCT
ejpam-5293	167	12	sufficiently	sufficiently	ADV
ejpam-5293	167	13	large	large	ADJ
ejpam-5293	167	14	,	,	PUNCT
ejpam-5293	167	15	there	there	PRON
ejpam-5293	167	16	are	be	VERB
ejpam-5293	167	17	an	an	DET
ejpam-5293	167	18	open	open	ADJ
ejpam-5293	167	19	neighborhood	neighborhood	NOUN
ejpam-5293	167	20	v	v	NOUN
ejpam-5293	167	21	of	of	ADP
ejpam-5293	167	22	λ	λ	PROPN
ejpam-5293	167	23	and	and	CCONJ
ejpam-5293	167	24	constants	constant	NOUN
ejpam-5293	167	25	c	c	PROPN
ejpam-5293	167	26	,	,	PUNCT
ejpam-5293	167	27	δ	δ	PROPN
ejpam-5293	167	28	>	>	X
ejpam-5293	167	29	0	0	NUM
ejpam-5293	167	30	such	such	ADJ
ejpam-5293	167	31	that	that	PRON
ejpam-5293	167	32	for	for	ADP
ejpam-5293	167	33	x	x	SYM
ejpam-5293	167	34	∈	∈	PROPN
ejpam-5293	167	35	λ	λ	NOUN
ejpam-5293	167	36	satisfying	satisfy	VERB
ejpam-5293	167	37	d(fnx	d(fnx	PROPN
ejpam-5293	167	38	,	,	PUNCT
ejpam-5293	167	39	x	x	X
ejpam-5293	167	40	)	)	PUNCT
ejpam-5293	167	41	<	<	X
ejpam-5293	167	42	δ	δ	PROPN
ejpam-5293	167	43	there	there	PRON
ejpam-5293	167	44	is	be	VERB
ejpam-5293	167	45	a	a	DET
ejpam-5293	167	46	point	point	NOUN
ejpam-5293	167	47	y	y	PROPN
ejpam-5293	167	48	∈	∈	PROPN
ejpam-5293	167	49	λ	λ	NOUN
ejpam-5293	167	50	such	such	ADJ
ejpam-5293	167	51	that	that	DET
ejpam-5293	167	52	fny	fny	NOUN
ejpam-5293	167	53	=	=	SYM
ejpam-5293	167	54	y	y	PROPN
ejpam-5293	167	55	and	and	CCONJ
ejpam-5293	167	56	is	be	AUX
ejpam-5293	167	57	valid	valid	ADJ
ejpam-5293	167	58	the	the	DET
ejpam-5293	167	59	inequality	inequality	NOUN
ejpam-5293	167	60	d(fkx	d(fkx	VERB
ejpam-5293	167	61	,	,	PUNCT
ejpam-5293	167	62	fky	fky	ADJ
ejpam-5293	167	63	)	)	PUNCT
ejpam-5293	167	64	≤	≤	NUM
ejpam-5293	167	65	cλmin{k	cλmin{k	NOUN
ejpam-5293	167	66	,	,	PUNCT
ejpam-5293	167	67	n−k}d	n−k}d	PROPN
ejpam-5293	167	68	(	(	PUNCT
ejpam-5293	167	69	fnx	fnx	PROPN
ejpam-5293	167	70	,	,	PUNCT
ejpam-5293	167	71	x	x	NOUN
ejpam-5293	167	72	)	)	PUNCT
ejpam-5293	167	73	(	(	PUNCT
ejpam-5293	167	74	5	5	NUM
ejpam-5293	167	75	)	)	PUNCT
ejpam-5293	167	76	for	for	ADP
ejpam-5293	167	77	k	k	PROPN
ejpam-5293	167	78	=	=	SYM
ejpam-5293	167	79	0	0	NUM
ejpam-5293	167	80	,	,	PUNCT
ejpam-5293	167	81	1	1	NUM
ejpam-5293	167	82	,	,	PUNCT
ejpam-5293	167	83	.	.	PUNCT
ejpam-5293	167	84	.	.	PUNCT
ejpam-5293	167	85	.	.	PUNCT
ejpam-5293	168	1	,	,	PUNCT
ejpam-5293	168	2	n.	n.	NOUN
ejpam-5293	168	3	in	in	ADP
ejpam-5293	168	4	what	what	PRON
ejpam-5293	168	5	follows	follow	VERB
ejpam-5293	168	6	,	,	PUNCT
ejpam-5293	168	7	we	we	PRON
ejpam-5293	168	8	present	present	VERB
ejpam-5293	168	9	an	an	DET
ejpam-5293	168	10	outline	outline	NOUN
ejpam-5293	168	11	of	of	ADP
ejpam-5293	168	12	the	the	DET
ejpam-5293	168	13	proof	proof	NOUN
ejpam-5293	168	14	for	for	ADP
ejpam-5293	168	15	m	m	PROPN
ejpam-5293	168	16	=	=	SYM
ejpam-5293	168	17	rn	rn	PROPN
ejpam-5293	168	18	where	where	SCONJ
ejpam-5293	168	19	,	,	PUNCT
ejpam-5293	168	20	excepting	except	VERB
ejpam-5293	168	21	the	the	DET
ejpam-5293	168	22	proof	proof	NOUN
ejpam-5293	168	23	of	of	ADP
ejpam-5293	168	24	inequality	inequality	NOUN
ejpam-5293	168	25	(	(	PUNCT
ejpam-5293	168	26	5	5	NUM
ejpam-5293	168	27	)	)	PUNCT
ejpam-5293	168	28	,	,	PUNCT
ejpam-5293	168	29	the	the	DET
ejpam-5293	168	30	suggestions	suggestion	NOUN
ejpam-5293	168	31	of	of	ADP
ejpam-5293	168	32	katok	katok	NOUN
ejpam-5293	168	33	and	and	CCONJ
ejpam-5293	168	34	hasselblatt	hasselblatt	NOUN
ejpam-5293	168	35	in	in	ADP
ejpam-5293	168	36	[	[	X
ejpam-5293	168	37	6	6	NUM
ejpam-5293	168	38	]	]	PUNCT
ejpam-5293	168	39	are	be	AUX
ejpam-5293	168	40	followed	follow	VERB
ejpam-5293	168	41	.	.	PUNCT
ejpam-5293	169	1	the	the	DET
ejpam-5293	169	2	inequality	inequality	NOUN
ejpam-5293	169	3	(	(	PUNCT
ejpam-5293	169	4	5	5	NUM
ejpam-5293	169	5	)	)	PUNCT
ejpam-5293	169	6	provides	provide	VERB
ejpam-5293	169	7	an	an	DET
ejpam-5293	169	8	important	important	ADJ
ejpam-5293	169	9	quantitative	quantitative	ADJ
ejpam-5293	169	10	data	datum	NOUN
ejpam-5293	169	11	since	since	SCONJ
ejpam-5293	169	12	it	it	PRON
ejpam-5293	169	13	establishes	establish	VERB
ejpam-5293	169	14	how	how	SCONJ
ejpam-5293	169	15	the	the	DET
ejpam-5293	169	16	constructed	construct	VERB
ejpam-5293	169	17	periodic	periodic	ADJ
ejpam-5293	169	18	orbit	orbit	NOUN
ejpam-5293	169	19	differs	differ	VERB
ejpam-5293	169	20	from	from	ADP
ejpam-5293	169	21	the	the	DET
ejpam-5293	169	22	initial	initial	ADJ
ejpam-5293	169	23	orbit	orbit	NOUN
ejpam-5293	169	24	:	:	PUNCT
ejpam-5293	169	25	it	it	PRON
ejpam-5293	169	26	states	state	VERB
ejpam-5293	169	27	how	how	SCONJ
ejpam-5293	169	28	the	the	DET
ejpam-5293	169	29	distance	distance	NOUN
ejpam-5293	169	30	between	between	ADP
ejpam-5293	169	31	corresponding	correspond	VERB
ejpam-5293	169	32	points	point	NOUN
ejpam-5293	169	33	of	of	ADP
ejpam-5293	169	34	the	the	DET
ejpam-5293	169	35	initial	initial	ADJ
ejpam-5293	169	36	orbit	orbit	NOUN
ejpam-5293	169	37	and	and	CCONJ
ejpam-5293	169	38	the	the	DET
ejpam-5293	169	39	constructed	construct	VERB
ejpam-5293	169	40	periodic	periodic	ADJ
ejpam-5293	169	41	orbit	orbit	NOUN
ejpam-5293	169	42	is	be	AUX
ejpam-5293	169	43	controlled	control	VERB
ejpam-5293	169	44	.	.	PUNCT
ejpam-5293	170	1	for	for	ADP
ejpam-5293	170	2	each	each	DET
ejpam-5293	170	3	x	x	SYM
ejpam-5293	170	4	∈	∈	PROPN
ejpam-5293	170	5	λ	λ	X
ejpam-5293	170	6	we	we	PRON
ejpam-5293	170	7	fix	fix	VERB
ejpam-5293	170	8	a	a	DET
ejpam-5293	170	9	local	local	ADJ
ejpam-5293	170	10	coordinate	coordinate	NOUN
ejpam-5293	170	11	system	system	NOUN
ejpam-5293	170	12	in	in	ADP
ejpam-5293	170	13	txm	txm	PROPN
ejpam-5293	170	14	such	such	ADJ
ejpam-5293	170	15	that	that	SCONJ
ejpam-5293	170	16	the	the	DET
ejpam-5293	170	17	decomposition	decomposition	NOUN
ejpam-5293	170	18	eu(x)⊕es(x	eu(x)⊕es(x	NOUN
ejpam-5293	170	19	)	)	PUNCT
ejpam-5293	170	20	is	be	AUX
ejpam-5293	170	21	identified	identify	VERB
ejpam-5293	170	22	with	with	ADP
ejpam-5293	170	23	the	the	DET
ejpam-5293	170	24	decomposition	decomposition	NOUN
ejpam-5293	170	25	rn	rn	NOUN
ejpam-5293	170	26	=	=	PROPN
ejpam-5293	170	27	rl⊕rn−l	rl⊕rn−l	PROPN
ejpam-5293	170	28	and	and	CCONJ
ejpam-5293	170	29	the	the	DET
ejpam-5293	170	30	metric	metric	NOUN
ejpam-5293	170	31	in	in	ADP
ejpam-5293	170	32	txm	txm	PROPN
ejpam-5293	170	33	is	be	AUX
ejpam-5293	170	34	the	the	DET
ejpam-5293	170	35	usual	usual	ADJ
ejpam-5293	170	36	metric	metric	NOUN
ejpam-5293	170	37	in	in	ADP
ejpam-5293	170	38	rn	rn	PROPN
ejpam-5293	170	39	.	.	PROPN
ejpam-5293	171	1	for	for	ADP
ejpam-5293	171	2	each	each	DET
ejpam-5293	171	3	x	x	SYM
ejpam-5293	171	4	∈	∈	PROPN
ejpam-5293	171	5	λ	λ	NOUN
ejpam-5293	171	6	there	there	PRON
ejpam-5293	171	7	is	be	VERB
ejpam-5293	171	8	an	an	DET
ejpam-5293	171	9	open	open	ADJ
ejpam-5293	171	10	neighborhood	neighborhood	NOUN
ejpam-5293	171	11	vfkx	vfkx	NOUN
ejpam-5293	171	12	of	of	ADP
ejpam-5293	171	13	fkx	fkx	PROPN
ejpam-5293	171	14	for	for	ADP
ejpam-5293	171	15	each	each	DET
ejpam-5293	171	16	k	k	PROPN
ejpam-5293	171	17	∈	∈	PROPN
ejpam-5293	171	18	z	z	NOUN
ejpam-5293	171	19	such	such	ADJ
ejpam-5293	171	20	that	that	SCONJ
ejpam-5293	171	21	f	f	PROPN
ejpam-5293	171	22	∣∣vfkx	∣∣vfkx	PROPN
ejpam-5293	171	23	can	can	AUX
ejpam-5293	171	24	be	be	AUX
ejpam-5293	171	25	written	write	VERB
ejpam-5293	171	26	as	as	ADP
ejpam-5293	171	27	fk(u	fk(u	NOUN
ejpam-5293	171	28	,	,	PUNCT
ejpam-5293	171	29	v	v	NOUN
ejpam-5293	171	30	)	)	PUNCT
ejpam-5293	172	1	=	=	SYM
ejpam-5293	172	2	(	(	PUNCT
ejpam-5293	172	3	aku+ak(u	aku+ak(u	X
ejpam-5293	172	4	,	,	PUNCT
ejpam-5293	172	5	v	v	NOUN
ejpam-5293	172	6	)	)	PUNCT
ejpam-5293	172	7	,	,	PUNCT
ejpam-5293	172	8	bkv	bkv	PROPN
ejpam-5293	172	9	+	+	X
ejpam-5293	172	10	βk(u	βk(u	NUM
ejpam-5293	172	11	,	,	PUNCT
ejpam-5293	172	12	v	v	NOUN
ejpam-5293	172	13	)	)	PUNCT
ejpam-5293	172	14	)	)	PUNCT
ejpam-5293	172	15	where	where	SCONJ
ejpam-5293	172	16	ak	ak	PROPN
ejpam-5293	172	17	:	:	PUNCT
ejpam-5293	172	18	rl	rl	PROPN
ejpam-5293	172	19	→	→	SYM
ejpam-5293	172	20	rl	rl	X
ejpam-5293	172	21	and	and	CCONJ
ejpam-5293	172	22	bk	bk	VERB
ejpam-5293	172	23	:	:	PUNCT
ejpam-5293	172	24	rn−l	rn−l	PROPN
ejpam-5293	172	25	→	→	SYM
ejpam-5293	172	26	rn−l	rn−l	PROPN
ejpam-5293	172	27	are	be	AUX
ejpam-5293	172	28	linear	linear	PROPN
ejpam-5293	172	29	maps	map	NOUN
ejpam-5293	172	30	defined	define	VERB
ejpam-5293	172	31	by	by	ADP
ejpam-5293	172	32	ak	ak	PROPN
ejpam-5293	172	33	=	=	PUNCT
ejpam-5293	172	34	dfkxf	dfkxf	NOUN
ejpam-5293	172	35	|eu(fkx	|eu(fkx	NOUN
ejpam-5293	172	36	)	)	PUNCT
ejpam-5293	172	37	and	and	CCONJ
ejpam-5293	172	38	bk	bk	VERB
ejpam-5293	172	39	=	=	SYM
ejpam-5293	172	40	dfkxf	dfkxf	ADJ
ejpam-5293	172	41	|es(fkx	|es(fkx	PROPN
ejpam-5293	172	42	)	)	PUNCT
ejpam-5293	172	43	.	.	PUNCT
ejpam-5293	173	1	redefining	redefine	VERB
ejpam-5293	173	2	the	the	DET
ejpam-5293	173	3	norms	norm	NOUN
ejpam-5293	173	4	on	on	ADP
ejpam-5293	173	5	the	the	DET
ejpam-5293	173	6	stable	stable	ADJ
ejpam-5293	173	7	and	and	CCONJ
ejpam-5293	173	8	unstable	unstable	ADJ
ejpam-5293	173	9	bundles	bundle	NOUN
ejpam-5293	173	10	(	(	PUNCT
ejpam-5293	173	11	see	see	VERB
ejpam-5293	173	12	[	[	X
ejpam-5293	173	13	17	17	NUM
ejpam-5293	173	14	]	]	NUM
ejpam-5293	173	15	)	)	PUNCT
ejpam-5293	173	16	,	,	PUNCT
ejpam-5293	173	17	we	we	PRON
ejpam-5293	173	18	can	can	AUX
ejpam-5293	173	19	suppose	suppose	VERB
ejpam-5293	173	20	that	that	SCONJ
ejpam-5293	173	21	c	c	NOUN
ejpam-5293	173	22	=	=	SYM
ejpam-5293	173	23	1	1	NUM
ejpam-5293	173	24	in	in	ADP
ejpam-5293	173	25	the	the	DET
ejpam-5293	173	26	definition	definition	NOUN
ejpam-5293	173	27	of	of	ADP
ejpam-5293	173	28	the	the	DET
ejpam-5293	173	29	hyperbolic	hyperbolic	ADJ
ejpam-5293	173	30	set	set	NOUN
ejpam-5293	173	31	,	,	PUNCT
ejpam-5293	173	32	there	there	PRON
ejpam-5293	173	33	is	be	VERB
ejpam-5293	173	34	τ	τ	PROPN
ejpam-5293	173	35	′	′	NUM
ejpam-5293	173	36	∈	∈	PROPN
ejpam-5293	173	37	(	(	PUNCT
ejpam-5293	173	38	τ	τ	PROPN
ejpam-5293	173	39	,	,	PUNCT
ejpam-5293	173	40	1	1	NUM
ejpam-5293	173	41	)	)	PUNCT
ejpam-5293	174	1	such	such	ADJ
ejpam-5293	174	2	that∥∥a−1	that∥∥a−1	X
ejpam-5293	174	3	k	k	X
ejpam-5293	174	4	∥∥	∥∥	PROPN
ejpam-5293	174	5	≤	≤	ADV
ejpam-5293	174	6	τ	τ	X
ejpam-5293	174	7	′	′	NUM
ejpam-5293	174	8	and	and	CCONJ
ejpam-5293	174	9	∥bk∥	∥bk∥	VERB
ejpam-5293	174	10	≤	≤	NUM
ejpam-5293	174	11	τ	τ	X
ejpam-5293	174	12	′	′	NUM
ejpam-5293	174	13	(	(	PUNCT
ejpam-5293	174	14	6	6	NUM
ejpam-5293	174	15	)	)	PUNCT
ejpam-5293	174	16	r.	r.	PROPN
ejpam-5293	174	17	d.	d.	PROPN
ejpam-5293	174	18	laureano	laureano	PROPN
ejpam-5293	174	19	/	/	SYM
ejpam-5293	174	20	eur	eur	PROPN
ejpam-5293	174	21	.	.	PUNCT
ejpam-5293	175	1	j.	j.	PROPN
ejpam-5293	175	2	pure	pure	PROPN
ejpam-5293	175	3	appl	appl	PROPN
ejpam-5293	175	4	.	.	PROPN
ejpam-5293	175	5	math	math	PROPN
ejpam-5293	175	6	,	,	PUNCT
ejpam-5293	175	7	17	17	NUM
ejpam-5293	175	8	(	(	PUNCT
ejpam-5293	175	9	3	3	NUM
ejpam-5293	175	10	)	)	PUNCT
ejpam-5293	175	11	(	(	PUNCT
ejpam-5293	175	12	2024	2024	NUM
ejpam-5293	175	13	)	)	PUNCT
ejpam-5293	175	14	,	,	PUNCT
ejpam-5293	175	15	1403	1403	NUM
ejpam-5293	175	16	-	-	SYM
ejpam-5293	175	17	1416	1416	NUM
ejpam-5293	175	18	1411	1411	NUM
ejpam-5293	175	19	for	for	ADP
ejpam-5293	175	20	all	all	DET
ejpam-5293	175	21	k	k	PROPN
ejpam-5293	175	22	∈	∈	PROPN
ejpam-5293	175	23	z	z	NOUN
ejpam-5293	175	24	(	(	PUNCT
ejpam-5293	175	25	when	when	SCONJ
ejpam-5293	175	26	c	c	X
ejpam-5293	175	27	>	>	X
ejpam-5293	175	28	1	1	NUM
ejpam-5293	175	29	we	we	PRON
ejpam-5293	175	30	can	can	AUX
ejpam-5293	175	31	remake	remake	VERB
ejpam-5293	175	32	the	the	DET
ejpam-5293	175	33	proof	proof	NOUN
ejpam-5293	175	34	with	with	ADP
ejpam-5293	175	35	minor	minor	ADJ
ejpam-5293	175	36	changes	change	NOUN
ejpam-5293	175	37	)	)	PUNCT
ejpam-5293	175	38	.	.	PUNCT
ejpam-5293	176	1	in	in	ADP
ejpam-5293	176	2	addition	addition	NOUN
ejpam-5293	176	3	,	,	PUNCT
ejpam-5293	176	4	eventually	eventually	ADV
ejpam-5293	176	5	by	by	ADP
ejpam-5293	176	6	further	further	ADJ
ejpam-5293	176	7	choice	choice	NOUN
ejpam-5293	176	8	of	of	ADP
ejpam-5293	176	9	vfkx	vfkx	NOUN
ejpam-5293	176	10	,	,	PUNCT
ejpam-5293	176	11	we	we	PRON
ejpam-5293	176	12	can	can	AUX
ejpam-5293	176	13	guarantee	guarantee	VERB
ejpam-5293	176	14	that	that	PRON
ejpam-5293	176	15	exists	exist	VERB
ejpam-5293	176	16	ε	ε	PROPN
ejpam-5293	176	17	<	<	X
ejpam-5293	176	18	d(fnx	d(fnx	PROPN
ejpam-5293	176	19	,	,	PUNCT
ejpam-5293	176	20	x	x	X
ejpam-5293	176	21	)	)	PUNCT
ejpam-5293	176	22	such	such	ADJ
ejpam-5293	176	23	that	that	SCONJ
ejpam-5293	176	24	∥ak∥c1	∥ak∥c1	VERB
ejpam-5293	176	25	<	<	X
ejpam-5293	176	26	ε	ε	PROPN
ejpam-5293	176	27	and	and	CCONJ
ejpam-5293	176	28	∥βk∥c1	∥βk∥c1	X
ejpam-5293	176	29	<	<	X
ejpam-5293	176	30	ε	ε	PROPN
ejpam-5293	176	31	(	(	PUNCT
ejpam-5293	176	32	7	7	NUM
ejpam-5293	176	33	)	)	PUNCT
ejpam-5293	176	34	for	for	ADP
ejpam-5293	176	35	all	all	DET
ejpam-5293	176	36	k	k	PROPN
ejpam-5293	176	37	∈	∈	PROPN
ejpam-5293	176	38	z.	z.	PROPN
ejpam-5293	176	39	note	note	VERB
ejpam-5293	176	40	that	that	SCONJ
ejpam-5293	176	41	the	the	DET
ejpam-5293	176	42	points	point	NOUN
ejpam-5293	176	43	(	(	PUNCT
ejpam-5293	176	44	uk	uk	PROPN
ejpam-5293	176	45	,	,	PUNCT
ejpam-5293	176	46	vk	vk	NOUN
ejpam-5293	176	47	)	)	PUNCT
ejpam-5293	176	48	∈	∈	NOUN
ejpam-5293	176	49	vfkx	vfkx	NOUN
ejpam-5293	176	50	for	for	ADP
ejpam-5293	176	51	k	k	PROPN
ejpam-5293	176	52	=	=	SYM
ejpam-5293	176	53	0	0	NUM
ejpam-5293	176	54	,	,	PUNCT
ejpam-5293	176	55	1	1	NUM
ejpam-5293	176	56	,	,	PUNCT
ejpam-5293	176	57	.	.	PUNCT
ejpam-5293	176	58	.	.	PUNCT
ejpam-5293	176	59	.	.	PUNCT
ejpam-5293	177	1	,	,	PUNCT
ejpam-5293	177	2	n	n	CCONJ
ejpam-5293	177	3	−	−	PROPN
ejpam-5293	177	4	1	1	NUM
ejpam-5293	177	5	constitute	constitute	VERB
ejpam-5293	177	6	a	a	DET
ejpam-5293	177	7	n	n	NOUN
ejpam-5293	177	8	-	-	PUNCT
ejpam-5293	177	9	periodic	periodic	ADJ
ejpam-5293	177	10	orbit	orbit	NOUN
ejpam-5293	177	11	of	of	ADP
ejpam-5293	177	12	f	f	PROPN
ejpam-5293	177	13	if	if	SCONJ
ejpam-5293	178	1	and	and	CCONJ
ejpam-5293	178	2	only	only	ADV
ejpam-5293	178	3	if	if	SCONJ
ejpam-5293	178	4	(	(	PUNCT
ejpam-5293	178	5	u	u	NOUN
ejpam-5293	178	6	,	,	PUNCT
ejpam-5293	178	7	v	v	NOUN
ejpam-5293	178	8	)	)	PUNCT
ejpam-5293	178	9	=	=	SYM
ejpam-5293	178	10	(	(	PUNCT
ejpam-5293	178	11	(	(	PUNCT
ejpam-5293	178	12	u0	u0	ADJ
ejpam-5293	178	13	,	,	PUNCT
ejpam-5293	178	14	v0	v0	PROPN
ejpam-5293	178	15	)	)	PUNCT
ejpam-5293	178	16	,	,	PUNCT
ejpam-5293	178	17	(	(	PUNCT
ejpam-5293	178	18	u1	u1	NOUN
ejpam-5293	178	19	,	,	PUNCT
ejpam-5293	178	20	v1	v1	NOUN
ejpam-5293	178	21	)	)	PUNCT
ejpam-5293	178	22	,	,	PUNCT
ejpam-5293	178	23	.	.	PUNCT
ejpam-5293	178	24	.	.	PUNCT
ejpam-5293	178	25	.	.	PUNCT
ejpam-5293	179	1	,	,	PUNCT
ejpam-5293	179	2	(	(	PUNCT
ejpam-5293	179	3	un−1	un−1	PROPN
ejpam-5293	179	4	,	,	PUNCT
ejpam-5293	179	5	vn−1	vn−1	ADJ
ejpam-5293	179	6	)	)	PUNCT
ejpam-5293	179	7	)	)	PUNCT
ejpam-5293	179	8	is	be	AUX
ejpam-5293	179	9	a	a	DET
ejpam-5293	179	10	fixed	fix	VERB
ejpam-5293	179	11	point	point	NOUN
ejpam-5293	179	12	of	of	ADP
ejpam-5293	179	13	the	the	DET
ejpam-5293	179	14	map	map	NOUN
ejpam-5293	180	1	f	f	X
ejpam-5293	180	2	:	:	PUNCT
ejpam-5293	180	3	rn	rn	PROPN
ejpam-5293	180	4	→	→	SYM
ejpam-5293	180	5	rn	rn	PROPN
ejpam-5293	180	6	,	,	PUNCT
ejpam-5293	180	7	where	where	SCONJ
ejpam-5293	180	8	n	n	NOUN
ejpam-5293	180	9	=	=	SYM
ejpam-5293	180	10	n	n	PRON
ejpam-5293	180	11	dimm	dimm	NOUN
ejpam-5293	180	12	,	,	PUNCT
ejpam-5293	180	13	given	give	VERB
ejpam-5293	180	14	by	by	ADP
ejpam-5293	180	15	f	f	PROPN
ejpam-5293	180	16	(	(	PUNCT
ejpam-5293	180	17	u	u	NOUN
ejpam-5293	180	18	,	,	PUNCT
ejpam-5293	180	19	v	v	NOUN
ejpam-5293	180	20	)	)	PUNCT
ejpam-5293	180	21	=	=	SYM
ejpam-5293	180	22	(	(	PUNCT
ejpam-5293	180	23	fn−1	fn−1	PROPN
ejpam-5293	180	24	(	(	PUNCT
ejpam-5293	180	25	un−1	un−1	PROPN
ejpam-5293	180	26	,	,	PUNCT
ejpam-5293	180	27	vn−1	vn−1	ADJ
ejpam-5293	180	28	)	)	PUNCT
ejpam-5293	180	29	,	,	PUNCT
ejpam-5293	180	30	f0	f0	PROPN
ejpam-5293	180	31	(	(	PUNCT
ejpam-5293	180	32	u0	u0	PROPN
ejpam-5293	180	33	,	,	PUNCT
ejpam-5293	180	34	v0	v0	PROPN
ejpam-5293	180	35	)	)	PUNCT
ejpam-5293	180	36	,	,	PUNCT
ejpam-5293	180	37	.	.	PUNCT
ejpam-5293	180	38	.	.	PUNCT
ejpam-5293	180	39	.	.	PUNCT
ejpam-5293	181	1	,	,	PUNCT
ejpam-5293	181	2	fn−2	fn−2	PROPN
ejpam-5293	181	3	(	(	PUNCT
ejpam-5293	181	4	un−2	un−2	PROPN
ejpam-5293	181	5	,	,	PUNCT
ejpam-5293	181	6	vn−2	vn−2	PROPN
ejpam-5293	181	7	)	)	PUNCT
ejpam-5293	181	8	)	)	PUNCT
ejpam-5293	181	9	.	.	PUNCT
ejpam-5293	182	1	we	we	PRON
ejpam-5293	182	2	write	write	VERB
ejpam-5293	182	3	f	f	PROPN
ejpam-5293	182	4	as	as	ADP
ejpam-5293	182	5	f	f	PROPN
ejpam-5293	182	6	(	(	PUNCT
ejpam-5293	182	7	u	u	NOUN
ejpam-5293	182	8	,	,	PUNCT
ejpam-5293	182	9	v	v	NOUN
ejpam-5293	182	10	)	)	PUNCT
ejpam-5293	182	11	=	=	SYM
ejpam-5293	183	1	l(u	l(u	PROPN
ejpam-5293	183	2	,	,	PUNCT
ejpam-5293	183	3	v	v	NOUN
ejpam-5293	183	4	)	)	PUNCT
ejpam-5293	184	1	+	+	ADJ
ejpam-5293	184	2	g(u	g(u	PROPN
ejpam-5293	184	3	,	,	PUNCT
ejpam-5293	184	4	v	v	NOUN
ejpam-5293	184	5	)	)	PUNCT
ejpam-5293	184	6	where	where	SCONJ
ejpam-5293	184	7	l(u	l(u	PROPN
ejpam-5293	184	8	,	,	PUNCT
ejpam-5293	184	9	v	v	NOUN
ejpam-5293	184	10	)	)	PUNCT
ejpam-5293	184	11	is	be	AUX
ejpam-5293	184	12	given	give	VERB
ejpam-5293	184	13	by	by	ADP
ejpam-5293	184	14	(	(	PUNCT
ejpam-5293	184	15	(	(	PUNCT
ejpam-5293	184	16	an−1un−1	an−1un−1	PROPN
ejpam-5293	184	17	,	,	PUNCT
ejpam-5293	184	18	bn−1vn−1	bn−1vn−1	NOUN
ejpam-5293	184	19	)	)	PUNCT
ejpam-5293	184	20	,	,	PUNCT
ejpam-5293	184	21	(	(	PUNCT
ejpam-5293	184	22	a0u0	a0u0	PROPN
ejpam-5293	184	23	,	,	PUNCT
ejpam-5293	184	24	b0v0	b0v0	NOUN
ejpam-5293	184	25	)	)	PUNCT
ejpam-5293	184	26	,	,	PUNCT
ejpam-5293	184	27	.	.	PUNCT
ejpam-5293	184	28	.	.	PUNCT
ejpam-5293	184	29	.	.	PUNCT
ejpam-5293	185	1	,	,	PUNCT
ejpam-5293	185	2	(	(	PUNCT
ejpam-5293	185	3	an−2un−2	an−2un−2	PROPN
ejpam-5293	185	4	,	,	PUNCT
ejpam-5293	185	5	bn−2vn−2	bn−2vn−2	NOUN
ejpam-5293	185	6	)	)	PUNCT
ejpam-5293	185	7	)	)	PUNCT
ejpam-5293	185	8	.	.	PUNCT
ejpam-5293	186	1	it	it	PRON
ejpam-5293	186	2	follows	follow	VERB
ejpam-5293	186	3	from	from	ADP
ejpam-5293	186	4	(	(	PUNCT
ejpam-5293	186	5	7	7	NUM
ejpam-5293	186	6	)	)	PUNCT
ejpam-5293	186	7	that∥∥g(u	that∥∥g(u	NOUN
ejpam-5293	186	8	,	,	PUNCT
ejpam-5293	186	9	v)−g(u′	v)−g(u′	NOUN
ejpam-5293	186	10	,	,	PUNCT
ejpam-5293	186	11	v′	v′	PROPN
ejpam-5293	186	12	)	)	PUNCT
ejpam-5293	186	13	∥∥	∥∥	PROPN
ejpam-5293	186	14	≤	≤	NUM
ejpam-5293	186	15	ε	ε	PROPN
ejpam-5293	186	16	∥∥(u	∥∥(u	PROPN
ejpam-5293	186	17	,	,	PUNCT
ejpam-5293	186	18	v)−	v)−	PROPN
ejpam-5293	186	19	(	(	PUNCT
ejpam-5293	186	20	u′	u′	PROPN
ejpam-5293	186	21	,	,	PUNCT
ejpam-5293	186	22	v′	v′	PROPN
ejpam-5293	186	23	)	)	PUNCT
ejpam-5293	186	24	∥∥	∥∥	X
ejpam-5293	187	1	(	(	PUNCT
ejpam-5293	187	2	8)	8)	NUM
ejpam-5293	187	3	with	with	ADP
ejpam-5293	187	4	the	the	DET
ejpam-5293	187	5	norm	norm	NOUN
ejpam-5293	187	6	∥(u	∥(u	NOUN
ejpam-5293	187	7	,	,	PUNCT
ejpam-5293	187	8	v)∥	v)∥	PUNCT
ejpam-5293	188	1	=	=	SYM
ejpam-5293	188	2	max	max	PROPN
ejpam-5293	188	3	{	{	PUNCT
ejpam-5293	188	4	|u|	|u|	PROPN
ejpam-5293	188	5	,	,	PUNCT
ejpam-5293	188	6	|v|	|v|	PROPN
ejpam-5293	188	7	}	}	PUNCT
ejpam-5293	188	8	.	.	PUNCT
ejpam-5293	189	1	on	on	ADP
ejpam-5293	189	2	the	the	DET
ejpam-5293	189	3	other	other	ADJ
ejpam-5293	189	4	hand	hand	NOUN
ejpam-5293	189	5	,	,	PUNCT
ejpam-5293	189	6	it	it	PRON
ejpam-5293	189	7	follows	follow	VERB
ejpam-5293	189	8	from	from	ADP
ejpam-5293	189	9	(	(	PUNCT
ejpam-5293	189	10	6	6	NUM
ejpam-5293	189	11	)	)	PUNCT
ejpam-5293	189	12	that	that	SCONJ
ejpam-5293	189	13	the	the	DET
ejpam-5293	189	14	matrix	matrix	NOUN
ejpam-5293	189	15	l−	l−	NOUN
ejpam-5293	189	16	i	i	PROPN
ejpam-5293	189	17	d	d	PROPN
ejpam-5293	189	18	is	be	AUX
ejpam-5293	189	19	invertible	invertible	ADJ
ejpam-5293	189	20	.	.	PUNCT
ejpam-5293	190	1	by	by	ADP
ejpam-5293	190	2	using	use	VERB
ejpam-5293	190	3	the	the	DET
ejpam-5293	190	4	decomposition	decomposition	NOUN
ejpam-5293	190	5	(	(	PUNCT
ejpam-5293	190	6	l−	l−	NOUN
ejpam-5293	190	7	id)−1	id)−1	NOUN
ejpam-5293	190	8	=	=	PUNCT
ejpam-5293	190	9	(	(	PUNCT
ejpam-5293	190	10	(	(	PUNCT
ejpam-5293	190	11	l−	l−	NOUN
ejpam-5293	190	12	id)−1|es	id)−1|es	X
ejpam-5293	190	13	,	,	PUNCT
ejpam-5293	190	14	l	l	PROPN
ejpam-5293	191	1	−1(id−	−1(id−	X
ejpam-5293	191	2	l−1)−1|eu	l−1)−1|eu	NOUN
ejpam-5293	191	3	)	)	PUNCT
ejpam-5293	191	4	we	we	PRON
ejpam-5293	191	5	obtain	obtain	VERB
ejpam-5293	191	6	∥(l−	∥(l−	NOUN
ejpam-5293	191	7	id)−1∥	id)−1∥	ADJ
ejpam-5293	191	8	=	=	PROPN
ejpam-5293	191	9	∥(l−	∥(l−	NOUN
ejpam-5293	191	10	id)−1|es∥+	id)−1|es∥+	X
ejpam-5293	191	11	∥l−1(id−	∥l−1(id−	X
ejpam-5293	191	12	l−1)−1|eu∥	l−1)−1|eu∥	NOUN
ejpam-5293	191	13	≤	≤	NUM
ejpam-5293	191	14	1	1	NUM
ejpam-5293	191	15	1−	1−	NUM
ejpam-5293	191	16	∥l|es∥	∥l|es∥	NOUN
ejpam-5293	191	17	+	+	CCONJ
ejpam-5293	191	18	∥l−1|eu∥	∥l−1|eu∥	PROPN
ejpam-5293	191	19	1−	1−	NUM
ejpam-5293	191	20	∥l−1|eu∥	∥l−1|eu∥	PROPN
ejpam-5293	191	21	and	and	CCONJ
ejpam-5293	191	22	then	then	ADV
ejpam-5293	191	23	∥	∥	PRON
ejpam-5293	191	24	(	(	PUNCT
ejpam-5293	191	25	l−	l−	NOUN
ejpam-5293	191	26	id)−1	id)−1	VERB
ejpam-5293	191	27	∥	∥	PUNCT
ejpam-5293	191	28	≤	≤	ADJ
ejpam-5293	191	29	c1	c1	NOUN
ejpam-5293	191	30	(	(	PUNCT
ejpam-5293	191	31	9	9	NUM
ejpam-5293	191	32	)	)	PUNCT
ejpam-5293	191	33	for	for	ADP
ejpam-5293	191	34	some	some	DET
ejpam-5293	191	35	constant	constant	ADJ
ejpam-5293	191	36	c1	c1	NOUN
ejpam-5293	191	37	>	>	X
ejpam-5293	191	38	0	0	PUNCT
ejpam-5293	192	1	that	that	PRON
ejpam-5293	192	2	only	only	ADV
ejpam-5293	192	3	depend	depend	VERB
ejpam-5293	192	4	on	on	ADP
ejpam-5293	192	5	τ	τ	PROPN
ejpam-5293	192	6	.	.	PUNCT
ejpam-5293	193	1	so	so	ADV
ejpam-5293	193	2	,	,	PUNCT
ejpam-5293	193	3	the	the	DET
ejpam-5293	193	4	solutions	solution	NOUN
ejpam-5293	193	5	of	of	ADP
ejpam-5293	193	6	f	f	PROPN
ejpam-5293	193	7	(	(	PUNCT
ejpam-5293	193	8	z	z	NOUN
ejpam-5293	193	9	)	)	PUNCT
ejpam-5293	193	10	=	=	NOUN
ejpam-5293	194	1	z	z	NOUN
ejpam-5293	194	2	are	be	AUX
ejpam-5293	194	3	precisely	precisely	ADV
ejpam-5293	194	4	the	the	DET
ejpam-5293	194	5	solutions	solution	NOUN
ejpam-5293	194	6	of	of	ADP
ejpam-5293	194	7	f	f	PROPN
ejpam-5293	194	8	(	(	PUNCT
ejpam-5293	194	9	z	z	NOUN
ejpam-5293	194	10	)	)	PUNCT
ejpam-5293	194	11	=	=	SYM
ejpam-5293	194	12	z	z	NOUN
ejpam-5293	194	13	where	where	SCONJ
ejpam-5293	194	14	f	f	PROPN
ejpam-5293	194	15	(	(	PUNCT
ejpam-5293	194	16	z	z	NOUN
ejpam-5293	194	17	)	)	PUNCT
ejpam-5293	194	18	=	=	SYM
ejpam-5293	194	19	−	−	PROPN
ejpam-5293	194	20	(	(	PUNCT
ejpam-5293	194	21	l−	l−	NOUN
ejpam-5293	194	22	id)−1g(z	id)−1g(z	PROPN
ejpam-5293	194	23	)	)	PUNCT
ejpam-5293	194	24	.	.	PUNCT
ejpam-5293	195	1	it	it	PRON
ejpam-5293	195	2	follows	follow	VERB
ejpam-5293	195	3	from	from	ADP
ejpam-5293	195	4	(	(	PUNCT
ejpam-5293	195	5	8)	8)	NUM
ejpam-5293	195	6	and	and	CCONJ
ejpam-5293	195	7	(	(	PUNCT
ejpam-5293	195	8	9	9	NUM
ejpam-5293	195	9	)	)	PUNCT
ejpam-5293	195	10	that	that	PRON
ejpam-5293	195	11	∥f(z)−f(z′)∥	∥f(z)−f(z′)∥	NOUN
ejpam-5293	195	12	≤	≤	ADV
ejpam-5293	195	13	c1ε∥z	c1ε∥z	ADV
ejpam-5293	195	14	−	−	PROPN
ejpam-5293	195	15	z′∥.	z′∥.	NOUN
ejpam-5293	195	16	(	(	PUNCT
ejpam-5293	195	17	10	10	NUM
ejpam-5293	195	18	)	)	PUNCT
ejpam-5293	195	19	taking	take	VERB
ejpam-5293	195	20	ε	ε	PROPN
ejpam-5293	195	21	small	small	ADJ
ejpam-5293	195	22	enough	enough	ADV
ejpam-5293	195	23	we	we	PRON
ejpam-5293	195	24	obtain	obtain	VERB
ejpam-5293	195	25	c1ε	c1ε	NOUN
ejpam-5293	195	26	<	<	X
ejpam-5293	195	27	1	1	NUM
ejpam-5293	195	28	that	that	PRON
ejpam-5293	195	29	allows	allow	VERB
ejpam-5293	195	30	to	to	PART
ejpam-5293	195	31	conclude	conclude	VERB
ejpam-5293	195	32	that	that	PRON
ejpam-5293	195	33	f	f	PROPN
ejpam-5293	195	34	:	:	PUNCT
ejpam-5293	195	35	rn	rn	PROPN
ejpam-5293	195	36	→	→	PROPN
ejpam-5293	195	37	rn	rn	PROPN
ejpam-5293	195	38	is	be	AUX
ejpam-5293	195	39	a	a	DET
ejpam-5293	195	40	contraction	contraction	NOUN
ejpam-5293	195	41	.	.	PUNCT
ejpam-5293	196	1	by	by	ADP
ejpam-5293	196	2	the	the	DET
ejpam-5293	196	3	contraction	contraction	NOUN
ejpam-5293	196	4	mapping	mapping	NOUN
ejpam-5293	196	5	principle	principle	NOUN
ejpam-5293	196	6	there	there	PRON
ejpam-5293	196	7	is	be	VERB
ejpam-5293	196	8	a	a	DET
ejpam-5293	196	9	unique	unique	ADJ
ejpam-5293	196	10	fixed	fix	VERB
ejpam-5293	196	11	point	point	NOUN
ejpam-5293	196	12	y0	y0	PROPN
ejpam-5293	196	13	∈	∈	PROPN
ejpam-5293	196	14	rn	rn	NOUN
ejpam-5293	196	15	of	of	ADP
ejpam-5293	196	16	f	f	PROPN
ejpam-5293	196	17	.	.	PUNCT
ejpam-5293	197	1	in	in	ADP
ejpam-5293	197	2	addition	addition	NOUN
ejpam-5293	197	3	,	,	PUNCT
ejpam-5293	197	4	y0	y0	NOUN
ejpam-5293	197	5	=	=	SYM
ejpam-5293	197	6	limk→+∞fk	limk→+∞fk	PRON
ejpam-5293	197	7	(	(	PUNCT
ejpam-5293	197	8	s	s	NOUN
ejpam-5293	197	9	)	)	PUNCT
ejpam-5293	197	10	where	where	SCONJ
ejpam-5293	197	11	s	s	VERB
ejpam-5293	197	12	=	=	SYM
ejpam-5293	197	13	(	(	PUNCT
ejpam-5293	197	14	x	x	NOUN
ejpam-5293	197	15	,	,	PUNCT
ejpam-5293	197	16	fx	fx	PROPN
ejpam-5293	197	17	,	,	PUNCT
ejpam-5293	197	18	.	.	PUNCT
ejpam-5293	197	19	.	.	PUNCT
ejpam-5293	197	20	.	.	PUNCT
ejpam-5293	198	1	,	,	PUNCT
ejpam-5293	198	2	fn−1x	fn−1x	NUM
ejpam-5293	198	3	)	)	PUNCT
ejpam-5293	198	4	.	.	PUNCT
ejpam-5293	199	1	so	so	ADV
ejpam-5293	199	2	we	we	PRON
ejpam-5293	199	3	have	have	VERB
ejpam-5293	199	4	∥y0	∥y0	NOUN
ejpam-5293	199	5	−	−	PROPN
ejpam-5293	199	6	s∥	s∥	VERB
ejpam-5293	199	7	≤	≤	NOUN
ejpam-5293	199	8	∞∑	∞∑	NUM
ejpam-5293	199	9	k=1	k=1	ADP
ejpam-5293	199	10	∥fk(s)−fk−1(s)∥.	∥fk(s)−fk−1(s)∥.	NUM
ejpam-5293	199	11	from	from	ADP
ejpam-5293	199	12	(	(	PUNCT
ejpam-5293	199	13	10	10	NUM
ejpam-5293	199	14	)	)	PUNCT
ejpam-5293	199	15	we	we	PRON
ejpam-5293	199	16	obtain	obtain	VERB
ejpam-5293	199	17	∥fk(s)−fk−1(s)∥	∥fk(s)−fk−1(s)∥	ADJ
ejpam-5293	199	18	≤	≤	NOUN
ejpam-5293	199	19	(	(	PUNCT
ejpam-5293	199	20	c1ε	c1ε	NOUN
ejpam-5293	199	21	)	)	PUNCT
ejpam-5293	199	22	k−1∥f(s)−	k−1∥f(s)−	NOUN
ejpam-5293	199	23	s∥	s∥	NOUN
ejpam-5293	199	24	,	,	PUNCT
ejpam-5293	199	25	and	and	CCONJ
ejpam-5293	199	26	hence	hence	ADV
ejpam-5293	199	27	∥y0	∥y0	AUX
ejpam-5293	199	28	−	−	NOUN
ejpam-5293	199	29	s∥	s∥	VERB
ejpam-5293	199	30	≤	≤	NOUN
ejpam-5293	199	31	∞∑	∞∑	NUM
ejpam-5293	199	32	k=1	k=1	PUNCT
ejpam-5293	199	33	∥fk(s)−fk−1(s)∥	∥fk(s)−fk−1(s)∥	NOUN
ejpam-5293	199	34	≤	≤	PROPN
ejpam-5293	200	1	∥f	∥f	PROPN
ejpam-5293	200	2	(	(	PUNCT
ejpam-5293	200	3	s)−	s)−	PROPN
ejpam-5293	200	4	s∥	s∥	NOUN
ejpam-5293	200	5	∞∑	∞∑	NUM
ejpam-5293	200	6	k=1	k=1	X
ejpam-5293	200	7	(	(	PUNCT
ejpam-5293	200	8	c1ε	c1ε	ADJ
ejpam-5293	200	9	)	)	PUNCT
ejpam-5293	200	10	k−1	k−1	PROPN
ejpam-5293	200	11	.	.	PUNCT
ejpam-5293	201	1	r.	r.	PROPN
ejpam-5293	201	2	d.	d.	PROPN
ejpam-5293	201	3	laureano	laureano	PROPN
ejpam-5293	201	4	/	/	SYM
ejpam-5293	201	5	eur	eur	PROPN
ejpam-5293	201	6	.	.	PUNCT
ejpam-5293	202	1	j.	j.	PROPN
ejpam-5293	202	2	pure	pure	PROPN
ejpam-5293	202	3	appl	appl	PROPN
ejpam-5293	202	4	.	.	PROPN
ejpam-5293	202	5	math	math	PROPN
ejpam-5293	202	6	,	,	PUNCT
ejpam-5293	202	7	17	17	NUM
ejpam-5293	202	8	(	(	PUNCT
ejpam-5293	202	9	3	3	NUM
ejpam-5293	202	10	)	)	PUNCT
ejpam-5293	202	11	(	(	PUNCT
ejpam-5293	202	12	2024	2024	NUM
ejpam-5293	202	13	)	)	PUNCT
ejpam-5293	202	14	,	,	PUNCT
ejpam-5293	202	15	1403	1403	NUM
ejpam-5293	202	16	-	-	SYM
ejpam-5293	202	17	1416	1416	NUM
ejpam-5293	202	18	1412	1412	NUM
ejpam-5293	202	19	since	since	SCONJ
ejpam-5293	202	20	l(s)+g(s	l(s)+g(s	NOUN
ejpam-5293	202	21	)	)	PUNCT
ejpam-5293	203	1	=	=	SYM
ejpam-5293	203	2	f	f	X
ejpam-5293	203	3	(	(	PUNCT
ejpam-5293	203	4	s	s	X
ejpam-5293	203	5	)	)	PUNCT
ejpam-5293	203	6	=	=	SYM
ejpam-5293	203	7	s+v	s+v	NUM
ejpam-5293	203	8	for	for	ADP
ejpam-5293	203	9	some	some	DET
ejpam-5293	203	10	v	v	NOUN
ejpam-5293	203	11	with	with	ADP
ejpam-5293	203	12	∥v∥	∥v∥	PROPN
ejpam-5293	203	13	<	<	X
ejpam-5293	203	14	ε	ε	PROPN
ejpam-5293	203	15	,	,	PUNCT
ejpam-5293	203	16	we	we	PRON
ejpam-5293	203	17	have	have	VERB
ejpam-5293	203	18	g(s	g(	NOUN
ejpam-5293	203	19	)	)	PUNCT
ejpam-5293	203	20	=	=	SYM
ejpam-5293	204	1	−	−	PROPN
ejpam-5293	204	2	(	(	PUNCT
ejpam-5293	204	3	l−	l−	NOUN
ejpam-5293	204	4	i	i	PROPN
ejpam-5293	204	5	d	d	PROPN
ejpam-5293	204	6	)	)	PUNCT
ejpam-5293	204	7	s+v	s+v	NUM
ejpam-5293	204	8	,	,	PUNCT
ejpam-5293	204	9	that	that	PRON
ejpam-5293	204	10	is	be	AUX
ejpam-5293	204	11	f	f	PROPN
ejpam-5293	204	12	(	(	PUNCT
ejpam-5293	204	13	s	s	NOUN
ejpam-5293	204	14	)	)	PUNCT
ejpam-5293	205	1	=	=	SYM
ejpam-5293	205	2	s−	s−	PROPN
ejpam-5293	205	3	(	(	PUNCT
ejpam-5293	205	4	l−	l−	NOUN
ejpam-5293	205	5	id)−1	id)−1	VERB
ejpam-5293	205	6	v.	v.	ADP
ejpam-5293	205	7	using	use	VERB
ejpam-5293	205	8	(	(	PUNCT
ejpam-5293	205	9	9	9	NUM
ejpam-5293	205	10	)	)	PUNCT
ejpam-5293	205	11	we	we	PRON
ejpam-5293	205	12	have	have	VERB
ejpam-5293	205	13	∥f	∥f	PROPN
ejpam-5293	205	14	(	(	PUNCT
ejpam-5293	205	15	s)−	s)−	PROPN
ejpam-5293	205	16	s∥	s∥	VERB
ejpam-5293	205	17	≤	≤	NOUN
ejpam-5293	205	18	c1ε	c1ε	ADJ
ejpam-5293	205	19	and	and	CCONJ
ejpam-5293	205	20	hence	hence	ADV
ejpam-5293	205	21	∥y0	∥y0	AUX
ejpam-5293	205	22	−	−	NOUN
ejpam-5293	205	23	s∥	s∥	VERB
ejpam-5293	205	24	≤	≤	NOUN
ejpam-5293	205	25	c1ε	c1ε	ADP
ejpam-5293	205	26	∞∑	∞∑	PROPN
ejpam-5293	205	27	k=1	k=1	X
ejpam-5293	205	28	(	(	PUNCT
ejpam-5293	205	29	c1ε	c1ε	ADJ
ejpam-5293	205	30	)	)	PUNCT
ejpam-5293	205	31	k−1	k−1	PROPN
ejpam-5293	205	32	=	=	PROPN
ejpam-5293	206	1	c1ε	c1ε	PROPN
ejpam-5293	206	2	1−	1−	NUM
ejpam-5293	206	3	c1ε	c1ε	NUM
ejpam-5293	206	4	.	.	PUNCT
ejpam-5293	207	1	let	let	VERB
ejpam-5293	207	2	y	y	PRON
ejpam-5293	207	3	be	be	AUX
ejpam-5293	207	4	such	such	ADJ
ejpam-5293	207	5	that	that	SCONJ
ejpam-5293	207	6	y0	y0	NOUN
ejpam-5293	207	7	=	=	SYM
ejpam-5293	207	8	(	(	PUNCT
ejpam-5293	207	9	y	y	PROPN
ejpam-5293	207	10	,	,	PUNCT
ejpam-5293	207	11	fy	fy	PROPN
ejpam-5293	207	12	,	,	PUNCT
ejpam-5293	207	13	.	.	PUNCT
ejpam-5293	207	14	.	.	PUNCT
ejpam-5293	208	1	.	.	PUNCT
ejpam-5293	209	1	,	,	PUNCT
ejpam-5293	209	2	fn−1y	fn−1y	PROPN
ejpam-5293	209	3	)	)	PUNCT
ejpam-5293	209	4	,	,	PUNCT
ejpam-5293	209	5	which	which	PRON
ejpam-5293	209	6	is	be	AUX
ejpam-5293	209	7	a	a	DET
ejpam-5293	209	8	n	n	CCONJ
ejpam-5293	209	9	-	-	PUNCT
ejpam-5293	209	10	periodic	periodic	ADJ
ejpam-5293	209	11	point	point	NOUN
ejpam-5293	209	12	.	.	PUNCT
ejpam-5293	210	1	by	by	ADP
ejpam-5293	210	2	the	the	DET
ejpam-5293	210	3	choice	choice	NOUN
ejpam-5293	210	4	of	of	ADP
ejpam-5293	210	5	ε	ε	PROPN
ejpam-5293	210	6	we	we	PRON
ejpam-5293	210	7	have	have	AUX
ejpam-5293	210	8	d(fkx	d(fkx	VERB
ejpam-5293	210	9	,	,	PUNCT
ejpam-5293	210	10	fky	fky	ADJ
ejpam-5293	210	11	)	)	PUNCT
ejpam-5293	210	12	≤	≤	NUM
ejpam-5293	210	13	c2d(f	c2d(f	PROPN
ejpam-5293	210	14	nx	nx	NUM
ejpam-5293	210	15	,	,	PUNCT
ejpam-5293	210	16	x	x	X
ejpam-5293	210	17	)	)	PUNCT
ejpam-5293	210	18	,	,	PUNCT
ejpam-5293	210	19	(	(	PUNCT
ejpam-5293	210	20	11	11	NUM
ejpam-5293	210	21	)	)	PUNCT
ejpam-5293	210	22	for	for	ADP
ejpam-5293	210	23	k	k	PROPN
ejpam-5293	210	24	=	=	SYM
ejpam-5293	210	25	0	0	NUM
ejpam-5293	210	26	,	,	PUNCT
ejpam-5293	210	27	1	1	NUM
ejpam-5293	210	28	,	,	PUNCT
ejpam-5293	210	29	.	.	PUNCT
ejpam-5293	210	30	.	.	PUNCT
ejpam-5293	211	1	.	.	PUNCT
ejpam-5293	212	1	,	,	PUNCT
ejpam-5293	212	2	n−	n−	NOUN
ejpam-5293	212	3	1	1	NUM
ejpam-5293	212	4	,	,	PUNCT
ejpam-5293	212	5	for	for	ADP
ejpam-5293	212	6	some	some	DET
ejpam-5293	212	7	constant	constant	ADJ
ejpam-5293	212	8	c2	c2	PROPN
ejpam-5293	212	9	>	>	X
ejpam-5293	212	10	0	0	X
ejpam-5293	212	11	.	.	PUNCT
ejpam-5293	213	1	it	it	PRON
ejpam-5293	213	2	follows	follow	VERB
ejpam-5293	213	3	from	from	ADP
ejpam-5293	213	4	(	(	PUNCT
ejpam-5293	213	5	11	11	NUM
ejpam-5293	213	6	)	)	PUNCT
ejpam-5293	214	1	that	that	SCONJ
ejpam-5293	214	2	d(fnx	d(fnx	PROPN
ejpam-5293	214	3	,	,	PUNCT
ejpam-5293	214	4	fny	fny	NOUN
ejpam-5293	214	5	)	)	PUNCT
ejpam-5293	214	6	=	=	SYM
ejpam-5293	214	7	d(fnx	d(fnx	PROPN
ejpam-5293	214	8	,	,	PUNCT
ejpam-5293	214	9	y	y	NOUN
ejpam-5293	214	10	)	)	PUNCT
ejpam-5293	214	11	≤	≤	NOUN
ejpam-5293	214	12	d(fnx	d(fnx	PROPN
ejpam-5293	214	13	,	,	PUNCT
ejpam-5293	214	14	x	x	X
ejpam-5293	214	15	)	)	PUNCT
ejpam-5293	214	16	+	+	CCONJ
ejpam-5293	214	17	d(x	d(x	PROPN
ejpam-5293	214	18	,	,	PUNCT
ejpam-5293	214	19	y	y	NOUN
ejpam-5293	214	20	)	)	PUNCT
ejpam-5293	214	21	≤	≤	NOUN
ejpam-5293	214	22	(	(	PUNCT
ejpam-5293	214	23	1	1	NUM
ejpam-5293	214	24	+	+	NUM
ejpam-5293	214	25	c2)d(f	c2)d(f	PROPN
ejpam-5293	214	26	nx	nx	NUM
ejpam-5293	214	27	,	,	PUNCT
ejpam-5293	214	28	x	x	NOUN
ejpam-5293	214	29	)	)	PUNCT
ejpam-5293	214	30	.	.	PUNCT
ejpam-5293	215	1	we	we	PRON
ejpam-5293	215	2	can	can	AUX
ejpam-5293	215	3	thus	thus	ADV
ejpam-5293	215	4	claim	claim	VERB
ejpam-5293	215	5	that	that	SCONJ
ejpam-5293	215	6	d(fkx	d(fkx	VERB
ejpam-5293	215	7	,	,	PUNCT
ejpam-5293	215	8	fky	fky	ADJ
ejpam-5293	215	9	)	)	PUNCT
ejpam-5293	215	10	≤	≤	NOUN
ejpam-5293	215	11	(	(	PUNCT
ejpam-5293	215	12	1	1	NUM
ejpam-5293	215	13	+	+	NUM
ejpam-5293	215	14	c2)ε	c2)ε	NOUN
ejpam-5293	215	15	(	(	PUNCT
ejpam-5293	215	16	12	12	NUM
ejpam-5293	215	17	)	)	PUNCT
ejpam-5293	215	18	for	for	ADP
ejpam-5293	215	19	k	k	PROPN
ejpam-5293	215	20	=	=	SYM
ejpam-5293	215	21	0	0	NUM
ejpam-5293	215	22	,	,	PUNCT
ejpam-5293	215	23	1	1	NUM
ejpam-5293	215	24	,	,	PUNCT
ejpam-5293	215	25	.	.	PUNCT
ejpam-5293	215	26	.	.	PUNCT
ejpam-5293	216	1	.	.	PUNCT
ejpam-5293	217	1	,	,	PUNCT
ejpam-5293	217	2	n.	n.	NOUN
ejpam-5293	217	3	being	be	AUX
ejpam-5293	217	4	λ	λ	PROPN
ejpam-5293	217	5	a	a	DET
ejpam-5293	217	6	locally	locally	ADV
ejpam-5293	217	7	maximal	maximal	ADJ
ejpam-5293	217	8	set	set	NOUN
ejpam-5293	217	9	,	,	PUNCT
ejpam-5293	217	10	there	there	PRON
ejpam-5293	217	11	is	be	VERB
ejpam-5293	217	12	an	an	DET
ejpam-5293	217	13	open	open	ADJ
ejpam-5293	217	14	neighborhood	neighborhood	NOUN
ejpam-5293	217	15	v	v	NOUN
ejpam-5293	217	16	of	of	ADP
ejpam-5293	217	17	λ	λ	NOUN
ejpam-5293	217	18	such	such	ADJ
ejpam-5293	217	19	that	that	SCONJ
ejpam-5293	217	20	λ	λ	NOUN
ejpam-5293	217	21	=	=	SYM
ejpam-5293	217	22	⋂	⋂	PROPN
ejpam-5293	217	23	n∈z	n∈z	PRON
ejpam-5293	217	24	f	f	PROPN
ejpam-5293	217	25	nv	nv	PROPN
ejpam-5293	217	26	.	.	PUNCT
ejpam-5293	218	1	as	as	SCONJ
ejpam-5293	218	2	y	y	PROPN
ejpam-5293	218	3	is	be	AUX
ejpam-5293	218	4	a	a	DET
ejpam-5293	218	5	periodic	periodic	ADJ
ejpam-5293	218	6	point	point	NOUN
ejpam-5293	218	7	,	,	PUNCT
ejpam-5293	218	8	we	we	PRON
ejpam-5293	218	9	have	have	VERB
ejpam-5293	218	10	y	y	PROPN
ejpam-5293	218	11	∈	∈	PROPN
ejpam-5293	218	12	⋂	⋂	PROPN
ejpam-5293	218	13	n∈z	n∈z	PRON
ejpam-5293	218	14	f	f	PROPN
ejpam-5293	218	15	nv	nv	PROPN
ejpam-5293	218	16	(	(	PUNCT
ejpam-5293	218	17	eventually	eventually	ADV
ejpam-5293	218	18	choosing	choose	VERB
ejpam-5293	218	19	again	again	ADV
ejpam-5293	218	20	ε	ε	PROPN
ejpam-5293	218	21	and	and	CCONJ
ejpam-5293	218	22	the	the	DET
ejpam-5293	218	23	neighborhoods	neighborhood	NOUN
ejpam-5293	218	24	vfkx	vfkx	VERB
ejpam-5293	218	25	)	)	PUNCT
ejpam-5293	218	26	,	,	PUNCT
ejpam-5293	218	27	and	and	CCONJ
ejpam-5293	218	28	then	then	ADV
ejpam-5293	218	29	y	y	PROPN
ejpam-5293	218	30	∈	∈	PROPN
ejpam-5293	218	31	λ	λ	PROPN
ejpam-5293	218	32	.	.	PUNCT
ejpam-5293	219	1	it	it	PRON
ejpam-5293	219	2	remains	remain	VERB
ejpam-5293	219	3	now	now	ADV
ejpam-5293	219	4	to	to	PART
ejpam-5293	219	5	establish	establish	VERB
ejpam-5293	219	6	the	the	DET
ejpam-5293	219	7	inequality	inequality	NOUN
ejpam-5293	219	8	(	(	PUNCT
ejpam-5293	219	9	5	5	NUM
ejpam-5293	219	10	)	)	PUNCT
ejpam-5293	219	11	.	.	PUNCT
ejpam-5293	220	1	since	since	SCONJ
ejpam-5293	220	2	λ	λ	PROPN
ejpam-5293	220	3	is	be	AUX
ejpam-5293	220	4	a	a	DET
ejpam-5293	220	5	compact	compact	ADJ
ejpam-5293	220	6	locally	locally	ADV
ejpam-5293	220	7	maximal	maximal	ADJ
ejpam-5293	220	8	hyperbolic	hyperbolic	ADJ
ejpam-5293	220	9	set	set	NOUN
ejpam-5293	220	10	,	,	PUNCT
ejpam-5293	220	11	it	it	PRON
ejpam-5293	220	12	has	have	VERB
ejpam-5293	220	13	local	local	ADJ
ejpam-5293	220	14	product	product	NOUN
ejpam-5293	220	15	structure	structure	NOUN
ejpam-5293	220	16	.	.	PUNCT
ejpam-5293	221	1	thus	thus	ADV
ejpam-5293	221	2	,	,	PUNCT
ejpam-5293	221	3	for	for	ADP
ejpam-5293	221	4	each	each	DET
ejpam-5293	221	5	γ	γ	X
ejpam-5293	221	6	>	>	X
ejpam-5293	221	7	0	0	PUNCT
ejpam-5293	221	8	small	small	ADJ
ejpam-5293	221	9	enough	enough	ADV
ejpam-5293	221	10	,	,	PUNCT
ejpam-5293	221	11	there	there	PRON
ejpam-5293	221	12	is	be	VERB
ejpam-5293	221	13	ε	ε	PROPN
ejpam-5293	221	14	>	>	X
ejpam-5293	221	15	0	0	NUM
ejpam-5293	221	16	such	such	ADJ
ejpam-5293	221	17	that	that	SCONJ
ejpam-5293	221	18	if	if	SCONJ
ejpam-5293	221	19	the	the	DET
ejpam-5293	221	20	points	point	NOUN
ejpam-5293	221	21	x	x	X
ejpam-5293	221	22	,	,	PUNCT
ejpam-5293	221	23	y	y	PROPN
ejpam-5293	221	24	∈	∈	PROPN
ejpam-5293	221	25	λ	λ	NOUN
ejpam-5293	221	26	verify	verify	VERB
ejpam-5293	221	27	d(x	d(x	PROPN
ejpam-5293	221	28	,	,	PUNCT
ejpam-5293	221	29	y	y	NOUN
ejpam-5293	221	30	)	)	PUNCT
ejpam-5293	221	31	<	<	X
ejpam-5293	221	32	ε	ε	PROPN
ejpam-5293	221	33	then	then	ADV
ejpam-5293	221	34	the	the	DET
ejpam-5293	221	35	intersection	intersection	NOUN
ejpam-5293	221	36	of	of	ADP
ejpam-5293	221	37	w	w	PROPN
ejpam-5293	221	38	s	s	PROPN
ejpam-5293	221	39	γ	γ	X
ejpam-5293	221	40	(	(	PUNCT
ejpam-5293	221	41	x	x	NOUN
ejpam-5293	221	42	)	)	PUNCT
ejpam-5293	221	43	with	with	ADP
ejpam-5293	221	44	w	w	PROPN
ejpam-5293	221	45	u	u	PROPN
ejpam-5293	221	46	γ	γ	X
ejpam-5293	221	47	(	(	PUNCT
ejpam-5293	221	48	y	y	NOUN
ejpam-5293	221	49	)	)	PUNCT
ejpam-5293	221	50	is	be	AUX
ejpam-5293	221	51	not	not	PART
ejpam-5293	221	52	empty	empty	ADJ
ejpam-5293	221	53	,	,	PUNCT
ejpam-5293	221	54	but	but	CCONJ
ejpam-5293	221	55	constituted	constitute	VERB
ejpam-5293	221	56	by	by	ADP
ejpam-5293	221	57	a	a	DET
ejpam-5293	221	58	single	single	ADJ
ejpam-5293	221	59	point	point	NOUN
ejpam-5293	221	60	which	which	PRON
ejpam-5293	221	61	we	we	PRON
ejpam-5293	221	62	denote	denote	VERB
ejpam-5293	221	63	by	by	ADP
ejpam-5293	221	64	[	[	X
ejpam-5293	221	65	x	x	X
ejpam-5293	221	66	,	,	PUNCT
ejpam-5293	221	67	y	y	PROPN
ejpam-5293	221	68	]	]	X
ejpam-5293	221	69	=	=	PUNCT
ejpam-5293	221	70	w.	w.	NOUN
ejpam-5293	221	71	we	we	PRON
ejpam-5293	221	72	have	have	VERB
ejpam-5293	221	73	fkw	fkw	PROPN
ejpam-5293	222	1	=	=	PUNCT
ejpam-5293	222	2	[	[	PUNCT
ejpam-5293	222	3	fkx	fkx	INTJ
ejpam-5293	222	4	,	,	PUNCT
ejpam-5293	222	5	fky	fky	X
ejpam-5293	222	6	]	]	PUNCT
ejpam-5293	222	7	and	and	CCONJ
ejpam-5293	222	8	the	the	DET
ejpam-5293	222	9	estimate	estimate	NOUN
ejpam-5293	222	10	d(fkx	d(fkx	VERB
ejpam-5293	222	11	,	,	PUNCT
ejpam-5293	222	12	fky	fky	ADJ
ejpam-5293	222	13	)	)	PUNCT
ejpam-5293	222	14	≤	≤	NOUN
ejpam-5293	222	15	d(fkx	d(fkx	VERB
ejpam-5293	222	16	,	,	PUNCT
ejpam-5293	222	17	fkw	fkw	PROPN
ejpam-5293	222	18	)	)	PUNCT
ejpam-5293	223	1	+	+	CCONJ
ejpam-5293	223	2	d(fkw	d(fkw	ADJ
ejpam-5293	223	3	,	,	PUNCT
ejpam-5293	223	4	fky	fky	ADJ
ejpam-5293	223	5	)	)	PUNCT
ejpam-5293	223	6	.	.	PUNCT
ejpam-5293	224	1	since	since	SCONJ
ejpam-5293	224	2	w	w	PROPN
ejpam-5293	224	3	∈	∈	PROPN
ejpam-5293	224	4	w	w	PROPN
ejpam-5293	224	5	s	s	PROPN
ejpam-5293	224	6	γ	γ	X
ejpam-5293	224	7	(	(	PUNCT
ejpam-5293	224	8	x	x	NOUN
ejpam-5293	224	9	)	)	PUNCT
ejpam-5293	224	10	,	,	PUNCT
ejpam-5293	224	11	the	the	DET
ejpam-5293	224	12	theorem	theorem	ADJ
ejpam-5293	224	13	2	2	NUM
ejpam-5293	224	14	guarantees	guarantee	VERB
ejpam-5293	224	15	that	that	SCONJ
ejpam-5293	224	16	,	,	PUNCT
ejpam-5293	224	17	for	for	ADP
ejpam-5293	224	18	each	each	DET
ejpam-5293	224	19	δ	δ	PROPN
ejpam-5293	224	20	>	>	X
ejpam-5293	224	21	0	0	PROPN
ejpam-5293	224	22	,	,	PUNCT
ejpam-5293	224	23	there	there	PRON
ejpam-5293	224	24	is	be	VERB
ejpam-5293	224	25	a	a	DET
ejpam-5293	224	26	constant	constant	ADJ
ejpam-5293	224	27	c3	c3	NOUN
ejpam-5293	224	28	=	=	SYM
ejpam-5293	224	29	c3(δ	c3(δ	X
ejpam-5293	224	30	)	)	PUNCT
ejpam-5293	224	31	such	such	ADJ
ejpam-5293	224	32	that	that	PRON
ejpam-5293	224	33	d(fkx	d(fkx	VERB
ejpam-5293	224	34	,	,	PUNCT
ejpam-5293	224	35	fkw	fkw	PROPN
ejpam-5293	224	36	)	)	PUNCT
ejpam-5293	224	37	≤	≤	NOUN
ejpam-5293	224	38	c3	c3	PROPN
ejpam-5293	224	39	(	(	PUNCT
ejpam-5293	224	40	τ	τ	X
ejpam-5293	224	41	+	+	PROPN
ejpam-5293	224	42	δ)k	δ)k	PROPN
ejpam-5293	224	43	d	d	X
ejpam-5293	224	44	(	(	PUNCT
ejpam-5293	224	45	x	x	X
ejpam-5293	224	46	,	,	PUNCT
ejpam-5293	224	47	w	w	NOUN
ejpam-5293	224	48	)	)	PUNCT
ejpam-5293	224	49	.	.	PUNCT
ejpam-5293	225	1	(	(	PUNCT
ejpam-5293	225	2	13	13	NUM
ejpam-5293	225	3	)	)	PUNCT
ejpam-5293	225	4	again	again	ADV
ejpam-5293	225	5	by	by	ADP
ejpam-5293	225	6	the	the	DET
ejpam-5293	225	7	theorem	theorem	NOUN
ejpam-5293	225	8	2	2	NUM
ejpam-5293	225	9	,	,	PUNCT
ejpam-5293	225	10	since	since	SCONJ
ejpam-5293	225	11	w	w	PROPN
ejpam-5293	225	12	∈w	∈w	PROPN
ejpam-5293	225	13	u	u	PRON
ejpam-5293	225	14	γ	γ	X
ejpam-5293	225	15	(	(	PUNCT
ejpam-5293	225	16	y	y	PROPN
ejpam-5293	225	17	)	)	PUNCT
ejpam-5293	225	18	,	,	PUNCT
ejpam-5293	225	19	we	we	PRON
ejpam-5293	225	20	can	can	AUX
ejpam-5293	225	21	claim	claim	VERB
ejpam-5293	225	22	that	that	SCONJ
ejpam-5293	225	23	d(fkw	d(fkw	NOUN
ejpam-5293	225	24	,	,	PUNCT
ejpam-5293	225	25	fky	fky	ADJ
ejpam-5293	225	26	)	)	PUNCT
ejpam-5293	225	27	=	=	SYM
ejpam-5293	225	28	d(fk−n(fnw	d(fk−n(fnw	PROPN
ejpam-5293	225	29	)	)	PUNCT
ejpam-5293	225	30	,	,	PUNCT
ejpam-5293	225	31	fk−n(fny	fk−n(fny	NOUN
ejpam-5293	225	32	)	)	PUNCT
ejpam-5293	225	33	)	)	PUNCT
ejpam-5293	226	1	≤	≤	PROPN
ejpam-5293	226	2	c3	c3	PROPN
ejpam-5293	226	3	(	(	PUNCT
ejpam-5293	226	4	τ	τ	PROPN
ejpam-5293	226	5	+	+	X
ejpam-5293	226	6	δ)n−k	δ)n−k	X
ejpam-5293	226	7	d(fnw	d(fnw	PROPN
ejpam-5293	226	8	,	,	PUNCT
ejpam-5293	226	9	fny	fny	NOUN
ejpam-5293	226	10	)	)	PUNCT
ejpam-5293	226	11	.	.	PUNCT
ejpam-5293	227	1	using	use	VERB
ejpam-5293	227	2	(	(	PUNCT
ejpam-5293	227	3	13	13	NUM
ejpam-5293	227	4	)	)	PUNCT
ejpam-5293	227	5	,	,	PUNCT
ejpam-5293	227	6	it	it	PRON
ejpam-5293	227	7	follows	follow	VERB
ejpam-5293	227	8	that	that	SCONJ
ejpam-5293	227	9	d(fkx	d(fkx	VERB
ejpam-5293	227	10	,	,	PUNCT
ejpam-5293	227	11	fky	fky	ADJ
ejpam-5293	227	12	)	)	PUNCT
ejpam-5293	227	13	≤	≤	NOUN
ejpam-5293	227	14	c3	c3	NOUN
ejpam-5293	227	15	(	(	PUNCT
ejpam-5293	227	16	τ	τ	X
ejpam-5293	227	17	+	+	PROPN
ejpam-5293	227	18	δ)k	δ)k	PROPN
ejpam-5293	227	19	d	d	X
ejpam-5293	227	20	(	(	PUNCT
ejpam-5293	227	21	x	x	X
ejpam-5293	227	22	,	,	PUNCT
ejpam-5293	227	23	w	w	NOUN
ejpam-5293	227	24	)	)	PUNCT
ejpam-5293	227	25	+	+	CCONJ
ejpam-5293	227	26	c3	c3	PROPN
ejpam-5293	227	27	(	(	PUNCT
ejpam-5293	227	28	τ	τ	PROPN
ejpam-5293	227	29	+	+	X
ejpam-5293	227	30	δ)n−k	δ)n−k	X
ejpam-5293	227	31	d(fnw	d(fnw	PROPN
ejpam-5293	227	32	,	,	PUNCT
ejpam-5293	227	33	y	y	NOUN
ejpam-5293	227	34	)	)	PUNCT
ejpam-5293	227	35	≤	≤	NOUN
ejpam-5293	227	36	c3	c3	PROPN
ejpam-5293	227	37	(	(	PUNCT
ejpam-5293	227	38	τ	τ	PROPN
ejpam-5293	227	39	+	+	NUM
ejpam-5293	227	40	δ)min{k	δ)min{k	NUM
ejpam-5293	227	41	,	,	PUNCT
ejpam-5293	227	42	n−k	n−k	NOUN
ejpam-5293	227	43	}	}	PUNCT
ejpam-5293	228	1	[	[	X
ejpam-5293	228	2	d(x	d(x	PROPN
ejpam-5293	228	3	,	,	PUNCT
ejpam-5293	228	4	w	w	NOUN
ejpam-5293	228	5	)	)	PUNCT
ejpam-5293	228	6	+	+	CCONJ
ejpam-5293	228	7	d(fnw	d(fnw	PROPN
ejpam-5293	228	8	,	,	PUNCT
ejpam-5293	228	9	fnx	fnx	PROPN
ejpam-5293	228	10	)	)	PUNCT
ejpam-5293	229	1	+	+	CCONJ
ejpam-5293	230	1	d(fnx	d(fnx	PROPN
ejpam-5293	230	2	,	,	PUNCT
ejpam-5293	230	3	y	y	PROPN
ejpam-5293	230	4	)	)	PUNCT
ejpam-5293	230	5	]	]	PUNCT
ejpam-5293	230	6	≤	≤	PROPN
ejpam-5293	230	7	c3	c3	NOUN
ejpam-5293	230	8	(	(	PUNCT
ejpam-5293	230	9	τ	τ	PROPN
ejpam-5293	230	10	+	+	NUM
ejpam-5293	230	11	δ)min{k	δ)min{k	NUM
ejpam-5293	230	12	,	,	PUNCT
ejpam-5293	230	13	n−k	n−k	NOUN
ejpam-5293	230	14	}	}	PUNCT
ejpam-5293	230	15	[	[	X
ejpam-5293	230	16	(	(	PUNCT
ejpam-5293	230	17	1	1	NUM
ejpam-5293	230	18	+	+	CCONJ
ejpam-5293	230	19	c3)d(x	c3)d(x	NOUN
ejpam-5293	230	20	,	,	PUNCT
ejpam-5293	230	21	w	w	NOUN
ejpam-5293	230	22	)	)	PUNCT
ejpam-5293	230	23	+	+	CCONJ
ejpam-5293	230	24	d(fnx	d(fnx	PROPN
ejpam-5293	230	25	,	,	PUNCT
ejpam-5293	230	26	y	y	PROPN
ejpam-5293	230	27	)	)	PUNCT
ejpam-5293	230	28	]	]	PUNCT
ejpam-5293	230	29	.	.	PUNCT
ejpam-5293	231	1	by	by	ADP
ejpam-5293	231	2	(	(	PUNCT
ejpam-5293	231	3	12	12	NUM
ejpam-5293	231	4	)	)	PUNCT
ejpam-5293	231	5	with	with	ADP
ejpam-5293	231	6	k	k	PROPN
ejpam-5293	231	7	=	=	SYM
ejpam-5293	231	8	n	n	CCONJ
ejpam-5293	231	9	,	,	PUNCT
ejpam-5293	231	10	we	we	PRON
ejpam-5293	231	11	obtain	obtain	VERB
ejpam-5293	231	12	d(fnx	d(fnx	PROPN
ejpam-5293	231	13	,	,	PUNCT
ejpam-5293	231	14	y	y	NOUN
ejpam-5293	231	15	)	)	PUNCT
ejpam-5293	231	16	≤	≤	NOUN
ejpam-5293	231	17	(	(	PUNCT
ejpam-5293	231	18	1+c2)d	1+c2)d	NUM
ejpam-5293	231	19	(	(	PUNCT
ejpam-5293	231	20	f	f	PROPN
ejpam-5293	231	21	nx	nx	PROPN
ejpam-5293	231	22	,	,	PUNCT
ejpam-5293	231	23	x	x	NOUN
ejpam-5293	231	24	)	)	PUNCT
ejpam-5293	231	25	.	.	PUNCT
ejpam-5293	232	1	as	as	ADP
ejpam-5293	232	2	a	a	DET
ejpam-5293	232	3	consequence	consequence	NOUN
ejpam-5293	232	4	of	of	ADP
ejpam-5293	232	5	uniform	uniform	NOUN
ejpam-5293	232	6	transversally	transversally	ADV
ejpam-5293	232	7	,	,	PUNCT
ejpam-5293	232	8	there	there	PRON
ejpam-5293	232	9	is	be	VERB
ejpam-5293	232	10	c4	c4	NOUN
ejpam-5293	232	11	>	>	X
ejpam-5293	232	12	0	0	NUM
ejpam-5293	233	1	such	such	ADJ
ejpam-5293	233	2	that	that	SCONJ
ejpam-5293	233	3	if	if	SCONJ
ejpam-5293	233	4	ε	ε	PROPN
ejpam-5293	233	5	is	be	AUX
ejpam-5293	233	6	small	small	ADJ
ejpam-5293	233	7	enough	enough	ADV
ejpam-5293	233	8	then	then	ADV
ejpam-5293	233	9	d(x	d(x	PROPN
ejpam-5293	233	10	,	,	PUNCT
ejpam-5293	233	11	w	w	NOUN
ejpam-5293	233	12	)	)	PUNCT
ejpam-5293	233	13	≤	≤	NUM
ejpam-5293	233	14	c4d(x	c4d(x	NOUN
ejpam-5293	233	15	,	,	PUNCT
ejpam-5293	233	16	y	y	NOUN
ejpam-5293	233	17	)	)	PUNCT
ejpam-5293	233	18	.	.	PUNCT
ejpam-5293	234	1	again	again	ADV
ejpam-5293	234	2	by	by	ADP
ejpam-5293	234	3	(	(	PUNCT
ejpam-5293	234	4	12	12	NUM
ejpam-5293	234	5	)	)	PUNCT
ejpam-5293	234	6	,	,	PUNCT
ejpam-5293	234	7	now	now	ADV
ejpam-5293	234	8	with	with	ADP
ejpam-5293	234	9	k	k	PROPN
ejpam-5293	234	10	=	=	SYM
ejpam-5293	234	11	0	0	PROPN
ejpam-5293	234	12	,	,	PUNCT
ejpam-5293	234	13	we	we	PRON
ejpam-5293	234	14	obtain	obtain	VERB
ejpam-5293	234	15	d(x	d(x	NOUN
ejpam-5293	234	16	,	,	PUNCT
ejpam-5293	234	17	w	w	NOUN
ejpam-5293	234	18	)	)	PUNCT
ejpam-5293	234	19	≤	≤	PUNCT
ejpam-5293	235	1	c4(1	c4(1	PROPN
ejpam-5293	235	2	+	+	CCONJ
ejpam-5293	235	3	c2)d(f	c2)d(f	PROPN
ejpam-5293	235	4	nx	nx	NUM
ejpam-5293	235	5	,	,	PUNCT
ejpam-5293	235	6	x	x	NOUN
ejpam-5293	235	7	)	)	PUNCT
ejpam-5293	235	8	.	.	PUNCT
ejpam-5293	236	1	choosing	choose	VERB
ejpam-5293	236	2	λ	λ	PROPN
ejpam-5293	236	3	∈	∈	PROPN
ejpam-5293	236	4	(	(	PUNCT
ejpam-5293	236	5	0	0	NUM
ejpam-5293	236	6	,	,	PUNCT
ejpam-5293	236	7	1	1	NUM
ejpam-5293	236	8	)	)	PUNCT
ejpam-5293	236	9	such	such	ADJ
ejpam-5293	236	10	that	that	SCONJ
ejpam-5293	236	11	λ	λ	PROPN
ejpam-5293	236	12	≥	≥	X
ejpam-5293	236	13	τ	τ	X
ejpam-5293	236	14	+	+	CCONJ
ejpam-5293	236	15	δ	δ	PROPN
ejpam-5293	236	16	,	,	PUNCT
ejpam-5293	236	17	we	we	PRON
ejpam-5293	236	18	finally	finally	ADV
ejpam-5293	236	19	obtain	obtain	VERB
ejpam-5293	236	20	the	the	DET
ejpam-5293	236	21	intended	intend	VERB
ejpam-5293	236	22	inequality	inequality	NOUN
ejpam-5293	236	23	(	(	PUNCT
ejpam-5293	236	24	5	5	NUM
ejpam-5293	236	25	)	)	PUNCT
ejpam-5293	236	26	with	with	ADP
ejpam-5293	236	27	c	c	NOUN
ejpam-5293	236	28	=	=	SYM
ejpam-5293	236	29	c3(1	c3(1	PROPN
ejpam-5293	236	30	+	+	CCONJ
ejpam-5293	236	31	c3)c4(1	c3)c4(1	PROPN
ejpam-5293	236	32	+	+	CCONJ
ejpam-5293	236	33	c2	c2	PROPN
ejpam-5293	236	34	)	)	PUNCT
ejpam-5293	237	1	+	+	CCONJ
ejpam-5293	237	2	c3(1	c3(1	PROPN
ejpam-5293	237	3	+	+	CCONJ
ejpam-5293	237	4	c2	c2	PROPN
ejpam-5293	237	5	)	)	PUNCT
ejpam-5293	237	6	.	.	PUNCT
ejpam-5293	238	1	r.	r.	PROPN
ejpam-5293	238	2	d.	d.	PROPN
ejpam-5293	238	3	laureano	laureano	PROPN
ejpam-5293	238	4	/	/	SYM
ejpam-5293	238	5	eur	eur	PROPN
ejpam-5293	238	6	.	.	PUNCT
ejpam-5293	239	1	j.	j.	PROPN
ejpam-5293	239	2	pure	pure	PROPN
ejpam-5293	239	3	appl	appl	PROPN
ejpam-5293	239	4	.	.	PROPN
ejpam-5293	239	5	math	math	PROPN
ejpam-5293	239	6	,	,	PUNCT
ejpam-5293	239	7	17	17	NUM
ejpam-5293	239	8	(	(	PUNCT
ejpam-5293	239	9	3	3	NUM
ejpam-5293	239	10	)	)	PUNCT
ejpam-5293	239	11	(	(	PUNCT
ejpam-5293	239	12	2024	2024	NUM
ejpam-5293	239	13	)	)	PUNCT
ejpam-5293	239	14	,	,	PUNCT
ejpam-5293	239	15	1403	1403	NUM
ejpam-5293	239	16	-	-	SYM
ejpam-5293	239	17	1416	1416	NUM
ejpam-5293	239	18	1413	1413	NUM
ejpam-5293	239	19	3.2	3.2	NUM
ejpam-5293	239	20	.	.	PUNCT
ejpam-5293	240	1	proof	proof	NOUN
ejpam-5293	240	2	of	of	ADP
ejpam-5293	240	3	the	the	DET
ejpam-5293	240	4	livschitz	livschitz	NOUN
ejpam-5293	240	5	theorem	theorem	NOUN
ejpam-5293	240	6	for	for	ADP
ejpam-5293	240	7	hyperbolic	hyperbolic	ADJ
ejpam-5293	240	8	diffeomorphisms	diffeomorphism	NOUN
ejpam-5293	240	9	note	note	VERB
ejpam-5293	240	10	that	that	SCONJ
ejpam-5293	240	11	the	the	DET
ejpam-5293	240	12	assumption	assumption	NOUN
ejpam-5293	240	13	that	that	SCONJ
ejpam-5293	240	14	the	the	DET
ejpam-5293	240	15	hyperbolic	hyperbolic	ADJ
ejpam-5293	240	16	set	set	NOUN
ejpam-5293	240	17	λ	λ	PROPN
ejpam-5293	240	18	is	be	AUX
ejpam-5293	240	19	locally	locally	ADV
ejpam-5293	240	20	maximal	maximal	ADJ
ejpam-5293	240	21	is	be	AUX
ejpam-5293	240	22	essential	essential	ADJ
ejpam-5293	240	23	to	to	PART
ejpam-5293	240	24	ensure	ensure	VERB
ejpam-5293	240	25	that	that	SCONJ
ejpam-5293	240	26	the	the	DET
ejpam-5293	240	27	periodic	periodic	ADJ
ejpam-5293	240	28	point	point	NOUN
ejpam-5293	240	29	constructed	construct	VERB
ejpam-5293	240	30	in	in	ADP
ejpam-5293	240	31	the	the	DET
ejpam-5293	240	32	development	development	NOUN
ejpam-5293	240	33	is	be	AUX
ejpam-5293	240	34	still	still	ADV
ejpam-5293	240	35	in	in	ADP
ejpam-5293	240	36	λ	λ	NOUN
ejpam-5293	240	37	.	.	PUNCT
ejpam-5293	241	1	this	this	DET
ejpam-5293	241	2	apparent	apparent	ADJ
ejpam-5293	241	3	detail	detail	NOUN
ejpam-5293	241	4	is	be	AUX
ejpam-5293	241	5	crucial	crucial	ADJ
ejpam-5293	241	6	in	in	ADP
ejpam-5293	241	7	the	the	DET
ejpam-5293	241	8	following	follow	VERB
ejpam-5293	241	9	proof	proof	NOUN
ejpam-5293	241	10	of	of	ADP
ejpam-5293	241	11	theorem	theorem	NOUN
ejpam-5293	241	12	1	1	NUM
ejpam-5293	241	13	.	.	PUNCT
ejpam-5293	242	1	since	since	SCONJ
ejpam-5293	242	2	f	f	PROPN
ejpam-5293	242	3	|λ	|λ	ADV
ejpam-5293	242	4	is	be	AUX
ejpam-5293	242	5	topologically	topologically	ADV
ejpam-5293	242	6	transitive	transitive	ADJ
ejpam-5293	242	7	there	there	PRON
ejpam-5293	242	8	is	be	VERB
ejpam-5293	242	9	a	a	DET
ejpam-5293	242	10	point	point	NOUN
ejpam-5293	242	11	x0	x0	PROPN
ejpam-5293	242	12	∈	∈	PROPN
ejpam-5293	242	13	λ	λ	PROPN
ejpam-5293	242	14	with	with	ADP
ejpam-5293	242	15	orbit	orbit	NOUN
ejpam-5293	242	16	dense	dense	ADJ
ejpam-5293	242	17	in	in	ADP
ejpam-5293	242	18	λ	λ	NOUN
ejpam-5293	242	19	.	.	PUNCT
ejpam-5293	243	1	by	by	ADP
ejpam-5293	243	2	choosing	choose	VERB
ejpam-5293	243	3	an	an	DET
ejpam-5293	243	4	arbitrary	arbitrary	ADJ
ejpam-5293	243	5	real	real	ADJ
ejpam-5293	243	6	value	value	NOUN
ejpam-5293	243	7	φ(x0	φ(x0	NOUN
ejpam-5293	243	8	)	)	PUNCT
ejpam-5293	243	9	we	we	PRON
ejpam-5293	243	10	define	define	VERB
ejpam-5293	243	11	φ	φ	PROPN
ejpam-5293	243	12	(	(	PUNCT
ejpam-5293	243	13	fnx0	fnx0	PROPN
ejpam-5293	243	14	)	)	PUNCT
ejpam-5293	243	15	=	=	PUNCT
ejpam-5293	243	16	φ(x0	φ(x0	NOUN
ejpam-5293	243	17	)	)	PUNCT
ejpam-5293	243	18	+	+	CCONJ
ejpam-5293	243	19	α(n	α(n	NOUN
ejpam-5293	243	20	,	,	PUNCT
ejpam-5293	243	21	x0	x0	PROPN
ejpam-5293	243	22	)	)	PUNCT
ejpam-5293	243	23	,	,	PUNCT
ejpam-5293	243	24	where	where	SCONJ
ejpam-5293	243	25	α(n	α(n	NOUN
ejpam-5293	243	26	,	,	PUNCT
ejpam-5293	243	27	x	x	PRON
ejpam-5293	243	28	)	)	PUNCT
ejpam-5293	243	29	is	be	AUX
ejpam-5293	243	30	defined	define	VERB
ejpam-5293	243	31	as	as	ADP
ejpam-5293	243	32	(	(	PUNCT
ejpam-5293	243	33	3	3	NUM
ejpam-5293	243	34	)	)	PUNCT
ejpam-5293	243	35	.	.	PUNCT
ejpam-5293	244	1	consider	consider	VERB
ejpam-5293	244	2	n	n	PRON
ejpam-5293	244	3	,	,	PUNCT
ejpam-5293	244	4	m	m	VERB
ejpam-5293	244	5	∈	∈	NOUN
ejpam-5293	244	6	n	n	PRON
ejpam-5293	244	7	such	such	ADJ
ejpam-5293	244	8	that	that	SCONJ
ejpam-5293	244	9	the	the	DET
ejpam-5293	244	10	distance	distance	NOUN
ejpam-5293	244	11	d(fnx0	d(fnx0	PROPN
ejpam-5293	244	12	,	,	PUNCT
ejpam-5293	244	13	f	f	PROPN
ejpam-5293	244	14	mx0	mx0	PROPN
ejpam-5293	244	15	)	)	PUNCT
ejpam-5293	244	16	is	be	AUX
ejpam-5293	244	17	small	small	ADJ
ejpam-5293	244	18	enough	enough	ADV
ejpam-5293	244	19	in	in	ADP
ejpam-5293	244	20	order	order	NOUN
ejpam-5293	244	21	to	to	PART
ejpam-5293	244	22	apply	apply	VERB
ejpam-5293	244	23	the	the	DET
ejpam-5293	244	24	acl	acl	PROPN
ejpam-5293	244	25	for	for	ADP
ejpam-5293	244	26	hyperbolic	hyperbolic	ADJ
ejpam-5293	244	27	diffeomorphisms	diffeomorphism	NOUN
ejpam-5293	244	28	.	.	PUNCT
ejpam-5293	245	1	assuming	assume	VERB
ejpam-5293	245	2	that	that	SCONJ
ejpam-5293	245	3	m	m	VERB
ejpam-5293	245	4	>	>	X
ejpam-5293	245	5	n	n	CCONJ
ejpam-5293	245	6	,	,	PUNCT
ejpam-5293	245	7	this	this	DET
ejpam-5293	245	8	lemma	lemma	PROPN
ejpam-5293	245	9	provides	provide	VERB
ejpam-5293	245	10	constants	constant	NOUN
ejpam-5293	245	11	c	c	X
ejpam-5293	245	12	>	>	X
ejpam-5293	245	13	0	0	PROPN
ejpam-5293	245	14	,	,	PUNCT
ejpam-5293	245	15	λ	λ	PROPN
ejpam-5293	245	16	∈	∈	PROPN
ejpam-5293	245	17	(	(	PUNCT
ejpam-5293	245	18	0	0	NUM
ejpam-5293	245	19	,	,	PUNCT
ejpam-5293	245	20	1	1	NUM
ejpam-5293	245	21	)	)	PUNCT
ejpam-5293	245	22	and	and	CCONJ
ejpam-5293	245	23	a	a	DET
ejpam-5293	245	24	point	point	NOUN
ejpam-5293	245	25	y	y	PROPN
ejpam-5293	245	26	∈	∈	PROPN
ejpam-5293	245	27	λ	λ	NOUN
ejpam-5293	246	1	such	such	ADJ
ejpam-5293	246	2	that	that	SCONJ
ejpam-5293	246	3	y	y	PROPN
ejpam-5293	246	4	=	=	PUNCT
ejpam-5293	246	5	fm−ny	fm−ny	NOUN
ejpam-5293	246	6	and	and	CCONJ
ejpam-5293	246	7	d(fn+ix0	d(fn+ix0	PROPN
ejpam-5293	246	8	,	,	PUNCT
ejpam-5293	246	9	f	f	PROPN
ejpam-5293	246	10	iy	iy	PROPN
ejpam-5293	246	11	)	)	PUNCT
ejpam-5293	246	12	≤	≤	PROPN
ejpam-5293	246	13	cλmin{i	cλmin{i	PROPN
ejpam-5293	246	14	,	,	PUNCT
ejpam-5293	246	15	m−n−i}d(fnx0	m−n−i}d(fnx0	PROPN
ejpam-5293	246	16	,	,	PUNCT
ejpam-5293	246	17	f	f	PROPN
ejpam-5293	246	18	mx0	mx0	PROPN
ejpam-5293	246	19	)	)	PUNCT
ejpam-5293	246	20	(	(	PUNCT
ejpam-5293	246	21	14	14	NUM
ejpam-5293	246	22	)	)	PUNCT
ejpam-5293	246	23	for	for	ADP
ejpam-5293	246	24	i	i	PROPN
ejpam-5293	246	25	=	=	SYM
ejpam-5293	246	26	0	0	NUM
ejpam-5293	246	27	,	,	PUNCT
ejpam-5293	246	28	1	1	NUM
ejpam-5293	246	29	,	,	PUNCT
ejpam-5293	246	30	.	.	PUNCT
ejpam-5293	246	31	.	.	PUNCT
ejpam-5293	246	32	.	.	PUNCT
ejpam-5293	247	1	,	,	PUNCT
ejpam-5293	247	2	m	m	AUX
ejpam-5293	247	3	−	−	PROPN
ejpam-5293	247	4	n.	n.	NOUN
ejpam-5293	247	5	taking	take	VERB
ejpam-5293	247	6	into	into	ADP
ejpam-5293	247	7	account	account	NOUN
ejpam-5293	247	8	the	the	DET
ejpam-5293	247	9	definition	definition	NOUN
ejpam-5293	247	10	of	of	ADP
ejpam-5293	247	11	φ	φ	PROPN
ejpam-5293	247	12	in	in	ADP
ejpam-5293	247	13	the	the	DET
ejpam-5293	247	14	dense	dense	ADJ
ejpam-5293	247	15	orbit	orbit	NOUN
ejpam-5293	247	16	of	of	ADP
ejpam-5293	247	17	x0	x0	PROPN
ejpam-5293	247	18	,	,	PUNCT
ejpam-5293	247	19	we	we	PRON
ejpam-5293	247	20	observe	observe	VERB
ejpam-5293	247	21	that	that	SCONJ
ejpam-5293	247	22	|φ	|φ	PROPN
ejpam-5293	247	23	(	(	PUNCT
ejpam-5293	247	24	fnx0)−	fnx0)−	PROPN
ejpam-5293	247	25	φ	φ	X
ejpam-5293	247	26	(	(	PUNCT
ejpam-5293	247	27	fmx0)|	fmx0)|	NOUN
ejpam-5293	247	28	=	=	SYM
ejpam-5293	247	29	|φ(x0	|φ(x0	NOUN
ejpam-5293	247	30	)	)	PUNCT
ejpam-5293	248	1	+	+	CCONJ
ejpam-5293	248	2	α(n	α(n	NOUN
ejpam-5293	248	3	,	,	PUNCT
ejpam-5293	248	4	x0)−	x0)−	PROPN
ejpam-5293	248	5	φ(x0)−	φ(x0)−	PROPN
ejpam-5293	248	6	α(m	α(m	PROPN
ejpam-5293	248	7	,	,	PUNCT
ejpam-5293	248	8	x0)|	x0)|	PROPN
ejpam-5293	248	9	=	=	SYM
ejpam-5293	248	10	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-5293	248	11	n−1∑	n−1∑	PROPN
ejpam-5293	248	12	i=0	i=0	PROPN
ejpam-5293	248	13	φ(f	φ(f	PROPN
ejpam-5293	248	14	ix0)−	ix0)−	NOUN
ejpam-5293	248	15	m−1∑	m−1∑	PROPN
ejpam-5293	248	16	j=0	j=0	PROPN
ejpam-5293	248	17	φ(f	φ(f	PROPN
ejpam-5293	248	18	jx0	jx0	PROPN
ejpam-5293	248	19	)	)	PUNCT
ejpam-5293	248	20	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-5293	248	21	=	=	SYM
ejpam-5293	249	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5293	249	2	m−n−1∑	m−n−1∑	PROPN
ejpam-5293	249	3	i=0	i=0	PROPN
ejpam-5293	249	4	φ(fn+ix0	φ(fn+ix0	PROPN
ejpam-5293	249	5	)	)	PUNCT
ejpam-5293	249	6	∣∣∣∣∣	∣∣∣∣∣	PUNCT
ejpam-5293	249	7	.	.	PUNCT
ejpam-5293	250	1	given	give	VERB
ejpam-5293	250	2	the	the	DET
ejpam-5293	250	3	hypothesis	hypothesis	NOUN
ejpam-5293	250	4	concerning	concern	VERB
ejpam-5293	250	5	the	the	DET
ejpam-5293	250	6	periodic	periodic	ADJ
ejpam-5293	250	7	points	point	NOUN
ejpam-5293	250	8	,	,	PUNCT
ejpam-5293	250	9	we	we	PRON
ejpam-5293	250	10	have	have	VERB
ejpam-5293	250	11	|φ	|φ	PROPN
ejpam-5293	250	12	(	(	PUNCT
ejpam-5293	250	13	fnx0)−	fnx0)−	PROPN
ejpam-5293	250	14	φ	φ	X
ejpam-5293	250	15	(	(	PUNCT
ejpam-5293	250	16	fmx0)|	fmx0)|	NOUN
ejpam-5293	250	17	=	=	PUNCT
ejpam-5293	251	1	∣∣∣∣∣	∣∣∣∣∣	NOUN
ejpam-5293	251	2	m−n−1∑	m−n−1∑	PROPN
ejpam-5293	251	3	i=0	i=0	PROPN
ejpam-5293	252	1	[	[	X
ejpam-5293	252	2	φ(fn+ix0)−	φ(fn+ix0)−	PROPN
ejpam-5293	252	3	φ(f	φ(f	PROPN
ejpam-5293	252	4	iy	iy	PROPN
ejpam-5293	252	5	)	)	PUNCT
ejpam-5293	252	6	]	]	PUNCT
ejpam-5293	253	1	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-5293	253	2	≤	≤	NOUN
ejpam-5293	253	3	m−n−1∑	m−n−1∑	PROPN
ejpam-5293	253	4	i=0	i=0	PROPN
ejpam-5293	253	5	∣∣φ(fn+ix0)−	∣∣φ(fn+ix0)−	PROPN
ejpam-5293	253	6	φ(f	φ(f	PROPN
ejpam-5293	253	7	iy	iy	PROPN
ejpam-5293	253	8	)	)	PUNCT
ejpam-5293	253	9	∣∣	∣∣	X
ejpam-5293	253	10	.	.	PUNCT
ejpam-5293	254	1	since	since	SCONJ
ejpam-5293	254	2	φ	φ	PROPN
ejpam-5293	254	3	is	be	AUX
ejpam-5293	254	4	hölder	hölder	NOUN
ejpam-5293	254	5	with	with	ADP
ejpam-5293	254	6	exponent	exponent	NOUN
ejpam-5293	254	7	θ	θ	PROPN
ejpam-5293	254	8	∈	∈	PROPN
ejpam-5293	254	9	(	(	PUNCT
ejpam-5293	254	10	0	0	NUM
ejpam-5293	254	11	,	,	PUNCT
ejpam-5293	254	12	1	1	NUM
ejpam-5293	254	13	]	]	PUNCT
ejpam-5293	254	14	,	,	PUNCT
ejpam-5293	254	15	there	there	PRON
ejpam-5293	254	16	is	be	VERB
ejpam-5293	254	17	a	a	DET
ejpam-5293	254	18	constantk	constantk	NOUN
ejpam-5293	254	19	>	>	X
ejpam-5293	254	20	0	0	NUM
ejpam-5293	255	1	such	such	ADJ
ejpam-5293	255	2	that	that	DET
ejpam-5293	255	3	|φ(x1)−	|φ(x1)−	NOUN
ejpam-5293	255	4	φ(x2)|	φ(x2)|	PROPN
ejpam-5293	255	5	≤	≤	PROPN
ejpam-5293	255	6	kd(x1	kd(x1	PROPN
ejpam-5293	255	7	,	,	PUNCT
ejpam-5293	255	8	x2	x2	PROPN
ejpam-5293	255	9	)	)	PUNCT
ejpam-5293	255	10	θ	θ	PROPN
ejpam-5293	255	11	.	.	PUNCT
ejpam-5293	256	1	then	then	ADV
ejpam-5293	256	2	we	we	PRON
ejpam-5293	256	3	obtain	obtain	VERB
ejpam-5293	256	4	|φ	|φ	PROPN
ejpam-5293	256	5	(	(	PUNCT
ejpam-5293	256	6	fnx0)−	fnx0)−	PROPN
ejpam-5293	256	7	φ	φ	X
ejpam-5293	256	8	(	(	PUNCT
ejpam-5293	256	9	fmx0)|	fmx0)|	PROPN
ejpam-5293	256	10	≤	≤	PUNCT
ejpam-5293	256	11	m−n−1∑	m−n−1∑	PROPN
ejpam-5293	256	12	i=0	i=0	PROPN
ejpam-5293	256	13	k	k	PROPN
ejpam-5293	256	14	d(fn+ix0	d(fn+ix0	PROPN
ejpam-5293	256	15	,	,	PUNCT
ejpam-5293	256	16	f	f	PROPN
ejpam-5293	256	17	iy)θ	iy)θ	PROPN
ejpam-5293	256	18	.	.	PUNCT
ejpam-5293	257	1	it	it	PRON
ejpam-5293	257	2	follows	follow	VERB
ejpam-5293	257	3	from	from	ADP
ejpam-5293	257	4	(	(	PUNCT
ejpam-5293	257	5	14	14	NUM
ejpam-5293	257	6	)	)	PUNCT
ejpam-5293	257	7	that	that	PRON
ejpam-5293	257	8	|φ	|φ	PROPN
ejpam-5293	257	9	(	(	PUNCT
ejpam-5293	257	10	fnx0)−	fnx0)−	PROPN
ejpam-5293	257	11	φ	φ	X
ejpam-5293	257	12	(	(	PUNCT
ejpam-5293	257	13	fmx0)|	fmx0)|	PROPN
ejpam-5293	257	14	≤	≤	PUNCT
ejpam-5293	257	15	m−n−1∑	m−n−1∑	PROPN
ejpam-5293	257	16	i=0	i=0	PROPN
ejpam-5293	257	17	k(cλmin{i	k(cλmin{i	PROPN
ejpam-5293	257	18	,	,	PUNCT
ejpam-5293	257	19	m−n−i	m−n−i	ADJ
ejpam-5293	257	20	}	}	PUNCT
ejpam-5293	257	21	d(fnx0	d(fnx0	PROPN
ejpam-5293	257	22	,	,	PUNCT
ejpam-5293	257	23	f	f	PROPN
ejpam-5293	257	24	mx0	mx0	PROPN
ejpam-5293	257	25	)	)	PUNCT
ejpam-5293	257	26	)	)	PUNCT
ejpam-5293	258	1	θ	θ	PROPN
ejpam-5293	258	2	,	,	PUNCT
ejpam-5293	258	3	leading	lead	VERB
ejpam-5293	258	4	to	to	ADP
ejpam-5293	258	5	|φ	|φ	PROPN
ejpam-5293	258	6	(	(	PUNCT
ejpam-5293	258	7	fnx0)−	fnx0)−	PROPN
ejpam-5293	258	8	φ	φ	X
ejpam-5293	258	9	(	(	PUNCT
ejpam-5293	258	10	fmx0)|	fmx0)|	NOUN
ejpam-5293	258	11	≤	≤	NUM
ejpam-5293	258	12	2kcθ	2kcθ	PROPN
ejpam-5293	258	13	d(fnx0	d(fnx0	PROPN
ejpam-5293	258	14	,	,	PUNCT
ejpam-5293	258	15	f	f	PROPN
ejpam-5293	258	16	mx0	mx0	PROPN
ejpam-5293	258	17	)	)	PUNCT
ejpam-5293	258	18	θ	θ	PROPN
ejpam-5293	258	19	m−n−1∑	m−n−1∑	PROPN
ejpam-5293	258	20	i=0	i=0	PROPN
ejpam-5293	258	21	λθi	λθi	VERB
ejpam-5293	258	22	<	<	X
ejpam-5293	258	23	2kcθ	2kcθ	PROPN
ejpam-5293	258	24	1−	1−	NUM
ejpam-5293	258	25	λθ	λθ	ADP
ejpam-5293	258	26	d(fnx0	d(fnx0	PROPN
ejpam-5293	258	27	,	,	PUNCT
ejpam-5293	258	28	f	f	PROPN
ejpam-5293	258	29	mx0	mx0	PROPN
ejpam-5293	258	30	)	)	PUNCT
ejpam-5293	258	31	θ	θ	PROPN
ejpam-5293	258	32	.	.	PUNCT
ejpam-5293	258	33	r.	r.	PROPN
ejpam-5293	258	34	d.	d.	PROPN
ejpam-5293	258	35	laureano	laureano	PROPN
ejpam-5293	258	36	/	/	SYM
ejpam-5293	258	37	eur	eur	PROPN
ejpam-5293	258	38	.	.	PUNCT
ejpam-5293	259	1	j.	j.	PROPN
ejpam-5293	259	2	pure	pure	PROPN
ejpam-5293	259	3	appl	appl	PROPN
ejpam-5293	259	4	.	.	PROPN
ejpam-5293	259	5	math	math	PROPN
ejpam-5293	259	6	,	,	PUNCT
ejpam-5293	259	7	17	17	NUM
ejpam-5293	259	8	(	(	PUNCT
ejpam-5293	259	9	3	3	NUM
ejpam-5293	259	10	)	)	PUNCT
ejpam-5293	259	11	(	(	PUNCT
ejpam-5293	259	12	2024	2024	NUM
ejpam-5293	259	13	)	)	PUNCT
ejpam-5293	259	14	,	,	PUNCT
ejpam-5293	259	15	1403	1403	NUM
ejpam-5293	259	16	-	-	SYM
ejpam-5293	259	17	1416	1416	NUM
ejpam-5293	259	18	1414	1414	NUM
ejpam-5293	260	1	so	so	ADV
ejpam-5293	260	2	,	,	PUNCT
ejpam-5293	260	3	we	we	PRON
ejpam-5293	260	4	obtain	obtain	VERB
ejpam-5293	260	5	the	the	DET
ejpam-5293	260	6	inequality	inequality	NOUN
ejpam-5293	260	7	|φ	|φ	PROPN
ejpam-5293	260	8	(	(	PUNCT
ejpam-5293	260	9	fnx0)−	fnx0)−	PROPN
ejpam-5293	260	10	φ	φ	X
ejpam-5293	260	11	(	(	PUNCT
ejpam-5293	260	12	fmx0)|	fmx0)|	VERB
ejpam-5293	260	13	<	<	X
ejpam-5293	260	14	2kcθ	2kcθ	NUM
ejpam-5293	260	15	1−	1−	NUM
ejpam-5293	260	16	λθ	λθ	ADP
ejpam-5293	260	17	d(fnx0	d(fnx0	PROPN
ejpam-5293	260	18	,	,	PUNCT
ejpam-5293	260	19	f	f	PROPN
ejpam-5293	260	20	mx0	mx0	PROPN
ejpam-5293	260	21	)	)	PUNCT
ejpam-5293	260	22	θ	θ	PROPN
ejpam-5293	260	23	.	.	PUNCT
ejpam-5293	261	1	(	(	PUNCT
ejpam-5293	261	2	15	15	NUM
ejpam-5293	261	3	)	)	PUNCT
ejpam-5293	261	4	in	in	ADP
ejpam-5293	261	5	a	a	DET
ejpam-5293	261	6	very	very	ADV
ejpam-5293	261	7	similar	similar	ADJ
ejpam-5293	261	8	way	way	NOUN
ejpam-5293	261	9	we	we	PRON
ejpam-5293	261	10	can	can	AUX
ejpam-5293	261	11	prove	prove	VERB
ejpam-5293	261	12	that	that	SCONJ
ejpam-5293	261	13	the	the	DET
ejpam-5293	261	14	inequality	inequality	NOUN
ejpam-5293	261	15	(	(	PUNCT
ejpam-5293	261	16	15	15	NUM
ejpam-5293	261	17	)	)	PUNCT
ejpam-5293	261	18	is	be	AUX
ejpam-5293	261	19	also	also	ADV
ejpam-5293	261	20	valid	valid	ADJ
ejpam-5293	261	21	for	for	ADP
ejpam-5293	261	22	any	any	DET
ejpam-5293	261	23	n	n	CCONJ
ejpam-5293	261	24	,	,	PUNCT
ejpam-5293	261	25	m	m	PROPN
ejpam-5293	261	26	∈	∈	PROPN
ejpam-5293	261	27	z.	z.	PROPN
ejpam-5293	261	28	since	since	SCONJ
ejpam-5293	261	29	φ	φ	PROPN
ejpam-5293	261	30	is	be	AUX
ejpam-5293	261	31	hölder	hölder	NOUN
ejpam-5293	261	32	in	in	ADP
ejpam-5293	261	33	the	the	DET
ejpam-5293	261	34	orbit	orbit	NOUN
ejpam-5293	261	35	of	of	ADP
ejpam-5293	261	36	x0	x0	PROPN
ejpam-5293	261	37	and	and	CCONJ
ejpam-5293	261	38	this	this	DET
ejpam-5293	261	39	orbit	orbit	NOUN
ejpam-5293	261	40	is	be	AUX
ejpam-5293	261	41	dense	dense	ADJ
ejpam-5293	261	42	in	in	ADP
ejpam-5293	261	43	λ	λ	PROPN
ejpam-5293	261	44	,	,	PUNCT
ejpam-5293	261	45	the	the	DET
ejpam-5293	261	46	function	function	NOUN
ejpam-5293	261	47	φ	φ	PROPN
ejpam-5293	261	48	is	be	AUX
ejpam-5293	261	49	uniquely	uniquely	ADV
ejpam-5293	261	50	extendable	extendable	ADJ
ejpam-5293	261	51	to	to	ADP
ejpam-5293	261	52	a	a	DET
ejpam-5293	261	53	continuous	continuous	ADJ
ejpam-5293	261	54	function	function	NOUN
ejpam-5293	261	55	in	in	ADP
ejpam-5293	261	56	λ	λ	PROPN
ejpam-5293	261	57	,	,	PUNCT
ejpam-5293	261	58	which	which	PRON
ejpam-5293	261	59	we	we	PRON
ejpam-5293	261	60	still	still	ADV
ejpam-5293	261	61	denote	denote	VERB
ejpam-5293	261	62	by	by	ADP
ejpam-5293	261	63	φ	φ	PROPN
ejpam-5293	261	64	.	.	PUNCT
ejpam-5293	262	1	immediately	immediately	ADV
ejpam-5293	262	2	follows	follow	VERB
ejpam-5293	262	3	from	from	ADP
ejpam-5293	262	4	(	(	PUNCT
ejpam-5293	262	5	15	15	NUM
ejpam-5293	262	6	)	)	PUNCT
ejpam-5293	262	7	that	that	SCONJ
ejpam-5293	262	8	the	the	DET
ejpam-5293	262	9	extension	extension	NOUN
ejpam-5293	262	10	of	of	ADP
ejpam-5293	262	11	φ	φ	PROPN
ejpam-5293	262	12	into	into	ADP
ejpam-5293	262	13	λ	λ	PROPN
ejpam-5293	262	14	has	have	VERB
ejpam-5293	262	15	at	at	ADP
ejpam-5293	262	16	least	least	ADJ
ejpam-5293	262	17	the	the	DET
ejpam-5293	262	18	same	same	ADJ
ejpam-5293	262	19	hölder	hölder	NOUN
ejpam-5293	262	20	exponent	exponent	NOUN
ejpam-5293	262	21	as	as	ADP
ejpam-5293	262	22	φ	φ	PROPN
ejpam-5293	262	23	.	.	PUNCT
ejpam-5293	263	1	since	since	SCONJ
ejpam-5293	263	2	f	f	PROPN
ejpam-5293	263	3	is	be	AUX
ejpam-5293	263	4	continuous	continuous	ADJ
ejpam-5293	263	5	and	and	CCONJ
ejpam-5293	263	6	φ	φ	PROPN
ejpam-5293	263	7	is	be	AUX
ejpam-5293	263	8	hölder	hölder	NOUN
ejpam-5293	263	9	continuous	continuous	ADJ
ejpam-5293	263	10	,	,	PUNCT
ejpam-5293	263	11	then	then	ADV
ejpam-5293	263	12	φ	φ	PROPN
ejpam-5293	263	13	and	and	CCONJ
ejpam-5293	263	14	φ	φ	PROPN
ejpam-5293	263	15	◦	◦	PROPN
ejpam-5293	263	16	f	f	PROPN
ejpam-5293	263	17	−φ	−φ	NOUN
ejpam-5293	263	18	are	be	AUX
ejpam-5293	263	19	continuous	continuous	ADJ
ejpam-5293	263	20	functions	function	NOUN
ejpam-5293	263	21	in	in	ADP
ejpam-5293	263	22	λ	λ	PROPN
ejpam-5293	263	23	which	which	PRON
ejpam-5293	263	24	coincide	coincide	VERB
ejpam-5293	263	25	on	on	ADP
ejpam-5293	263	26	the	the	DET
ejpam-5293	263	27	dense	dense	ADJ
ejpam-5293	263	28	orbit	orbit	NOUN
ejpam-5293	263	29	of	of	ADP
ejpam-5293	263	30	x0	x0	PROPN
ejpam-5293	263	31	.	.	PUNCT
ejpam-5293	264	1	therefore	therefore	ADV
ejpam-5293	264	2	,	,	PUNCT
ejpam-5293	264	3	they	they	PRON
ejpam-5293	264	4	coincide	coincide	VERB
ejpam-5293	264	5	in	in	ADP
ejpam-5293	264	6	the	the	DET
ejpam-5293	264	7	whole	whole	ADJ
ejpam-5293	264	8	set	set	NOUN
ejpam-5293	264	9	λ	λ	PROPN
ejpam-5293	264	10	and	and	CCONJ
ejpam-5293	264	11	φ	φ	PROPN
ejpam-5293	264	12	is	be	AUX
ejpam-5293	264	13	a	a	DET
ejpam-5293	264	14	continuous	continuous	ADJ
ejpam-5293	264	15	solution	solution	NOUN
ejpam-5293	264	16	of	of	ADP
ejpam-5293	264	17	the	the	DET
ejpam-5293	264	18	cohomological	cohomological	ADJ
ejpam-5293	264	19	equation	equation	NOUN
ejpam-5293	264	20	.	.	PUNCT
ejpam-5293	265	1	the	the	DET
ejpam-5293	265	2	claim	claim	NOUN
ejpam-5293	265	3	of	of	ADP
ejpam-5293	265	4	uniqueness	uniqueness	NOUN
ejpam-5293	265	5	is	be	AUX
ejpam-5293	265	6	a	a	DET
ejpam-5293	265	7	consequence	consequence	NOUN
ejpam-5293	265	8	of	of	ADP
ejpam-5293	265	9	the	the	DET
ejpam-5293	265	10	choice	choice	NOUN
ejpam-5293	265	11	of	of	ADP
ejpam-5293	265	12	φ(x0	φ(x0	NOUN
ejpam-5293	265	13	)	)	PUNCT
ejpam-5293	265	14	determine	determine	VERB
ejpam-5293	265	15	φ	φ	PROPN
ejpam-5293	265	16	in	in	ADP
ejpam-5293	265	17	a	a	DET
ejpam-5293	265	18	unique	unique	ADJ
ejpam-5293	265	19	way	way	NOUN
ejpam-5293	265	20	.	.	PUNCT
ejpam-5293	266	1	4	4	X
ejpam-5293	266	2	.	.	X
ejpam-5293	266	3	conclusions	conclusion	NOUN
ejpam-5293	266	4	acl	acl	PROPN
ejpam-5293	266	5	plays	play	VERB
ejpam-5293	266	6	a	a	DET
ejpam-5293	266	7	pivotal	pivotal	ADJ
ejpam-5293	266	8	role	role	NOUN
ejpam-5293	266	9	in	in	ADP
ejpam-5293	266	10	establishing	establish	VERB
ejpam-5293	266	11	the	the	DET
ejpam-5293	266	12	livschitz	livschitz	NOUN
ejpam-5293	266	13	theorem	theorem	NOUN
ejpam-5293	266	14	,	,	PUNCT
ejpam-5293	266	15	which	which	PRON
ejpam-5293	266	16	provides	provide	VERB
ejpam-5293	266	17	a	a	DET
ejpam-5293	266	18	necessary	necessary	ADJ
ejpam-5293	266	19	and	and	CCONJ
ejpam-5293	266	20	sufficient	sufficient	ADJ
ejpam-5293	266	21	condition	condition	NOUN
ejpam-5293	266	22	for	for	ADP
ejpam-5293	266	23	the	the	DET
ejpam-5293	266	24	existence	existence	NOUN
ejpam-5293	266	25	of	of	ADP
ejpam-5293	266	26	cohomological	cohomological	ADJ
ejpam-5293	266	27	equations	equation	NOUN
ejpam-5293	266	28	with	with	ADP
ejpam-5293	266	29	sufficiently	sufficiently	ADV
ejpam-5293	266	30	regular	regular	ADJ
ejpam-5293	266	31	solutions	solution	NOUN
ejpam-5293	266	32	.	.	PUNCT
ejpam-5293	267	1	this	this	DET
ejpam-5293	267	2	lemma	lemma	PROPN
ejpam-5293	267	3	ensures	ensure	VERB
ejpam-5293	267	4	that	that	SCONJ
ejpam-5293	267	5	for	for	ADP
ejpam-5293	267	6	hyperbolic	hyperbolic	ADJ
ejpam-5293	267	7	diffeomorphisms	diffeomorphism	NOUN
ejpam-5293	267	8	,	,	PUNCT
ejpam-5293	267	9	any	any	DET
ejpam-5293	267	10	orbit	orbit	NOUN
ejpam-5293	267	11	that	that	PRON
ejpam-5293	267	12	comes	come	VERB
ejpam-5293	267	13	close	close	ADV
ejpam-5293	267	14	to	to	ADP
ejpam-5293	267	15	a	a	DET
ejpam-5293	267	16	periodic	periodic	ADJ
ejpam-5293	267	17	orbit	orbit	NOUN
ejpam-5293	267	18	can	can	AUX
ejpam-5293	267	19	be	be	AUX
ejpam-5293	267	20	perturbed	perturb	VERB
ejpam-5293	267	21	to	to	ADP
ejpam-5293	267	22	an	an	DET
ejpam-5293	267	23	actual	actual	ADJ
ejpam-5293	267	24	periodic	periodic	ADJ
ejpam-5293	267	25	orbit	orbit	NOUN
ejpam-5293	267	26	.	.	PUNCT
ejpam-5293	268	1	this	this	DET
ejpam-5293	268	2	property	property	NOUN
ejpam-5293	268	3	is	be	AUX
ejpam-5293	268	4	crucial	crucial	ADJ
ejpam-5293	268	5	for	for	SCONJ
ejpam-5293	268	6	the	the	DET
ejpam-5293	268	7	livschitz	livschitz	NOUN
ejpam-5293	268	8	theorem	theorem	NOUN
ejpam-5293	268	9	,	,	PUNCT
ejpam-5293	268	10	as	as	SCONJ
ejpam-5293	268	11	it	it	PRON
ejpam-5293	268	12	allows	allow	VERB
ejpam-5293	268	13	relating	relate	VERB
ejpam-5293	268	14	the	the	DET
ejpam-5293	268	15	behavior	behavior	NOUN
ejpam-5293	268	16	of	of	ADP
ejpam-5293	268	17	cocycles	cocycle	NOUN
ejpam-5293	268	18	along	along	ADP
ejpam-5293	268	19	periodic	periodic	ADJ
ejpam-5293	268	20	orbits	orbit	NOUN
ejpam-5293	268	21	to	to	ADP
ejpam-5293	268	22	the	the	DET
ejpam-5293	268	23	existence	existence	NOUN
ejpam-5293	268	24	of	of	ADP
ejpam-5293	268	25	solutions	solution	NOUN
ejpam-5293	268	26	to	to	ADP
ejpam-5293	268	27	the	the	DET
ejpam-5293	268	28	cohomological	cohomological	ADJ
ejpam-5293	268	29	equation	equation	NOUN
ejpam-5293	268	30	.	.	PUNCT
ejpam-5293	269	1	throughout	throughout	ADP
ejpam-5293	269	2	the	the	DET
ejpam-5293	269	3	article	article	NOUN
ejpam-5293	269	4	,	,	PUNCT
ejpam-5293	269	5	the	the	DET
ejpam-5293	269	6	necessary	necessary	ADJ
ejpam-5293	269	7	elements	element	NOUN
ejpam-5293	269	8	to	to	PART
ejpam-5293	269	9	demonstrate	demonstrate	VERB
ejpam-5293	269	10	the	the	DET
ejpam-5293	269	11	livschitz	livschitz	NOUN
ejpam-5293	269	12	theorem	theorem	VERB
ejpam-5293	269	13	in	in	ADP
ejpam-5293	269	14	discrete	discrete	ADJ
ejpam-5293	269	15	time	time	NOUN
ejpam-5293	269	16	are	be	AUX
ejpam-5293	269	17	detailed	detail	VERB
ejpam-5293	269	18	,	,	PUNCT
ejpam-5293	269	19	emphasizing	emphasize	VERB
ejpam-5293	269	20	the	the	DET
ejpam-5293	269	21	development	development	NOUN
ejpam-5293	269	22	that	that	PRON
ejpam-5293	269	23	leads	lead	VERB
ejpam-5293	269	24	to	to	ADP
ejpam-5293	269	25	a	a	DET
ejpam-5293	269	26	distance	distance	NOUN
ejpam-5293	269	27	control	control	NOUN
ejpam-5293	269	28	inequality	inequality	NOUN
ejpam-5293	269	29	provided	provide	VERB
ejpam-5293	269	30	by	by	ADP
ejpam-5293	269	31	the	the	DET
ejpam-5293	269	32	acl	acl	PROPN
ejpam-5293	269	33	for	for	ADP
ejpam-5293	269	34	hyperbolic	hyperbolic	ADJ
ejpam-5293	269	35	diffeomorphisms	diffeomorphism	NOUN
ejpam-5293	269	36	.	.	PUNCT
ejpam-5293	270	1	in	in	ADP
ejpam-5293	270	2	this	this	DET
ejpam-5293	270	3	way	way	NOUN
ejpam-5293	270	4	,	,	PUNCT
ejpam-5293	270	5	it	it	PRON
ejpam-5293	270	6	is	be	AUX
ejpam-5293	270	7	worth	worth	ADJ
ejpam-5293	270	8	mentioning	mention	VERB
ejpam-5293	270	9	that	that	SCONJ
ejpam-5293	270	10	the	the	DET
ejpam-5293	270	11	acl	acl	PROPN
ejpam-5293	270	12	is	be	AUX
ejpam-5293	270	13	crucial	crucial	ADJ
ejpam-5293	270	14	in	in	ADP
ejpam-5293	270	15	the	the	DET
ejpam-5293	270	16	livschitz	livschitz	NOUN
ejpam-5293	270	17	theorem	theorem	ADJ
ejpam-5293	270	18	proof	proof	NOUN
ejpam-5293	270	19	and	and	CCONJ
ejpam-5293	270	20	consequently	consequently	ADV
ejpam-5293	270	21	ensures	ensure	VERB
ejpam-5293	270	22	the	the	DET
ejpam-5293	270	23	existence	existence	NOUN
ejpam-5293	270	24	of	of	ADP
ejpam-5293	270	25	cohomological	cohomological	ADJ
ejpam-5293	270	26	equations	equation	NOUN
ejpam-5293	270	27	with	with	ADP
ejpam-5293	270	28	sufficiently	sufficiently	ADV
ejpam-5293	270	29	regular	regular	ADJ
ejpam-5293	270	30	solutions	solution	NOUN
ejpam-5293	270	31	.	.	PUNCT
ejpam-5293	271	1	the	the	DET
ejpam-5293	271	2	inequality	inequality	NOUN
ejpam-5293	271	3	(	(	PUNCT
ejpam-5293	271	4	5	5	NUM
ejpam-5293	271	5	)	)	PUNCT
ejpam-5293	271	6	is	be	AUX
ejpam-5293	271	7	crucial	crucial	ADJ
ejpam-5293	271	8	quantitative	quantitative	ADJ
ejpam-5293	271	9	data	datum	NOUN
ejpam-5293	271	10	that	that	PRON
ejpam-5293	271	11	states	state	VERB
ejpam-5293	271	12	the	the	DET
ejpam-5293	271	13	control	control	NOUN
ejpam-5293	271	14	of	of	ADP
ejpam-5293	271	15	the	the	DET
ejpam-5293	271	16	distance	distance	NOUN
ejpam-5293	271	17	between	between	ADP
ejpam-5293	271	18	corresponding	corresponding	ADJ
ejpam-5293	271	19	points	point	NOUN
ejpam-5293	271	20	of	of	ADP
ejpam-5293	271	21	an	an	DET
ejpam-5293	271	22	initial	initial	ADJ
ejpam-5293	271	23	orbit	orbit	NOUN
ejpam-5293	271	24	and	and	CCONJ
ejpam-5293	271	25	the	the	DET
ejpam-5293	271	26	constructed	construct	VERB
ejpam-5293	271	27	periodic	periodic	ADJ
ejpam-5293	271	28	orbit	orbit	NOUN
ejpam-5293	271	29	.	.	PUNCT
ejpam-5293	272	1	given	give	VERB
ejpam-5293	272	2	the	the	DET
ejpam-5293	272	3	exposed	expose	VERB
ejpam-5293	272	4	relationship	relationship	NOUN
ejpam-5293	272	5	between	between	ADP
ejpam-5293	272	6	solving	solve	VERB
ejpam-5293	272	7	cohomological	cohomological	ADJ
ejpam-5293	272	8	equations	equation	NOUN
ejpam-5293	272	9	and	and	CCONJ
ejpam-5293	272	10	obtaining	obtain	VERB
ejpam-5293	272	11	coboundaries	coboundarie	NOUN
ejpam-5293	272	12	,	,	PUNCT
ejpam-5293	272	13	the	the	DET
ejpam-5293	272	14	livschitz	livschitz	NOUN
ejpam-5293	272	15	theorem	theorem	NOUN
ejpam-5293	272	16	can	can	AUX
ejpam-5293	272	17	be	be	AUX
ejpam-5293	272	18	understood	understand	VERB
ejpam-5293	272	19	as	as	ADP
ejpam-5293	272	20	:	:	PUNCT
ejpam-5293	272	21	in	in	ADP
ejpam-5293	272	22	hyperbolic	hyperbolic	ADJ
ejpam-5293	272	23	dynamics	dynamic	NOUN
ejpam-5293	272	24	and	and	CCONJ
ejpam-5293	272	25	hölder	hölder	NOUN
ejpam-5293	272	26	functions	function	NOUN
ejpam-5293	272	27	,	,	PUNCT
ejpam-5293	272	28	the	the	DET
ejpam-5293	272	29	periodic	periodic	ADJ
ejpam-5293	272	30	data	datum	NOUN
ejpam-5293	272	31	are	be	AUX
ejpam-5293	272	32	necessary	necessary	ADJ
ejpam-5293	272	33	and	and	CCONJ
ejpam-5293	272	34	sufficient	sufficient	ADJ
ejpam-5293	272	35	to	to	PART
ejpam-5293	272	36	identify	identify	VERB
ejpam-5293	272	37	hölder	hölder	NOUN
ejpam-5293	272	38	coboundaries	coboundarie	NOUN
ejpam-5293	272	39	.	.	PUNCT
ejpam-5293	273	1	the	the	DET
ejpam-5293	273	2	class	class	NOUN
ejpam-5293	273	3	of	of	ADP
ejpam-5293	273	4	hyperbolic	hyperbolic	ADJ
ejpam-5293	273	5	dynamical	dynamical	ADJ
ejpam-5293	273	6	systems	system	NOUN
ejpam-5293	273	7	contains	contain	VERB
ejpam-5293	273	8	several	several	ADJ
ejpam-5293	273	9	examples	example	NOUN
ejpam-5293	273	10	of	of	ADP
ejpam-5293	273	11	invertible	invertible	ADJ
ejpam-5293	273	12	smooth	smooth	ADJ
ejpam-5293	273	13	dynamical	dynamical	ADJ
ejpam-5293	273	14	systems	system	NOUN
ejpam-5293	273	15	with	with	ADP
ejpam-5293	273	16	complicated	complicated	ADJ
ejpam-5293	273	17	orbit	orbit	NOUN
ejpam-5293	273	18	structure	structure	NOUN
ejpam-5293	273	19	,	,	PUNCT
ejpam-5293	273	20	namely	namely	ADV
ejpam-5293	273	21	hyperbolic	hyperbolic	ADJ
ejpam-5293	273	22	toral	toral	ADJ
ejpam-5293	273	23	automorphisms	automorphism	NOUN
ejpam-5293	273	24	,	,	PUNCT
ejpam-5293	273	25	their	their	PRON
ejpam-5293	273	26	c1	c1	NOUN
ejpam-5293	273	27	-	-	PUNCT
ejpam-5293	273	28	perturbations	perturbation	NOUN
ejpam-5293	273	29	,	,	PUNCT
ejpam-5293	273	30	as	as	ADV
ejpam-5293	273	31	well	well	ADV
ejpam-5293	273	32	as	as	ADP
ejpam-5293	273	33	expanding	expand	VERB
ejpam-5293	273	34	maps	map	NOUN
ejpam-5293	273	35	of	of	ADP
ejpam-5293	273	36	the	the	DET
ejpam-5293	273	37	circle	circle	NOUN
ejpam-5293	273	38	.	.	PUNCT
ejpam-5293	274	1	acknowledgements	acknowledgement	NOUN
ejpam-5293	274	2	this	this	DET
ejpam-5293	274	3	research	research	NOUN
ejpam-5293	274	4	was	be	AUX
ejpam-5293	274	5	initiated	initiate	VERB
ejpam-5293	274	6	under	under	ADP
ejpam-5293	274	7	the	the	DET
ejpam-5293	274	8	supervision	supervision	NOUN
ejpam-5293	274	9	of	of	ADP
ejpam-5293	274	10	lúıs	lúıs	PROPN
ejpam-5293	274	11	barreira	barreira	NOUN
ejpam-5293	274	12	,	,	PUNCT
ejpam-5293	274	13	ist	ist	VERB
ejpam-5293	274	14	technical	technical	ADJ
ejpam-5293	274	15	university	university	PROPN
ejpam-5293	274	16	of	of	ADP
ejpam-5293	274	17	lisbon	lisbon	PROPN
ejpam-5293	274	18	.	.	PUNCT
ejpam-5293	275	1	references	reference	NOUN
ejpam-5293	275	2	1415	1415	NUM
ejpam-5293	275	3	references	reference	NOUN
ejpam-5293	275	4	[	[	X
ejpam-5293	275	5	1	1	NUM
ejpam-5293	275	6	]	]	SYM
ejpam-5293	275	7	v	v	ADP
ejpam-5293	275	8	niţiçă	niţiçă	PROPN
ejpam-5293	275	9	a	a	DET
ejpam-5293	275	10	katok	katok	NOUN
ejpam-5293	275	11	and	and	CCONJ
ejpam-5293	275	12	a	a	DET
ejpam-5293	275	13	török	török	NUM
ejpam-5293	275	14	.	.	PUNCT
ejpam-5293	276	1	nonabelian	nonabelian	ADJ
ejpam-5293	276	2	cohomology	cohomology	NOUN
ejpam-5293	276	3	of	of	ADP
ejpam-5293	276	4	abelian	abelian	PROPN
ejpam-5293	276	5	anosov	anosov	PROPN
ejpam-5293	276	6	actions	action	NOUN
ejpam-5293	276	7	.	.	PUNCT
ejpam-5293	277	1	ergodic	ergodic	ADJ
ejpam-5293	277	2	theory	theory	NOUN
ejpam-5293	277	3	dynam	dynam	PROPN
ejpam-5293	277	4	.	.	PUNCT
ejpam-5293	278	1	systems	system	NOUN
ejpam-5293	278	2	,	,	PUNCT
ejpam-5293	278	3	20:259–288	20:259–288	NUM
ejpam-5293	278	4	,	,	PUNCT
ejpam-5293	278	5	2000	2000	NUM
ejpam-5293	278	6	.	.	PUNCT
ejpam-5293	279	1	[	[	X
ejpam-5293	279	2	2	2	NUM
ejpam-5293	279	3	]	]	SYM
ejpam-5293	279	4	f	f	PROPN
ejpam-5293	279	5	barbaresco	barbaresco	PROPN
ejpam-5293	279	6	.	.	PUNCT
ejpam-5293	280	1	geometric	geometric	ADJ
ejpam-5293	280	2	theory	theory	NOUN
ejpam-5293	280	3	of	of	ADP
ejpam-5293	280	4	heat	heat	NOUN
ejpam-5293	280	5	from	from	ADP
ejpam-5293	280	6	souriau	souriau	NOUN
ejpam-5293	280	7	lie	lie	VERB
ejpam-5293	280	8	groups	group	NOUN
ejpam-5293	280	9	thermodynamics	thermodynamic	NOUN
ejpam-5293	280	10	and	and	CCONJ
ejpam-5293	280	11	koszul	koszul	ADJ
ejpam-5293	280	12	hessian	hessian	ADJ
ejpam-5293	280	13	geometry	geometry	NOUN
ejpam-5293	280	14	:	:	PUNCT
ejpam-5293	280	15	applications	application	NOUN
ejpam-5293	280	16	in	in	ADP
ejpam-5293	280	17	information	information	NOUN
ejpam-5293	280	18	geometry	geometry	NOUN
ejpam-5293	280	19	for	for	ADP
ejpam-5293	280	20	exponential	exponential	ADJ
ejpam-5293	280	21	families	family	NOUN
ejpam-5293	280	22	.	.	PUNCT
ejpam-5293	281	1	entropy	entropy	PROPN
ejpam-5293	281	2	,	,	PUNCT
ejpam-5293	281	3	18:386–458	18:386–458	NUM
ejpam-5293	281	4	,	,	PUNCT
ejpam-5293	281	5	2016	2016	NUM
ejpam-5293	281	6	.	.	PUNCT
ejpam-5293	282	1	[	[	X
ejpam-5293	282	2	3	3	X
ejpam-5293	282	3	]	]	X
ejpam-5293	282	4	c	c	NOUN
ejpam-5293	282	5	cafaro	cafaro	NOUN
ejpam-5293	282	6	and	and	CCONJ
ejpam-5293	282	7	s	s	PROPN
ejpam-5293	282	8	a	a	DET
ejpam-5293	282	9	ali	ali	PROPN
ejpam-5293	282	10	.	.	PUNCT
ejpam-5293	283	1	jacobi	jacobi	PROPN
ejpam-5293	283	2	fields	field	NOUN
ejpam-5293	283	3	on	on	ADP
ejpam-5293	283	4	statistical	statistical	ADJ
ejpam-5293	283	5	manifolds	manifold	NOUN
ejpam-5293	283	6	of	of	ADP
ejpam-5293	283	7	negative	negative	ADJ
ejpam-5293	283	8	curvature	curvature	NOUN
ejpam-5293	283	9	.	.	PUNCT
ejpam-5293	284	1	physica	physica	PROPN
ejpam-5293	284	2	d	d	PROPN
ejpam-5293	284	3	,	,	PUNCT
ejpam-5293	284	4	234:70–80	234:70–80	PROPN
ejpam-5293	284	5	,	,	PUNCT
ejpam-5293	284	6	2007	2007	NUM
ejpam-5293	284	7	.	.	PUNCT
ejpam-5293	285	1	[	[	X
ejpam-5293	285	2	4	4	NUM
ejpam-5293	285	3	]	]	X
ejpam-5293	285	4	r	r	X
ejpam-5293	285	5	de	de	X
ejpam-5293	285	6	la	la	X
ejpam-5293	285	7	llave	llave	PROPN
ejpam-5293	285	8	.	.	PUNCT
ejpam-5293	286	1	analytic	analytic	ADJ
ejpam-5293	286	2	regularity	regularity	NOUN
ejpam-5293	286	3	of	of	ADP
ejpam-5293	286	4	solutions	solution	NOUN
ejpam-5293	286	5	of	of	ADP
ejpam-5293	286	6	livsic	livsic	ADJ
ejpam-5293	286	7	cohomology	cohomology	NOUN
ejpam-5293	286	8	equations	equation	NOUN
ejpam-5293	286	9	and	and	CCONJ
ejpam-5293	286	10	some	some	DET
ejpam-5293	286	11	applications	application	NOUN
ejpam-5293	286	12	to	to	ADP
ejpam-5293	286	13	analytic	analytic	ADJ
ejpam-5293	286	14	conjugacy	conjugacy	NOUN
ejpam-5293	286	15	of	of	ADP
ejpam-5293	286	16	hyperbolic	hyperbolic	ADJ
ejpam-5293	286	17	dynamical	dynamical	ADJ
ejpam-5293	286	18	systems	system	NOUN
ejpam-5293	286	19	.	.	PUNCT
ejpam-5293	287	1	ergodic	ergodic	ADJ
ejpam-5293	287	2	theory	theory	NOUN
ejpam-5293	287	3	dynam	dynam	PROPN
ejpam-5293	287	4	.	.	PUNCT
ejpam-5293	288	1	systems	system	NOUN
ejpam-5293	288	2	,	,	PUNCT
ejpam-5293	288	3	17:649–662	17:649–662	NUM
ejpam-5293	288	4	,	,	PUNCT
ejpam-5293	288	5	1997	1997	NUM
ejpam-5293	288	6	.	.	PUNCT
ejpam-5293	289	1	[	[	X
ejpam-5293	289	2	5	5	NUM
ejpam-5293	289	3	]	]	PUNCT
ejpam-5293	289	4	t	t	PROPN
ejpam-5293	289	5	foth	foth	PROPN
ejpam-5293	289	6	and	and	CCONJ
ejpam-5293	289	7	s	s	VERB
ejpam-5293	289	8	katok	katok	NOUN
ejpam-5293	289	9	.	.	PUNCT
ejpam-5293	290	1	spanning	span	VERB
ejpam-5293	290	2	sets	set	NOUN
ejpam-5293	290	3	for	for	ADP
ejpam-5293	290	4	automorphic	automorphic	ADJ
ejpam-5293	290	5	forms	form	NOUN
ejpam-5293	290	6	and	and	CCONJ
ejpam-5293	290	7	dynamics	dynamic	NOUN
ejpam-5293	290	8	of	of	ADP
ejpam-5293	290	9	the	the	DET
ejpam-5293	290	10	frame	frame	NOUN
ejpam-5293	290	11	flow	flow	NOUN
ejpam-5293	290	12	on	on	ADP
ejpam-5293	290	13	complex	complex	ADJ
ejpam-5293	290	14	hyperbolic	hyperbolic	ADJ
ejpam-5293	290	15	spaces	space	NOUN
ejpam-5293	290	16	.	.	PUNCT
ejpam-5293	291	1	ergodic	ergodic	ADJ
ejpam-5293	291	2	theory	theory	NOUN
ejpam-5293	291	3	dynam	dynam	PROPN
ejpam-5293	291	4	.	.	PUNCT
ejpam-5293	292	1	systems	system	NOUN
ejpam-5293	292	2	,	,	PUNCT
ejpam-5293	292	3	21:1071–1099	21:1071–1099	NUM
ejpam-5293	292	4	,	,	PUNCT
ejpam-5293	292	5	2001	2001	NUM
ejpam-5293	292	6	.	.	PUNCT
ejpam-5293	293	1	[	[	X
ejpam-5293	293	2	6	6	NUM
ejpam-5293	293	3	]	]	PUNCT
ejpam-5293	293	4	a	a	DET
ejpam-5293	293	5	katok	katok	NOUN
ejpam-5293	293	6	and	and	CCONJ
ejpam-5293	293	7	b	b	NOUN
ejpam-5293	293	8	hasselblatt	hasselblatt	NOUN
ejpam-5293	293	9	.	.	PUNCT
ejpam-5293	294	1	introduction	introduction	NOUN
ejpam-5293	294	2	to	to	ADP
ejpam-5293	294	3	the	the	DET
ejpam-5293	294	4	modern	modern	ADJ
ejpam-5293	294	5	theory	theory	NOUN
ejpam-5293	294	6	of	of	ADP
ejpam-5293	294	7	dynamical	dynamical	ADJ
ejpam-5293	294	8	systems	system	NOUN
ejpam-5293	294	9	.	.	PUNCT
ejpam-5293	295	1	cambridge	cambridge	PROPN
ejpam-5293	295	2	university	university	PROPN
ejpam-5293	295	3	press	press	NOUN
ejpam-5293	295	4	,	,	PUNCT
ejpam-5293	295	5	1995	1995	NUM
ejpam-5293	295	6	.	.	PUNCT
ejpam-5293	296	1	[	[	X
ejpam-5293	296	2	7	7	X
ejpam-5293	296	3	]	]	X
ejpam-5293	296	4	a	a	DET
ejpam-5293	296	5	katok	katok	NOUN
ejpam-5293	296	6	and	and	CCONJ
ejpam-5293	296	7	s	s	VERB
ejpam-5293	296	8	katok	katok	NOUN
ejpam-5293	296	9	.	.	PUNCT
ejpam-5293	297	1	higher	high	ADJ
ejpam-5293	297	2	cohomology	cohomology	NOUN
ejpam-5293	297	3	for	for	ADP
ejpam-5293	297	4	abelian	abelian	ADJ
ejpam-5293	297	5	groups	group	NOUN
ejpam-5293	297	6	of	of	ADP
ejpam-5293	297	7	toral	toral	ADJ
ejpam-5293	297	8	automorphisms	automorphism	NOUN
ejpam-5293	297	9	.	.	PUNCT
ejpam-5293	298	1	ergodic	ergodic	ADJ
ejpam-5293	298	2	theory	theory	NOUN
ejpam-5293	298	3	dynam	dynam	PROPN
ejpam-5293	298	4	.	.	PUNCT
ejpam-5293	299	1	systems	system	NOUN
ejpam-5293	299	2	,	,	PUNCT
ejpam-5293	299	3	15:569–592	15:569–592	NUM
ejpam-5293	299	4	,	,	PUNCT
ejpam-5293	299	5	1995	1995	NUM
ejpam-5293	299	6	.	.	PUNCT
ejpam-5293	300	1	[	[	X
ejpam-5293	300	2	8	8	NUM
ejpam-5293	300	3	]	]	X
ejpam-5293	300	4	a	a	DET
ejpam-5293	300	5	katok	katok	NOUN
ejpam-5293	300	6	and	and	CCONJ
ejpam-5293	300	7	r	r	NOUN
ejpam-5293	300	8	spatzier	spatzier	ADJ
ejpam-5293	300	9	.	.	PUNCT
ejpam-5293	301	1	first	first	ADJ
ejpam-5293	301	2	cohomology	cohomology	NOUN
ejpam-5293	301	3	of	of	ADP
ejpam-5293	301	4	anosov	anosov	NOUN
ejpam-5293	301	5	actions	action	NOUN
ejpam-5293	301	6	of	of	ADP
ejpam-5293	301	7	higher	high	ADJ
ejpam-5293	301	8	rank	rank	NOUN
ejpam-5293	301	9	abelian	abelian	NOUN
ejpam-5293	301	10	groups	group	NOUN
ejpam-5293	301	11	and	and	CCONJ
ejpam-5293	301	12	applications	application	NOUN
ejpam-5293	301	13	to	to	AUX
ejpam-5293	301	14	rigidity	rigidity	NOUN
ejpam-5293	301	15	.	.	PUNCT
ejpam-5293	302	1	inst	inst	PROPN
ejpam-5293	302	2	.	.	PUNCT
ejpam-5293	302	3	hautes	haute	VERB
ejpam-5293	302	4	études	études	PROPN
ejpam-5293	302	5	sci	sci	PROPN
ejpam-5293	302	6	.	.	PROPN
ejpam-5293	302	7	publ	publ	PROPN
ejpam-5293	302	8	.	.	PUNCT
ejpam-5293	303	1	math	math	NOUN
ejpam-5293	303	2	.	.	PUNCT
ejpam-5293	303	3	,	,	PUNCT
ejpam-5293	304	1	79:131–156	79:131–156	PROPN
ejpam-5293	304	2	,	,	PUNCT
ejpam-5293	304	3	1994	1994	NUM
ejpam-5293	304	4	.	.	PUNCT
ejpam-5293	305	1	[	[	X
ejpam-5293	305	2	9	9	NUM
ejpam-5293	305	3	]	]	X
ejpam-5293	305	4	s	s	PART
ejpam-5293	305	5	krantz	krantz	PROPN
ejpam-5293	305	6	and	and	CCONJ
ejpam-5293	305	7	h	h	NOUN
ejpam-5293	305	8	parks	park	NOUN
ejpam-5293	305	9	.	.	PUNCT
ejpam-5293	306	1	the	the	DET
ejpam-5293	306	2	implicit	implicit	ADJ
ejpam-5293	306	3	function	function	NOUN
ejpam-5293	306	4	theorem	theorem	VERB
ejpam-5293	306	5	.	.	PUNCT
ejpam-5293	307	1	modern	modern	ADJ
ejpam-5293	307	2	birkhauser	birkhauser	NOUN
ejpam-5293	307	3	classics	classic	NOUN
ejpam-5293	307	4	,	,	PUNCT
ejpam-5293	307	5	birkhauser	birkhauser	NOUN
ejpam-5293	307	6	,	,	PUNCT
ejpam-5293	307	7	2003	2003	NUM
ejpam-5293	307	8	.	.	PUNCT
ejpam-5293	308	1	[	[	X
ejpam-5293	308	2	10	10	NUM
ejpam-5293	308	3	]	]	X
ejpam-5293	308	4	r	r	NOUN
ejpam-5293	308	5	d	d	X
ejpam-5293	308	6	laureano	laureano	NOUN
ejpam-5293	308	7	.	.	PUNCT
ejpam-5293	309	1	livschitz	livschitz	PROPN
ejpam-5293	309	2	theorem	theorem	VERB
ejpam-5293	309	3	in	in	ADP
ejpam-5293	309	4	suspension	suspension	NOUN
ejpam-5293	309	5	flows	flow	NOUN
ejpam-5293	309	6	and	and	CCONJ
ejpam-5293	309	7	markov	markov	NOUN
ejpam-5293	309	8	systems	system	NOUN
ejpam-5293	309	9	:	:	PUNCT
ejpam-5293	309	10	approach	approach	NOUN
ejpam-5293	309	11	in	in	ADP
ejpam-5293	309	12	cohomology	cohomology	NOUN
ejpam-5293	309	13	of	of	ADP
ejpam-5293	309	14	systems	system	NOUN
ejpam-5293	309	15	.	.	PUNCT
ejpam-5293	310	1	symmetry	symmetry	PROPN
ejpam-5293	310	2	,	,	PUNCT
ejpam-5293	310	3	12:338–351	12:338–351	PROPN
ejpam-5293	310	4	,	,	PUNCT
ejpam-5293	310	5	2020	2020	NUM
ejpam-5293	310	6	.	.	PUNCT
ejpam-5293	311	1	[	[	X
ejpam-5293	311	2	11	11	NUM
ejpam-5293	311	3	]	]	PUNCT
ejpam-5293	311	4	a	a	DET
ejpam-5293	311	5	livšic	livšic	NOUN
ejpam-5293	311	6	.	.	PUNCT
ejpam-5293	312	1	some	some	DET
ejpam-5293	312	2	homology	homology	NOUN
ejpam-5293	312	3	properties	property	NOUN
ejpam-5293	312	4	of	of	ADP
ejpam-5293	312	5	y	y	PROPN
ejpam-5293	312	6	-	-	PUNCT
ejpam-5293	312	7	systems	system	NOUN
ejpam-5293	312	8	.	.	PUNCT
ejpam-5293	313	1	math	math	NOUN
ejpam-5293	313	2	.	.	PUNCT
ejpam-5293	314	1	notes	note	NOUN
ejpam-5293	314	2	of	of	ADP
ejpam-5293	314	3	u.s.s.r	u.s.s.r	PROPN
ejpam-5293	314	4	.	.	PROPN
ejpam-5293	314	5	academy	academy	PROPN
ejpam-5293	314	6	of	of	ADP
ejpam-5293	314	7	sciences	sciences	PROPN
ejpam-5293	314	8	,	,	PUNCT
ejpam-5293	314	9	10:758–763	10:758–763	NUM
ejpam-5293	314	10	,	,	PUNCT
ejpam-5293	314	11	1971	1971	NUM
ejpam-5293	314	12	.	.	PUNCT
ejpam-5293	315	1	[	[	X
ejpam-5293	315	2	12	12	NUM
ejpam-5293	315	3	]	]	PUNCT
ejpam-5293	315	4	a	a	DET
ejpam-5293	315	5	livšic	livšic	PROPN
ejpam-5293	315	6	.	.	PUNCT
ejpam-5293	316	1	cohomology	cohomology	NOUN
ejpam-5293	316	2	of	of	ADP
ejpam-5293	316	3	dynamical	dynamical	ADJ
ejpam-5293	316	4	systems	system	NOUN
ejpam-5293	316	5	.	.	PUNCT
ejpam-5293	317	1	math	math	NOUN
ejpam-5293	317	2	.	.	PUNCT
ejpam-5293	318	1	u.s.s.r.-izv	u.s.s.r.-izv	PROPN
ejpam-5293	318	2	.	.	PROPN
ejpam-5293	318	3	,	,	PUNCT
ejpam-5293	318	4	6:1278–1301	6:1278–1301	NUM
ejpam-5293	318	5	,	,	PUNCT
ejpam-5293	318	6	1972	1972	NUM
ejpam-5293	318	7	.	.	PUNCT
ejpam-5293	319	1	[	[	X
ejpam-5293	319	2	13	13	NUM
ejpam-5293	319	3	]	]	X
ejpam-5293	319	4	f	f	PROPN
ejpam-5293	319	5	m	m	PROPN
ejpam-5293	319	6	oudina	oudina	PROPN
ejpam-5293	319	7	p	p	PROPN
ejpam-5293	319	8	priyanka	priyanka	PROPN
ejpam-5293	319	9	,	,	PUNCT
ejpam-5293	319	10	s	s	PART
ejpam-5293	319	11	arora	arora	PROPN
ejpam-5293	319	12	and	and	CCONJ
ejpam-5293	319	13	s	s	VERB
ejpam-5293	319	14	sahani	sahani	ADJ
ejpam-5293	319	15	.	.	PUNCT
ejpam-5293	320	1	super	super	ADJ
ejpam-5293	320	2	convergence	convergence	NOUN
ejpam-5293	320	3	analysis	analysis	NOUN
ejpam-5293	320	4	of	of	ADP
ejpam-5293	320	5	fully	fully	ADV
ejpam-5293	320	6	discrete	discrete	ADJ
ejpam-5293	320	7	hermite	hermite	ADJ
ejpam-5293	320	8	splines	spline	NOUN
ejpam-5293	320	9	to	to	PART
ejpam-5293	320	10	simulate	simulate	VERB
ejpam-5293	320	11	wave	wave	NOUN
ejpam-5293	320	12	behavior	behavior	NOUN
ejpam-5293	320	13	of	of	ADP
ejpam-5293	320	14	kuramoto	kuramoto	NOUN
ejpam-5293	320	15	-	-	PUNCT
ejpam-5293	320	16	sivashinsky	sivashinsky	NOUN
ejpam-5293	320	17	equation	equation	NOUN
ejpam-5293	320	18	.	.	PUNCT
ejpam-5293	321	1	wave	wave	PROPN
ejpam-5293	321	2	motion	motion	NOUN
ejpam-5293	321	3	,	,	PUNCT
ejpam-5293	321	4	121	121	NUM
ejpam-5293	321	5	,	,	PUNCT
ejpam-5293	321	6	2023	2023	NUM
ejpam-5293	321	7	.	.	PUNCT
ejpam-5293	322	1	[	[	X
ejpam-5293	322	2	14	14	NUM
ejpam-5293	322	3	]	]	SYM
ejpam-5293	322	4	s	s	X
ejpam-5293	322	5	sahani	sahani	PROPN
ejpam-5293	322	6	p	p	PROPN
ejpam-5293	322	7	priyanka	priyanka	PROPN
ejpam-5293	322	8	,	,	PUNCT
ejpam-5293	322	9	f	f	PROPN
ejpam-5293	322	10	m	m	VERB
ejpam-5293	322	11	oudina	oudina	PROPN
ejpam-5293	322	12	and	and	CCONJ
ejpam-5293	322	13	s	s	PROPN
ejpam-5293	322	14	arora	arora	PROPN
ejpam-5293	322	15	.	.	PUNCT
ejpam-5293	323	1	travelling	travel	VERB
ejpam-5293	323	2	wave	wave	NOUN
ejpam-5293	323	3	solution	solution	NOUN
ejpam-5293	323	4	of	of	ADP
ejpam-5293	323	5	fourth	fourth	ADJ
ejpam-5293	323	6	order	order	NOUN
ejpam-5293	323	7	reaction	reaction	NOUN
ejpam-5293	323	8	diffusion	diffusion	NOUN
ejpam-5293	323	9	equation	equation	NOUN
ejpam-5293	323	10	using	use	VERB
ejpam-5293	323	11	hybrid	hybrid	ADJ
ejpam-5293	323	12	quintic	quintic	ADJ
ejpam-5293	323	13	hermite	hermite	ADJ
ejpam-5293	323	14	splines	spline	NOUN
ejpam-5293	323	15	collocation	collocation	NOUN
ejpam-5293	323	16	technique	technique	NOUN
ejpam-5293	323	17	.	.	PUNCT
ejpam-5293	324	1	arabian	arabian	ADJ
ejpam-5293	324	2	journal	journal	PROPN
ejpam-5293	324	3	of	of	ADP
ejpam-5293	324	4	mathematics	mathematic	NOUN
ejpam-5293	324	5	,	,	PUNCT
ejpam-5293	324	6	2024	2024	NUM
ejpam-5293	324	7	.	.	PUNCT
ejpam-5293	325	1	references	reference	NOUN
ejpam-5293	325	2	1416	1416	NUM
ejpam-5293	326	1	[	[	X
ejpam-5293	326	2	15	15	NUM
ejpam-5293	326	3	]	]	X
ejpam-5293	326	4	w	w	PROPN
ejpam-5293	326	5	parry	parry	PROPN
ejpam-5293	326	6	.	.	PUNCT
ejpam-5293	327	1	the	the	DET
ejpam-5293	327	2	livsic	livsic	ADJ
ejpam-5293	327	3	periodic	periodic	ADJ
ejpam-5293	327	4	point	point	NOUN
ejpam-5293	327	5	theorem	theorem	NOUN
ejpam-5293	327	6	for	for	ADP
ejpam-5293	327	7	two	two	NUM
ejpam-5293	327	8	non	non	ADJ
ejpam-5293	327	9	-	-	ADJ
ejpam-5293	327	10	abelian	abelian	ADJ
ejpam-5293	327	11	cocycles	cocycle	NOUN
ejpam-5293	327	12	.	.	PUNCT
ejpam-5293	328	1	ergodic	ergodic	ADJ
ejpam-5293	328	2	theory	theory	NOUN
ejpam-5293	328	3	dynam	dynam	PROPN
ejpam-5293	328	4	.	.	PUNCT
ejpam-5293	329	1	systems	system	NOUN
ejpam-5293	329	2	,	,	PUNCT
ejpam-5293	329	3	19:687–701	19:687–701	PROPN
ejpam-5293	329	4	,	,	PUNCT
ejpam-5293	329	5	1999	1999	NUM
ejpam-5293	329	6	.	.	PUNCT
ejpam-5293	330	1	[	[	X
ejpam-5293	330	2	16	16	NUM
ejpam-5293	330	3	]	]	X
ejpam-5293	330	4	h	h	NOUN
ejpam-5293	330	5	poincaré.	poincaré.	PROPN
ejpam-5293	330	6	the	the	DET
ejpam-5293	330	7	three	three	NUM
ejpam-5293	330	8	-	-	PUNCT
ejpam-5293	330	9	body	body	NOUN
ejpam-5293	330	10	problem	problem	NOUN
ejpam-5293	330	11	and	and	CCONJ
ejpam-5293	330	12	the	the	DET
ejpam-5293	330	13	equations	equation	NOUN
ejpam-5293	330	14	of	of	ADP
ejpam-5293	330	15	dynamics	dynamic	NOUN
ejpam-5293	330	16	-	-	PUNCT
ejpam-5293	330	17	poincaré	poincaré	ADJ
ejpam-5293	330	18	’s	’s	PART
ejpam-5293	330	19	foundational	foundational	ADJ
ejpam-5293	330	20	work	work	NOUN
ejpam-5293	330	21	on	on	ADP
ejpam-5293	330	22	dynamical	dynamical	ADJ
ejpam-5293	330	23	systems	system	NOUN
ejpam-5293	330	24	theory	theory	NOUN
ejpam-5293	330	25	.	.	PUNCT
ejpam-5293	331	1	b.d	b.d	PROPN
ejpam-5293	331	2	.	.	PROPN
ejpam-5293	331	3	popp	popp	PROPN
ejpam-5293	331	4	(	(	PUNCT
ejpam-5293	331	5	translator	translator	NOUN
ejpam-5293	331	6	)	)	PUNCT
ejpam-5293	331	7	,	,	PUNCT
ejpam-5293	331	8	springer	springer	NOUN
ejpam-5293	331	9	international	international	ADJ
ejpam-5293	331	10	publishing	publishing	NOUN
ejpam-5293	331	11	,	,	PUNCT
ejpam-5293	331	12	2017	2017	NUM
ejpam-5293	331	13	.	.	PUNCT
ejpam-5293	332	1	[	[	X
ejpam-5293	332	2	17	17	NUM
ejpam-5293	332	3	]	]	X
ejpam-5293	332	4	r	r	NOUN
ejpam-5293	332	5	clark	clark	NOUN
ejpam-5293	332	6	robinsob	robinsob	NOUN
ejpam-5293	332	7	.	.	PUNCT
ejpam-5293	333	1	an	an	DET
ejpam-5293	333	2	introduction	introduction	NOUN
ejpam-5293	333	3	to	to	ADP
ejpam-5293	333	4	dynamical	dynamical	ADJ
ejpam-5293	333	5	systems	system	NOUN
ejpam-5293	333	6	:	:	PUNCT
ejpam-5293	333	7	continuous	continuous	ADJ
ejpam-5293	333	8	and	and	CCONJ
ejpam-5293	333	9	discrete	discrete	ADJ
ejpam-5293	333	10	.	.	PUNCT
ejpam-5293	334	1	american	american	PROPN
ejpam-5293	334	2	mathematical	mathematical	PROPN
ejpam-5293	334	3	society	society	NOUN
ejpam-5293	334	4	,	,	PUNCT
ejpam-5293	334	5	2013	2013	NUM
ejpam-5293	334	6	.	.	PUNCT
ejpam-5293	335	1	[	[	X
ejpam-5293	335	2	18	18	NUM
ejpam-5293	335	3	]	]	X
ejpam-5293	335	4	c	c	X
ejpam-5293	335	5	walkden	walkden	PROPN
ejpam-5293	335	6	.	.	PUNCT
ejpam-5293	336	1	livsic	livsic	ADJ
ejpam-5293	336	2	regularity	regularity	NOUN
ejpam-5293	336	3	theorems	theorem	NOUN
ejpam-5293	336	4	for	for	ADP
ejpam-5293	336	5	twisted	twisted	ADJ
ejpam-5293	336	6	cocycle	cocycle	NOUN
ejpam-5293	336	7	equations	equation	NOUN
ejpam-5293	336	8	over	over	ADP
ejpam-5293	336	9	hyperbolic	hyperbolic	ADJ
ejpam-5293	336	10	systems	system	NOUN
ejpam-5293	336	11	.	.	PUNCT
ejpam-5293	337	1	j.	j.	PROPN
ejpam-5293	337	2	london	london	PROPN
ejpam-5293	337	3	math	math	PROPN
ejpam-5293	337	4	.	.	PUNCT
ejpam-5293	338	1	soc	soc	PROPN
ejpam-5293	338	2	.	.	PUNCT
ejpam-5293	338	3	,	,	PUNCT
ejpam-5293	338	4	61:286–300	61:286–300	NUM
ejpam-5293	338	5	,	,	PUNCT
ejpam-5293	338	6	2000	2000	NUM
ejpam-5293	338	7	.	.	PUNCT