id	sid	tid	token	lemma	pos
ejpam-5830	1	1	european	european	PROPN
ejpam-5830	1	2	journal	journal	PROPN
ejpam-5830	1	3	of	of	ADP
ejpam-5830	1	4	pure	pure	ADJ
ejpam-5830	1	5	and	and	CCONJ
ejpam-5830	1	6	applied	applied	ADJ
ejpam-5830	1	7	mathematics	mathematic	NOUN
ejpam-5830	1	8	2025	2025	NUM
ejpam-5830	1	9	,	,	PUNCT
ejpam-5830	1	10	vol	vol	NOUN
ejpam-5830	1	11	.	.	PROPN
ejpam-5830	1	12	18	18	NUM
ejpam-5830	1	13	,	,	PUNCT
ejpam-5830	1	14	issue	issue	NOUN
ejpam-5830	1	15	2	2	NUM
ejpam-5830	1	16	,	,	PUNCT
ejpam-5830	1	17	article	article	NOUN
ejpam-5830	1	18	number	number	NOUN
ejpam-5830	1	19	5830	5830	NUM
ejpam-5830	1	20	issn	issn	PROPN
ejpam-5830	1	21	1307	1307	NUM
ejpam-5830	1	22	-	-	SYM
ejpam-5830	1	23	5543	5543	NUM
ejpam-5830	1	24	–	–	PUNCT
ejpam-5830	1	25	ejpam.com	ejpam.com	X
ejpam-5830	1	26	published	publish	VERB
ejpam-5830	1	27	by	by	ADP
ejpam-5830	1	28	new	new	PROPN
ejpam-5830	1	29	york	york	PROPN
ejpam-5830	1	30	business	business	PROPN
ejpam-5830	1	31	global	global	ADJ
ejpam-5830	1	32	cocycles	cocycle	NOUN
ejpam-5830	1	33	in	in	ADP
ejpam-5830	1	34	lie	lie	NOUN
ejpam-5830	1	35	groups	group	NOUN
ejpam-5830	1	36	,	,	PUNCT
ejpam-5830	1	37	cochains	cochain	NOUN
ejpam-5830	1	38	and	and	CCONJ
ejpam-5830	1	39	regularity	regularity	NOUN
ejpam-5830	1	40	problem	problem	NOUN
ejpam-5830	1	41	rosário	rosário	X
ejpam-5830	1	42	d.	d.	PROPN
ejpam-5830	1	43	laureano	laureano	PROPN
ejpam-5830	1	44	istar	istar	PROPN
ejpam-5830	1	45	information	information	PROPN
ejpam-5830	1	46	sciences	sciences	PROPN
ejpam-5830	1	47	,	,	PUNCT
ejpam-5830	1	48	technologies	technology	NOUN
ejpam-5830	1	49	and	and	CCONJ
ejpam-5830	1	50	architecture	architecture	NOUN
ejpam-5830	1	51	research	research	NOUN
ejpam-5830	1	52	center	center	NOUN
ejpam-5830	1	53	,	,	PUNCT
ejpam-5830	1	54	department	department	NOUN
ejpam-5830	1	55	of	of	ADP
ejpam-5830	1	56	mathematics	mathematic	NOUN
ejpam-5830	1	57	,	,	PUNCT
ejpam-5830	1	58	iscte	iscte	NOUN
ejpam-5830	1	59	-	-	PUNCT
ejpam-5830	1	60	iul	iul	NOUN
ejpam-5830	1	61	instituto	instituto	PROPN
ejpam-5830	1	62	universitário	universitário	PROPN
ejpam-5830	1	63	de	de	PROPN
ejpam-5830	1	64	lisboa	lisboa	PROPN
ejpam-5830	1	65	,	,	PUNCT
ejpam-5830	1	66	av	av	PROPN
ejpam-5830	1	67	.	.	PUNCT
ejpam-5830	1	68	das	das	PROPN
ejpam-5830	1	69	forças	forças	ADP
ejpam-5830	1	70	armadas	armada	NOUN
ejpam-5830	1	71	,	,	PUNCT
ejpam-5830	1	72	lisboa	lisboa	PROPN
ejpam-5830	1	73	1649	1649	NUM
ejpam-5830	1	74	-	-	SYM
ejpam-5830	1	75	026	026	NUM
ejpam-5830	1	76	,	,	PUNCT
ejpam-5830	1	77	portugal	portugal	PROPN
ejpam-5830	1	78	abstract	abstract	NOUN
ejpam-5830	1	79	.	.	PUNCT
ejpam-5830	2	1	after	after	ADP
ejpam-5830	2	2	the	the	DET
ejpam-5830	2	3	fundamental	fundamental	ADJ
ejpam-5830	2	4	work	work	NOUN
ejpam-5830	2	5	of	of	ADP
ejpam-5830	2	6	livschitz	livschitz	NOUN
ejpam-5830	2	7	in	in	ADP
ejpam-5830	2	8	[	[	X
ejpam-5830	2	9	1	1	NUM
ejpam-5830	2	10	,	,	PUNCT
ejpam-5830	2	11	2	2	NUM
ejpam-5830	2	12	]	]	PUNCT
ejpam-5830	2	13	,	,	PUNCT
ejpam-5830	2	14	various	various	ADJ
ejpam-5830	2	15	research	research	NOUN
ejpam-5830	2	16	directions	direction	NOUN
ejpam-5830	2	17	emerged	emerge	VERB
ejpam-5830	2	18	,	,	PUNCT
ejpam-5830	2	19	among	among	ADP
ejpam-5830	2	20	which	which	PRON
ejpam-5830	2	21	the	the	DET
ejpam-5830	2	22	following	follow	VERB
ejpam-5830	2	23	stand	stand	VERB
ejpam-5830	2	24	out	out	ADP
ejpam-5830	2	25	:	:	PUNCT
ejpam-5830	2	26	(	(	PUNCT
ejpam-5830	2	27	i	i	NOUN
ejpam-5830	2	28	)	)	PUNCT
ejpam-5830	2	29	the	the	DET
ejpam-5830	2	30	study	study	NOUN
ejpam-5830	2	31	of	of	ADP
ejpam-5830	2	32	cocycles	cocycle	NOUN
ejpam-5830	2	33	with	with	ADP
ejpam-5830	2	34	values	value	NOUN
ejpam-5830	2	35	in	in	ADP
ejpam-5830	2	36	groups	group	NOUN
ejpam-5830	2	37	and	and	CCONJ
ejpam-5830	2	38	semigroups	semigroup	NOUN
ejpam-5830	2	39	beyond	beyond	ADP
ejpam-5830	2	40	r	r	NOUN
ejpam-5830	2	41	,	,	PUNCT
ejpam-5830	2	42	as	as	ADV
ejpam-5830	2	43	well	well	ADV
ejpam-5830	2	44	as	as	ADP
ejpam-5830	2	45	the	the	DET
ejpam-5830	2	46	investigation	investigation	NOUN
ejpam-5830	2	47	of	of	ADP
ejpam-5830	2	48	corresponding	correspond	VERB
ejpam-5830	2	49	regularity	regularity	NOUN
ejpam-5830	2	50	results	result	NOUN
ejpam-5830	2	51	;	;	PUNCT
ejpam-5830	2	52	(	(	PUNCT
ejpam-5830	2	53	ii	ii	X
ejpam-5830	2	54	)	)	PUNCT
ejpam-5830	2	55	the	the	DET
ejpam-5830	2	56	analysis	analysis	NOUN
ejpam-5830	2	57	of	of	ADP
ejpam-5830	2	58	how	how	SCONJ
ejpam-5830	2	59	a	a	DET
ejpam-5830	2	60	certain	certain	ADJ
ejpam-5830	2	61	degree	degree	NOUN
ejpam-5830	2	62	of	of	ADP
ejpam-5830	2	63	regularity	regularity	NOUN
ejpam-5830	2	64	(	(	PUNCT
ejpam-5830	2	65	ck	ck	INTJ
ejpam-5830	2	66	for	for	ADP
ejpam-5830	2	67	k	k	PROPN
ejpam-5830	2	68	=	=	SYM
ejpam-5830	2	69	1	1	NUM
ejpam-5830	2	70	,	,	PUNCT
ejpam-5830	2	71	2	2	NUM
ejpam-5830	2	72	,	,	PUNCT
ejpam-5830	2	73	.	.	PUNCT
ejpam-5830	2	74	.	.	PUNCT
ejpam-5830	3	1	.	.	PUNCT
ejpam-5830	4	1	,	,	PUNCT
ejpam-5830	4	2	∞	∞	PROPN
ejpam-5830	4	3	,	,	PUNCT
ejpam-5830	4	4	ω	ω	NOUN
ejpam-5830	4	5	)	)	PUNCT
ejpam-5830	4	6	of	of	ADP
ejpam-5830	4	7	the	the	DET
ejpam-5830	4	8	cocycle	cocycle	NOUN
ejpam-5830	4	9	can	can	AUX
ejpam-5830	4	10	confer	confer	VERB
ejpam-5830	4	11	corresponding	corresponding	ADJ
ejpam-5830	4	12	regularity	regularity	NOUN
ejpam-5830	4	13	to	to	ADP
ejpam-5830	4	14	the	the	DET
ejpam-5830	4	15	solution	solution	NOUN
ejpam-5830	4	16	of	of	ADP
ejpam-5830	4	17	the	the	DET
ejpam-5830	4	18	cohomological	cohomological	ADJ
ejpam-5830	4	19	equation	equation	NOUN
ejpam-5830	4	20	;	;	PUNCT
ejpam-5830	4	21	and	and	CCONJ
ejpam-5830	4	22	(	(	PUNCT
ejpam-5830	4	23	iii	iii	X
ejpam-5830	4	24	)	)	PUNCT
ejpam-5830	4	25	the	the	DET
ejpam-5830	4	26	study	study	NOUN
ejpam-5830	4	27	of	of	ADP
ejpam-5830	4	28	higher	high	ADJ
ejpam-5830	4	29	-	-	PUNCT
ejpam-5830	4	30	dimensional	dimensional	ADJ
ejpam-5830	4	31	cohomology	cohomology	NOUN
ejpam-5830	4	32	naturally	naturally	ADV
ejpam-5830	4	33	associated	associate	VERB
ejpam-5830	4	34	with	with	ADP
ejpam-5830	4	35	the	the	DET
ejpam-5830	4	36	action	action	NOUN
ejpam-5830	4	37	of	of	ADP
ejpam-5830	4	38	groups	group	NOUN
ejpam-5830	4	39	such	such	ADJ
ejpam-5830	4	40	as	as	ADP
ejpam-5830	4	41	zk	zk	PROPN
ejpam-5830	4	42	or	or	CCONJ
ejpam-5830	4	43	rk	rk	NOUN
ejpam-5830	4	44	.	.	PUNCT
ejpam-5830	5	1	the	the	DET
ejpam-5830	5	2	aim	aim	NOUN
ejpam-5830	5	3	of	of	ADP
ejpam-5830	5	4	this	this	DET
ejpam-5830	5	5	article	article	NOUN
ejpam-5830	5	6	is	be	AUX
ejpam-5830	5	7	to	to	PART
ejpam-5830	5	8	present	present	VERB
ejpam-5830	5	9	,	,	PUNCT
ejpam-5830	5	10	as	as	SCONJ
ejpam-5830	5	11	self	self	NOUN
ejpam-5830	5	12	-	-	PUNCT
ejpam-5830	5	13	contained	contain	VERB
ejpam-5830	5	14	as	as	ADP
ejpam-5830	5	15	possible	possible	ADJ
ejpam-5830	5	16	,	,	PUNCT
ejpam-5830	5	17	a	a	DET
ejpam-5830	5	18	review	review	NOUN
ejpam-5830	5	19	of	of	ADP
ejpam-5830	5	20	the	the	DET
ejpam-5830	5	21	natural	natural	ADJ
ejpam-5830	5	22	generalizations	generalization	NOUN
ejpam-5830	5	23	of	of	ADP
ejpam-5830	5	24	the	the	DET
ejpam-5830	5	25	notions	notion	NOUN
ejpam-5830	5	26	of	of	ADP
ejpam-5830	5	27	cocycles	cocycle	NOUN
ejpam-5830	5	28	and	and	CCONJ
ejpam-5830	5	29	cochains	cochain	NOUN
ejpam-5830	5	30	,	,	PUNCT
ejpam-5830	5	31	as	as	ADV
ejpam-5830	5	32	well	well	ADV
ejpam-5830	5	33	as	as	ADP
ejpam-5830	5	34	their	their	PRON
ejpam-5830	5	35	corresponding	corresponding	ADJ
ejpam-5830	5	36	results	result	NOUN
ejpam-5830	5	37	,	,	PUNCT
ejpam-5830	5	38	in	in	ADP
ejpam-5830	5	39	the	the	DET
ejpam-5830	5	40	study	study	NOUN
ejpam-5830	5	41	of	of	ADP
ejpam-5830	5	42	cohomological	cohomological	ADJ
ejpam-5830	5	43	equations	equation	NOUN
ejpam-5830	5	44	.	.	PUNCT
ejpam-5830	6	1	2020	2020	NUM
ejpam-5830	6	2	mathematics	mathematic	NOUN
ejpam-5830	6	3	subject	subject	NOUN
ejpam-5830	6	4	classifications	classification	NOUN
ejpam-5830	6	5	:	:	PUNCT
ejpam-5830	6	6	37a20	37a20	NUM
ejpam-5830	6	7	,	,	PUNCT
ejpam-5830	6	8	37c05	37c05	NUM
ejpam-5830	6	9	,	,	PUNCT
ejpam-5830	6	10	37c50	37c50	NUM
ejpam-5830	6	11	,	,	PUNCT
ejpam-5830	6	12	37c55	37c55	NUM
ejpam-5830	6	13	,	,	PUNCT
ejpam-5830	6	14	37d05	37d05	NUM
ejpam-5830	6	15	,	,	PUNCT
ejpam-5830	6	16	37d20	37d20	NUM
ejpam-5830	6	17	key	key	ADJ
ejpam-5830	6	18	words	word	NOUN
ejpam-5830	6	19	and	and	CCONJ
ejpam-5830	6	20	phrases	phrase	NOUN
ejpam-5830	6	21	:	:	PUNCT
ejpam-5830	6	22	cocycle	cocycle	NOUN
ejpam-5830	6	23	,	,	PUNCT
ejpam-5830	6	24	cohomological	cohomological	ADJ
ejpam-5830	6	25	equation	equation	NOUN
ejpam-5830	6	26	,	,	PUNCT
ejpam-5830	6	27	coboundary	coboundary	ADJ
ejpam-5830	6	28	,	,	PUNCT
ejpam-5830	6	29	cochain	cochain	NOUN
ejpam-5830	6	30	,	,	PUNCT
ejpam-5830	6	31	livschitz	livschitz	NOUN
ejpam-5830	6	32	theorem	theorem	NOUN
ejpam-5830	6	33	,	,	PUNCT
ejpam-5830	6	34	lie	lie	NOUN
ejpam-5830	6	35	group	group	NOUN
ejpam-5830	6	36	,	,	PUNCT
ejpam-5830	6	37	anosov	anosov	NOUN
ejpam-5830	6	38	flow	flow	NOUN
ejpam-5830	6	39	,	,	PUNCT
ejpam-5830	6	40	anosov	anosov	NOUN
ejpam-5830	6	41	diffeomorphism	diffeomorphism	NOUN
ejpam-5830	6	42	1	1	NUM
ejpam-5830	6	43	.	.	PUNCT
ejpam-5830	6	44	introduction	introduction	NOUN
ejpam-5830	6	45	cohomology	cohomology	NOUN
ejpam-5830	6	46	,	,	PUNCT
ejpam-5830	6	47	originally	originally	ADV
ejpam-5830	6	48	from	from	ADP
ejpam-5830	6	49	algebraic	algebraic	ADJ
ejpam-5830	6	50	topology	topology	NOUN
ejpam-5830	6	51	,	,	PUNCT
ejpam-5830	6	52	is	be	AUX
ejpam-5830	6	53	being	be	AUX
ejpam-5830	6	54	innovatively	innovatively	ADV
ejpam-5830	6	55	extended	extend	VERB
ejpam-5830	6	56	to	to	PART
ejpam-5830	6	57	study	study	VERB
ejpam-5830	6	58	the	the	DET
ejpam-5830	6	59	qualitative	qualitative	ADJ
ejpam-5830	6	60	features	feature	NOUN
ejpam-5830	6	61	of	of	ADP
ejpam-5830	6	62	dynamical	dynamical	ADJ
ejpam-5830	6	63	systems	system	NOUN
ejpam-5830	6	64	,	,	PUNCT
ejpam-5830	6	65	such	such	ADJ
ejpam-5830	6	66	as	as	ADP
ejpam-5830	6	67	invariant	invariant	ADJ
ejpam-5830	6	68	structures	structure	NOUN
ejpam-5830	6	69	and	and	CCONJ
ejpam-5830	6	70	foliations	foliation	NOUN
ejpam-5830	6	71	.	.	PUNCT
ejpam-5830	7	1	it	it	PRON
ejpam-5830	7	2	creates	create	VERB
ejpam-5830	7	3	a	a	DET
ejpam-5830	7	4	conceptual	conceptual	ADJ
ejpam-5830	7	5	bridge	bridge	NOUN
ejpam-5830	7	6	between	between	ADP
ejpam-5830	7	7	topology	topology	NOUN
ejpam-5830	7	8	,	,	PUNCT
ejpam-5830	7	9	geometry	geometry	NOUN
ejpam-5830	7	10	,	,	PUNCT
ejpam-5830	7	11	and	and	CCONJ
ejpam-5830	7	12	dynamics	dynamic	NOUN
ejpam-5830	7	13	,	,	PUNCT
ejpam-5830	7	14	opening	open	VERB
ejpam-5830	7	15	new	new	ADJ
ejpam-5830	7	16	interdisciplinary	interdisciplinary	ADJ
ejpam-5830	7	17	research	research	NOUN
ejpam-5830	7	18	directions	direction	NOUN
ejpam-5830	7	19	and	and	CCONJ
ejpam-5830	7	20	offering	offer	VERB
ejpam-5830	7	21	new	new	ADJ
ejpam-5830	7	22	insights	insight	NOUN
ejpam-5830	7	23	,	,	PUNCT
ejpam-5830	7	24	tools	tool	NOUN
ejpam-5830	7	25	,	,	PUNCT
ejpam-5830	7	26	or	or	CCONJ
ejpam-5830	7	27	classifications	classification	NOUN
ejpam-5830	7	28	that	that	PRON
ejpam-5830	7	29	were	be	AUX
ejpam-5830	7	30	previously	previously	ADV
ejpam-5830	7	31	inaccessible	inaccessible	ADJ
ejpam-5830	7	32	or	or	CCONJ
ejpam-5830	7	33	underdeveloped	underdeveloped	ADJ
ejpam-5830	7	34	using	use	VERB
ejpam-5830	7	35	traditional	traditional	ADJ
ejpam-5830	7	36	approaches	approach	NOUN
ejpam-5830	7	37	.	.	PUNCT
ejpam-5830	8	1	in	in	ADP
ejpam-5830	8	2	dynamical	dynamical	ADJ
ejpam-5830	8	3	systems	system	NOUN
ejpam-5830	8	4	theory	theory	NOUN
ejpam-5830	8	5	,	,	PUNCT
ejpam-5830	8	6	various	various	ADJ
ejpam-5830	8	7	problems	problem	NOUN
ejpam-5830	8	8	of	of	ADP
ejpam-5830	8	9	considerable	considerable	ADJ
ejpam-5830	8	10	importance	importance	NOUN
ejpam-5830	8	11	can	can	AUX
ejpam-5830	8	12	be	be	AUX
ejpam-5830	8	13	reduced	reduce	VERB
ejpam-5830	8	14	to	to	ADP
ejpam-5830	8	15	solving	solve	VERB
ejpam-5830	8	16	an	an	DET
ejpam-5830	8	17	equation	equation	NOUN
ejpam-5830	8	18	of	of	ADP
ejpam-5830	8	19	the	the	DET
ejpam-5830	8	20	form	form	NOUN
ejpam-5830	8	21	φ	φ	X
ejpam-5830	8	22	=	=	SYM
ejpam-5830	8	23	φ	φ	PROPN
ejpam-5830	8	24	◦	◦	NOUN
ejpam-5830	8	25	f	f	PROPN
ejpam-5830	9	1	−	−	PROPN
ejpam-5830	9	2	φ	φ	PROPN
ejpam-5830	9	3	,	,	PUNCT
ejpam-5830	9	4	(	(	PUNCT
ejpam-5830	9	5	1	1	X
ejpam-5830	9	6	)	)	PUNCT
ejpam-5830	9	7	where	where	SCONJ
ejpam-5830	9	8	f	f	X
ejpam-5830	9	9	:	:	PUNCT
ejpam-5830	9	10	x	x	X
ejpam-5830	9	11	→	→	PUNCT
ejpam-5830	9	12	x	x	X
ejpam-5830	9	13	is	be	AUX
ejpam-5830	9	14	a	a	DET
ejpam-5830	9	15	dynamical	dynamical	ADJ
ejpam-5830	9	16	system	system	NOUN
ejpam-5830	9	17	,	,	PUNCT
ejpam-5830	9	18	φ	φ	PROPN
ejpam-5830	9	19	:	:	PUNCT
ejpam-5830	9	20	x	x	X
ejpam-5830	9	21	→	→	SYM
ejpam-5830	9	22	r	r	NOUN
ejpam-5830	9	23	is	be	AUX
ejpam-5830	9	24	a	a	DET
ejpam-5830	9	25	known	know	VERB
ejpam-5830	9	26	function	function	NOUN
ejpam-5830	9	27	and	and	CCONJ
ejpam-5830	9	28	φ	φ	NOUN
ejpam-5830	9	29	:	:	PUNCT
ejpam-5830	10	1	x	x	X
ejpam-5830	10	2	→	→	SYM
ejpam-5830	10	3	r	r	NOUN
ejpam-5830	10	4	is	be	AUX
ejpam-5830	10	5	unknown	unknown	ADJ
ejpam-5830	10	6	.	.	PUNCT
ejpam-5830	11	1	equation	equation	NOUN
ejpam-5830	11	2	(	(	PUNCT
ejpam-5830	11	3	1	1	X
ejpam-5830	11	4	)	)	PUNCT
ejpam-5830	11	5	is	be	AUX
ejpam-5830	11	6	called	call	VERB
ejpam-5830	11	7	a	a	DET
ejpam-5830	11	8	cohomological	cohomological	ADJ
ejpam-5830	11	9	equation	equation	NOUN
ejpam-5830	11	10	.	.	PUNCT
ejpam-5830	12	1	doi	doi	NOUN
ejpam-5830	12	2	:	:	PUNCT
ejpam-5830	12	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5830	https://doi.org/10.29020/nybg.ejpam.v18i2.5830	PRON
ejpam-5830	12	4	email	email	NOUN
ejpam-5830	12	5	address	address	NOUN
ejpam-5830	12	6	:	:	PUNCT
ejpam-5830	12	7	maria.laureano@iscte-iul.pt	maria.laureano@iscte-iul.pt	PROPN
ejpam-5830	12	8	(	(	PUNCT
ejpam-5830	12	9	r.	r.	PROPN
ejpam-5830	12	10	d.	d.	PROPN
ejpam-5830	12	11	laureano	laureano	PROPN
ejpam-5830	12	12	)	)	PUNCT
ejpam-5830	12	13	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5830	13	1	1	1	NUM
ejpam-5830	13	2	copyright	copyright	NOUN
ejpam-5830	13	3	:	:	PUNCT
ejpam-5830	13	4	©	©	PROPN
ejpam-5830	13	5	2025	2025	NUM
ejpam-5830	13	6	the	the	DET
ejpam-5830	13	7	author(s	author(s	NOUN
ejpam-5830	13	8	)	)	PUNCT
ejpam-5830	13	9	.	.	PUNCT
ejpam-5830	14	1	(	(	PUNCT
ejpam-5830	14	2	cc	cc	NOUN
ejpam-5830	14	3	by	by	ADP
ejpam-5830	14	4	-	-	PUNCT
ejpam-5830	14	5	nc	nc	PROPN
ejpam-5830	14	6	4.0	4.0	NUM
ejpam-5830	14	7	)	)	PUNCT
ejpam-5830	14	8	r.	r.	PROPN
ejpam-5830	14	9	d.	d.	PROPN
ejpam-5830	14	10	laureano	laureano	PROPN
ejpam-5830	14	11	/	/	SYM
ejpam-5830	14	12	eur	eur	PROPN
ejpam-5830	14	13	.	.	PUNCT
ejpam-5830	15	1	j.	j.	PROPN
ejpam-5830	15	2	pure	pure	PROPN
ejpam-5830	15	3	appl	appl	PROPN
ejpam-5830	15	4	.	.	PROPN
ejpam-5830	15	5	math	math	PROPN
ejpam-5830	15	6	,	,	PUNCT
ejpam-5830	15	7	18	18	NUM
ejpam-5830	15	8	(	(	PUNCT
ejpam-5830	15	9	2	2	NUM
ejpam-5830	15	10	)	)	PUNCT
ejpam-5830	15	11	(	(	PUNCT
ejpam-5830	15	12	2025	2025	NUM
ejpam-5830	15	13	)	)	PUNCT
ejpam-5830	15	14	,	,	PUNCT
ejpam-5830	15	15	5830	5830	NUM
ejpam-5830	15	16	2	2	NUM
ejpam-5830	15	17	of	of	ADP
ejpam-5830	15	18	11	11	NUM
ejpam-5830	15	19	the	the	DET
ejpam-5830	15	20	study	study	NOUN
ejpam-5830	15	21	of	of	ADP
ejpam-5830	15	22	cohomological	cohomological	ADJ
ejpam-5830	15	23	equations	equation	NOUN
ejpam-5830	15	24	is	be	AUX
ejpam-5830	15	25	related	relate	VERB
ejpam-5830	15	26	,	,	PUNCT
ejpam-5830	15	27	in	in	ADP
ejpam-5830	15	28	particular	particular	ADJ
ejpam-5830	15	29	,	,	PUNCT
ejpam-5830	15	30	to	to	ADP
ejpam-5830	15	31	the	the	DET
ejpam-5830	15	32	analysis	analysis	NOUN
ejpam-5830	15	33	of	of	ADP
ejpam-5830	15	34	conjugacies	conjugacie	NOUN
ejpam-5830	15	35	to	to	ADP
ejpam-5830	15	36	irrational	irrational	ADJ
ejpam-5830	15	37	rotations	rotation	NOUN
ejpam-5830	15	38	of	of	ADP
ejpam-5830	15	39	the	the	DET
ejpam-5830	15	40	circle	circle	NOUN
ejpam-5830	15	41	,	,	PUNCT
ejpam-5830	15	42	the	the	DET
ejpam-5830	15	43	existence	existence	NOUN
ejpam-5830	15	44	of	of	ADP
ejpam-5830	15	45	absolutely	absolutely	ADV
ejpam-5830	15	46	continuous	continuous	ADJ
ejpam-5830	15	47	measures	measure	NOUN
ejpam-5830	15	48	for	for	ADP
ejpam-5830	15	49	expanding	expand	VERB
ejpam-5830	15	50	transformations	transformation	NOUN
ejpam-5830	15	51	of	of	ADP
ejpam-5830	15	52	the	the	DET
ejpam-5830	15	53	circle	circle	NOUN
ejpam-5830	15	54	,	,	PUNCT
ejpam-5830	15	55	and	and	CCONJ
ejpam-5830	15	56	the	the	DET
ejpam-5830	15	57	topological	topological	ADJ
ejpam-5830	15	58	stability	stability	NOUN
ejpam-5830	15	59	of	of	ADP
ejpam-5830	15	60	hyperbolic	hyperbolic	ADJ
ejpam-5830	15	61	automorphisms	automorphism	NOUN
ejpam-5830	15	62	of	of	ADP
ejpam-5830	15	63	the	the	DET
ejpam-5830	15	64	torus	torus	NOUN
ejpam-5830	15	65	.	.	PUNCT
ejpam-5830	16	1	such	such	ADJ
ejpam-5830	16	2	equations	equation	NOUN
ejpam-5830	16	3	also	also	ADV
ejpam-5830	16	4	naturally	naturally	ADV
ejpam-5830	16	5	arise	arise	VERB
ejpam-5830	16	6	in	in	ADP
ejpam-5830	16	7	statistical	statistical	ADJ
ejpam-5830	16	8	mechanics	mechanic	NOUN
ejpam-5830	16	9	and	and	CCONJ
ejpam-5830	16	10	celestial	celestial	ADJ
ejpam-5830	16	11	mechanics	mechanic	NOUN
ejpam-5830	16	12	.	.	PUNCT
ejpam-5830	17	1	some	some	DET
ejpam-5830	17	2	results	result	NOUN
ejpam-5830	17	3	established	establish	VERB
ejpam-5830	17	4	by	by	ADP
ejpam-5830	17	5	livschitz	livschitz	NOUN
ejpam-5830	17	6	in	in	ADP
ejpam-5830	17	7	the	the	DET
ejpam-5830	17	8	1970s	1970	NOUN
ejpam-5830	17	9	[	[	X
ejpam-5830	17	10	2	2	NUM
ejpam-5830	17	11	]	]	PUNCT
ejpam-5830	17	12	address	address	NOUN
ejpam-5830	17	13	precisely	precisely	ADV
ejpam-5830	17	14	the	the	DET
ejpam-5830	17	15	possibility	possibility	NOUN
ejpam-5830	17	16	of	of	ADP
ejpam-5830	17	17	obtaining	obtain	VERB
ejpam-5830	17	18	solutions	solution	NOUN
ejpam-5830	17	19	to	to	ADP
ejpam-5830	17	20	cohomological	cohomological	ADJ
ejpam-5830	17	21	equations	equation	NOUN
ejpam-5830	17	22	in	in	ADP
ejpam-5830	17	23	the	the	DET
ejpam-5830	17	24	context	context	NOUN
ejpam-5830	17	25	of	of	ADP
ejpam-5830	17	26	hyperbolic	hyperbolic	ADJ
ejpam-5830	17	27	dynamics	dynamic	NOUN
ejpam-5830	17	28	.	.	PUNCT
ejpam-5830	18	1	for	for	ADP
ejpam-5830	18	2	a	a	DET
ejpam-5830	18	3	hyperbolic	hyperbolic	ADJ
ejpam-5830	18	4	dynamical	dynamical	ADJ
ejpam-5830	18	5	system	system	NOUN
ejpam-5830	18	6	,	,	PUNCT
ejpam-5830	18	7	livschitz	livschitz	PROPN
ejpam-5830	18	8	’s	’s	PART
ejpam-5830	18	9	theorem	theorem	NOUN
ejpam-5830	18	10	provides	provide	VERB
ejpam-5830	18	11	a	a	DET
ejpam-5830	18	12	necessary	necessary	ADJ
ejpam-5830	18	13	and	and	CCONJ
ejpam-5830	18	14	sufficient	sufficient	ADJ
ejpam-5830	18	15	condition	condition	NOUN
ejpam-5830	18	16	,	,	PUNCT
ejpam-5830	18	17	based	base	VERB
ejpam-5830	18	18	solely	solely	ADV
ejpam-5830	18	19	on	on	ADP
ejpam-5830	18	20	information	information	NOUN
ejpam-5830	18	21	from	from	ADP
ejpam-5830	18	22	periodic	periodic	ADJ
ejpam-5830	18	23	orbits	orbit	NOUN
ejpam-5830	18	24	,	,	PUNCT
ejpam-5830	18	25	for	for	ADP
ejpam-5830	18	26	the	the	DET
ejpam-5830	18	27	existence	existence	NOUN
ejpam-5830	18	28	of	of	ADP
ejpam-5830	18	29	hölder	hölder	NOUN
ejpam-5830	18	30	solutions	solution	NOUN
ejpam-5830	18	31	.	.	PUNCT
ejpam-5830	19	1	this	this	PRON
ejpam-5830	19	2	is	be	AUX
ejpam-5830	19	3	one	one	NUM
ejpam-5830	19	4	of	of	ADP
ejpam-5830	19	5	the	the	DET
ejpam-5830	19	6	main	main	ADJ
ejpam-5830	19	7	tools	tool	NOUN
ejpam-5830	19	8	for	for	ADP
ejpam-5830	19	9	obtaining	obtain	VERB
ejpam-5830	19	10	global	global	ADJ
ejpam-5830	19	11	cohomological	cohomological	ADJ
ejpam-5830	19	12	information	information	NOUN
ejpam-5830	19	13	from	from	ADP
ejpam-5830	19	14	periodic	periodic	ADJ
ejpam-5830	19	15	data	datum	NOUN
ejpam-5830	19	16	.	.	PUNCT
ejpam-5830	20	1	a	a	DET
ejpam-5830	20	2	pragmatic	pragmatic	ADJ
ejpam-5830	20	3	approach	approach	NOUN
ejpam-5830	20	4	to	to	ADP
ejpam-5830	20	5	livschitz	livschitz	PROPN
ejpam-5830	20	6	’s	’s	PART
ejpam-5830	20	7	theorem	theorem	ADJ
ejpam-5830	20	8	,	,	PUNCT
ejpam-5830	20	9	oriented	orient	VERB
ejpam-5830	20	10	towards	towards	ADP
ejpam-5830	20	11	the	the	DET
ejpam-5830	20	12	study	study	NOUN
ejpam-5830	20	13	of	of	ADP
ejpam-5830	20	14	cohomology	cohomology	NOUN
ejpam-5830	20	15	in	in	ADP
ejpam-5830	20	16	dynamical	dynamical	ADJ
ejpam-5830	20	17	systems	system	NOUN
ejpam-5830	20	18	,	,	PUNCT
ejpam-5830	20	19	was	be	AUX
ejpam-5830	20	20	presented	present	VERB
ejpam-5830	20	21	in	in	ADP
ejpam-5830	20	22	[	[	X
ejpam-5830	20	23	3	3	NUM
ejpam-5830	20	24	,	,	PUNCT
ejpam-5830	20	25	4	4	NUM
ejpam-5830	20	26	]	]	PUNCT
ejpam-5830	20	27	,	,	PUNCT
ejpam-5830	20	28	emphasizing	emphasize	VERB
ejpam-5830	20	29	the	the	DET
ejpam-5830	20	30	relationship	relationship	NOUN
ejpam-5830	20	31	between	between	ADP
ejpam-5830	20	32	the	the	DET
ejpam-5830	20	33	existence	existence	NOUN
ejpam-5830	20	34	of	of	ADP
ejpam-5830	20	35	solutions	solution	NOUN
ejpam-5830	20	36	to	to	ADP
ejpam-5830	20	37	cohomological	cohomological	ADJ
ejpam-5830	20	38	equations	equation	NOUN
ejpam-5830	20	39	and	and	CCONJ
ejpam-5830	20	40	the	the	DET
ejpam-5830	20	41	behaviour	behaviour	NOUN
ejpam-5830	20	42	of	of	ADP
ejpam-5830	20	43	cocycles	cocycle	NOUN
ejpam-5830	20	44	along	along	ADP
ejpam-5830	20	45	periodic	periodic	ADJ
ejpam-5830	20	46	orbits	orbit	NOUN
ejpam-5830	20	47	.	.	PUNCT
ejpam-5830	21	1	following	follow	VERB
ejpam-5830	21	2	a	a	DET
ejpam-5830	21	3	preliminary	preliminary	ADJ
ejpam-5830	21	4	demonstration	demonstration	NOUN
ejpam-5830	21	5	of	of	ADP
ejpam-5830	21	6	anosov	anosov	PROPN
ejpam-5830	21	7	’s	’s	PART
ejpam-5830	21	8	closing	close	VERB
ejpam-5830	21	9	lemma	lemma	PROPN
ejpam-5830	21	10	for	for	ADP
ejpam-5830	21	11	hyperbolic	hyperbolic	ADJ
ejpam-5830	21	12	diffeomorphisms	diffeomorphism	NOUN
ejpam-5830	21	13	,	,	PUNCT
ejpam-5830	21	14	a	a	DET
ejpam-5830	21	15	detailed	detailed	ADJ
ejpam-5830	21	16	proof	proof	NOUN
ejpam-5830	21	17	of	of	ADP
ejpam-5830	21	18	livschitz	livschitz	PROPN
ejpam-5830	21	19	’s	’s	PART
ejpam-5830	21	20	theorem	theorem	NOUN
ejpam-5830	21	21	for	for	ADP
ejpam-5830	21	22	hyperbolic	hyperbolic	ADJ
ejpam-5830	21	23	diffeomorphisms	diffeomorphism	NOUN
ejpam-5830	21	24	is	be	AUX
ejpam-5830	21	25	provided	provide	VERB
ejpam-5830	21	26	in	in	ADP
ejpam-5830	21	27	[	[	X
ejpam-5830	21	28	4	4	NUM
ejpam-5830	21	29	]	]	PUNCT
ejpam-5830	21	30	,	,	PUNCT
ejpam-5830	21	31	closely	closely	ADV
ejpam-5830	21	32	following	follow	VERB
ejpam-5830	21	33	the	the	DET
ejpam-5830	21	34	approach	approach	NOUN
ejpam-5830	21	35	of	of	ADP
ejpam-5830	21	36	katok	katok	NOUN
ejpam-5830	21	37	and	and	CCONJ
ejpam-5830	21	38	hasselblatt	hasselblatt	NOUN
ejpam-5830	21	39	in	in	ADP
ejpam-5830	21	40	[	[	X
ejpam-5830	21	41	5	5	NUM
ejpam-5830	21	42	]	]	PUNCT
ejpam-5830	21	43	.	.	PUNCT
ejpam-5830	22	1	the	the	DET
ejpam-5830	22	2	only	only	ADJ
ejpam-5830	22	3	published	publish	VERB
ejpam-5830	22	4	proof	proof	NOUN
ejpam-5830	22	5	of	of	ADP
ejpam-5830	22	6	livschitz	livschitz	PROPN
ejpam-5830	22	7	’s	’s	PART
ejpam-5830	22	8	theorem	theorem	NOUN
ejpam-5830	22	9	for	for	ADP
ejpam-5830	22	10	flows	flow	NOUN
ejpam-5830	22	11	is	be	AUX
ejpam-5830	22	12	by	by	AUX
ejpam-5830	22	13	livschitz	livschitz	VERB
ejpam-5830	22	14	himself	himself	PRON
ejpam-5830	23	1	[	[	X
ejpam-5830	23	2	2	2	NUM
ejpam-5830	23	3	]	]	PUNCT
ejpam-5830	23	4	.	.	PUNCT
ejpam-5830	24	1	in	in	ADP
ejpam-5830	24	2	[	[	X
ejpam-5830	24	3	3	3	NUM
ejpam-5830	24	4	]	]	PUNCT
ejpam-5830	24	5	,	,	PUNCT
ejpam-5830	24	6	a	a	DET
ejpam-5830	24	7	proof	proof	NOUN
ejpam-5830	24	8	of	of	ADP
ejpam-5830	24	9	livschitz	livschitz	PROPN
ejpam-5830	24	10	’s	’s	PART
ejpam-5830	24	11	theorem	theorem	NOUN
ejpam-5830	24	12	for	for	ADP
ejpam-5830	24	13	the	the	DET
ejpam-5830	24	14	continuous	continuous	ADJ
ejpam-5830	24	15	-	-	PUNCT
ejpam-5830	24	16	time	time	NOUN
ejpam-5830	24	17	case	case	NOUN
ejpam-5830	24	18	is	be	AUX
ejpam-5830	24	19	given	give	VERB
ejpam-5830	24	20	,	,	PUNCT
ejpam-5830	24	21	and	and	CCONJ
ejpam-5830	24	22	its	its	PRON
ejpam-5830	24	23	generalization	generalization	NOUN
ejpam-5830	24	24	to	to	ADP
ejpam-5830	24	25	suspension	suspension	NOUN
ejpam-5830	24	26	flows	flow	NOUN
ejpam-5830	24	27	is	be	AUX
ejpam-5830	24	28	discussed	discuss	VERB
ejpam-5830	24	29	;	;	PUNCT
ejpam-5830	24	30	this	this	DET
ejpam-5830	24	31	generalisation	generalisation	NOUN
ejpam-5830	24	32	enabled	enable	VERB
ejpam-5830	24	33	a	a	DET
ejpam-5830	24	34	second	second	ADJ
ejpam-5830	24	35	proof	proof	NOUN
ejpam-5830	24	36	of	of	ADP
ejpam-5830	24	37	livschitz	livschitz	PROPN
ejpam-5830	24	38	’s	’s	PART
ejpam-5830	24	39	theorem	theorem	NOUN
ejpam-5830	24	40	for	for	ADP
ejpam-5830	24	41	flows	flow	NOUN
ejpam-5830	24	42	,	,	PUNCT
ejpam-5830	24	43	based	base	VERB
ejpam-5830	24	44	on	on	ADP
ejpam-5830	24	45	the	the	DET
ejpam-5830	24	46	construction	construction	NOUN
ejpam-5830	24	47	of	of	ADP
ejpam-5830	24	48	markov	markov	NOUN
ejpam-5830	24	49	partitions	partition	NOUN
ejpam-5830	24	50	by	by	ADP
ejpam-5830	24	51	bowen	bowen	NOUN
ejpam-5830	25	1	[	[	X
ejpam-5830	25	2	6	6	NUM
ejpam-5830	25	3	]	]	PUNCT
ejpam-5830	25	4	and	and	CCONJ
ejpam-5830	25	5	ratner	ratner	X
ejpam-5830	26	1	[	[	X
ejpam-5830	26	2	7	7	NUM
ejpam-5830	26	3	]	]	PUNCT
ejpam-5830	26	4	for	for	ADP
ejpam-5830	26	5	hyperbolic	hyperbolic	ADJ
ejpam-5830	26	6	flows	flow	NOUN
ejpam-5830	26	7	.	.	PUNCT
ejpam-5830	27	1	in	in	ADP
ejpam-5830	27	2	this	this	DET
ejpam-5830	27	3	article	article	NOUN
ejpam-5830	27	4	,	,	PUNCT
ejpam-5830	27	5	we	we	PRON
ejpam-5830	27	6	present	present	VERB
ejpam-5830	27	7	a	a	DET
ejpam-5830	27	8	review	review	NOUN
ejpam-5830	27	9	of	of	ADP
ejpam-5830	27	10	cohomology	cohomology	NOUN
ejpam-5830	27	11	in	in	ADP
ejpam-5830	27	12	dynamical	dynamical	ADJ
ejpam-5830	27	13	systems	system	NOUN
ejpam-5830	27	14	,	,	PUNCT
ejpam-5830	27	15	with	with	ADP
ejpam-5830	27	16	the	the	DET
ejpam-5830	27	17	aim	aim	NOUN
ejpam-5830	27	18	of	of	ADP
ejpam-5830	27	19	understanding	understand	VERB
ejpam-5830	27	20	the	the	DET
ejpam-5830	27	21	concept	concept	NOUN
ejpam-5830	27	22	of	of	ADP
ejpam-5830	27	23	cocycles	cocycle	NOUN
ejpam-5830	27	24	and	and	CCONJ
ejpam-5830	27	25	coboundaries	coboundarie	NOUN
ejpam-5830	27	26	more	more	ADV
ejpam-5830	27	27	generally	generally	ADV
ejpam-5830	27	28	,	,	PUNCT
ejpam-5830	27	29	in	in	ADP
ejpam-5830	27	30	groups	group	NOUN
ejpam-5830	27	31	beyond	beyond	ADP
ejpam-5830	27	32	z	z	NOUN
ejpam-5830	27	33	or	or	CCONJ
ejpam-5830	27	34	r	r	NOUN
ejpam-5830	27	35	,	,	PUNCT
ejpam-5830	27	36	and	and	CCONJ
ejpam-5830	27	37	in	in	ADP
ejpam-5830	27	38	higher	high	ADJ
ejpam-5830	27	39	dimensions	dimension	NOUN
ejpam-5830	27	40	.	.	PUNCT
ejpam-5830	28	1	the	the	DET
ejpam-5830	28	2	problem	problem	NOUN
ejpam-5830	28	3	of	of	ADP
ejpam-5830	28	4	regularity	regularity	NOUN
ejpam-5830	28	5	of	of	ADP
ejpam-5830	28	6	the	the	DET
ejpam-5830	28	7	solution	solution	NOUN
ejpam-5830	28	8	of	of	ADP
ejpam-5830	28	9	a	a	DET
ejpam-5830	28	10	cohomological	cohomological	ADJ
ejpam-5830	28	11	equation	equation	NOUN
ejpam-5830	28	12	,	,	PUNCT
ejpam-5830	28	13	stemming	stem	VERB
ejpam-5830	28	14	from	from	ADP
ejpam-5830	28	15	the	the	DET
ejpam-5830	28	16	regularity	regularity	NOUN
ejpam-5830	28	17	of	of	ADP
ejpam-5830	28	18	the	the	DET
ejpam-5830	28	19	cocycle	cocycle	NOUN
ejpam-5830	28	20	,	,	PUNCT
ejpam-5830	28	21	is	be	AUX
ejpam-5830	28	22	addressed	address	VERB
ejpam-5830	28	23	,	,	PUNCT
ejpam-5830	28	24	and	and	CCONJ
ejpam-5830	28	25	regularity	regularity	NOUN
ejpam-5830	28	26	results	result	NOUN
ejpam-5830	28	27	are	be	AUX
ejpam-5830	28	28	presented	present	VERB
ejpam-5830	28	29	.	.	PUNCT
ejpam-5830	29	1	the	the	DET
ejpam-5830	29	2	study	study	NOUN
ejpam-5830	29	3	of	of	ADP
ejpam-5830	29	4	cohomology	cohomology	NOUN
ejpam-5830	29	5	in	in	ADP
ejpam-5830	29	6	dynamical	dynamical	ADJ
ejpam-5830	29	7	systems	system	NOUN
ejpam-5830	29	8	becomes	become	VERB
ejpam-5830	29	9	more	more	ADV
ejpam-5830	29	10	complex	complex	ADJ
ejpam-5830	29	11	in	in	ADP
ejpam-5830	29	12	non	non	ADJ
ejpam-5830	29	13	-	-	ADJ
ejpam-5830	29	14	hyperbolic	hyperbolic	ADJ
ejpam-5830	29	15	dynamics	dynamic	NOUN
ejpam-5830	29	16	,	,	PUNCT
ejpam-5830	29	17	even	even	ADV
ejpam-5830	29	18	when	when	SCONJ
ejpam-5830	29	19	dealing	deal	VERB
ejpam-5830	29	20	with	with	ADP
ejpam-5830	29	21	the	the	DET
ejpam-5830	29	22	cohomology	cohomology	NOUN
ejpam-5830	29	23	of	of	ADP
ejpam-5830	29	24	actions	action	NOUN
ejpam-5830	29	25	of	of	ADP
ejpam-5830	29	26	z	z	NOUN
ejpam-5830	29	27	or	or	CCONJ
ejpam-5830	29	28	r	r	NOUN
ejpam-5830	29	29	[	[	X
ejpam-5830	29	30	8	8	NUM
ejpam-5830	29	31	,	,	PUNCT
ejpam-5830	29	32	9	9	NUM
ejpam-5830	29	33	]	]	PUNCT
ejpam-5830	29	34	.	.	PUNCT
ejpam-5830	30	1	veech	veech	NOUN
ejpam-5830	30	2	obtained	obtain	VERB
ejpam-5830	30	3	an	an	DET
ejpam-5830	30	4	important	important	ADJ
ejpam-5830	30	5	result	result	NOUN
ejpam-5830	30	6	in	in	ADP
ejpam-5830	30	7	this	this	DET
ejpam-5830	30	8	direction	direction	NOUN
ejpam-5830	30	9	in	in	ADP
ejpam-5830	30	10	[	[	X
ejpam-5830	30	11	10	10	NUM
ejpam-5830	30	12	]	]	PUNCT
ejpam-5830	30	13	,	,	PUNCT
ejpam-5830	30	14	where	where	SCONJ
ejpam-5830	30	15	he	he	PRON
ejpam-5830	30	16	establishes	establish	VERB
ejpam-5830	30	17	the	the	DET
ejpam-5830	30	18	c∞	c∞	PROPN
ejpam-5830	30	19	livschitz	livschitz	NOUN
ejpam-5830	30	20	property	property	NOUN
ejpam-5830	30	21	for	for	ADP
ejpam-5830	30	22	partially	partially	ADV
ejpam-5830	30	23	hyperbolic	hyperbolic	ADJ
ejpam-5830	30	24	endomorphisms	endomorphism	NOUN
ejpam-5830	30	25	of	of	ADP
ejpam-5830	30	26	the	the	DET
ejpam-5830	30	27	torus	torus	NOUN
ejpam-5830	30	28	(	(	PUNCT
ejpam-5830	30	29	i.e.	i.e.	X
ejpam-5830	30	30	showing	show	VERB
ejpam-5830	30	31	that	that	SCONJ
ejpam-5830	30	32	c∞	c∞	PROPN
ejpam-5830	30	33	cocycles	cocycle	NOUN
ejpam-5830	30	34	satisfying	satisfy	VERB
ejpam-5830	30	35	conditions	condition	NOUN
ejpam-5830	30	36	relative	relative	ADJ
ejpam-5830	30	37	to	to	ADP
ejpam-5830	30	38	periodic	periodic	ADJ
ejpam-5830	30	39	orbits	orbit	NOUN
ejpam-5830	30	40	possess	possess	VERB
ejpam-5830	30	41	c∞	c∞	PROPN
ejpam-5830	30	42	trivializations	trivialization	NOUN
ejpam-5830	30	43	)	)	PUNCT
ejpam-5830	30	44	.	.	PUNCT
ejpam-5830	31	1	this	this	DET
ejpam-5830	31	2	research	research	NOUN
ejpam-5830	31	3	focused	focus	VERB
ejpam-5830	31	4	solely	solely	ADV
ejpam-5830	31	5	on	on	ADP
ejpam-5830	31	6	the	the	DET
ejpam-5830	31	7	hyperbolic	hyperbolic	ADJ
ejpam-5830	31	8	case	case	NOUN
ejpam-5830	31	9	,	,	PUNCT
ejpam-5830	31	10	presenting	present	VERB
ejpam-5830	31	11	a	a	DET
ejpam-5830	31	12	selection	selection	NOUN
ejpam-5830	31	13	of	of	ADP
ejpam-5830	31	14	results	result	NOUN
ejpam-5830	31	15	that	that	PRON
ejpam-5830	31	16	facilitate	facilitate	VERB
ejpam-5830	31	17	entry	entry	NOUN
ejpam-5830	31	18	into	into	ADP
ejpam-5830	31	19	theory	theory	NOUN
ejpam-5830	31	20	.	.	PUNCT
ejpam-5830	32	1	2	2	X
ejpam-5830	32	2	.	.	X
ejpam-5830	32	3	cocycles	cocycle	NOUN
ejpam-5830	32	4	with	with	ADP
ejpam-5830	32	5	values	value	NOUN
ejpam-5830	32	6	in	in	ADP
ejpam-5830	32	7	lie	lie	NOUN
ejpam-5830	32	8	groups	group	NOUN
ejpam-5830	32	9	let	let	VERB
ejpam-5830	32	10	g	g	NOUN
ejpam-5830	32	11	be	be	AUX
ejpam-5830	32	12	a	a	DET
ejpam-5830	32	13	group	group	NOUN
ejpam-5830	32	14	that	that	PRON
ejpam-5830	32	15	acts	act	VERB
ejpam-5830	32	16	on	on	ADP
ejpam-5830	32	17	a	a	DET
ejpam-5830	32	18	compact	compact	ADJ
ejpam-5830	32	19	riemannian	riemannian	NOUN
ejpam-5830	32	20	manifold	manifold	ADJ
ejpam-5830	32	21	m	m	VERB
ejpam-5830	32	22	through	through	ADP
ejpam-5830	32	23	the	the	DET
ejpam-5830	32	24	application	application	NOUN
ejpam-5830	32	25	t	t	NOUN
ejpam-5830	32	26	:	:	PUNCT
ejpam-5830	32	27	g×m	g×m	PROPN
ejpam-5830	32	28	→m	→m	PROPN
ejpam-5830	32	29	.	.	PUNCT
ejpam-5830	33	1	for	for	ADP
ejpam-5830	33	2	each	each	DET
ejpam-5830	33	3	g	g	PROPN
ejpam-5830	33	4	∈	∈	PROPN
ejpam-5830	33	5	g	g	NOUN
ejpam-5830	33	6	,	,	PUNCT
ejpam-5830	33	7	we	we	PRON
ejpam-5830	33	8	define	define	VERB
ejpam-5830	33	9	the	the	DET
ejpam-5830	33	10	transformation	transformation	NOUN
ejpam-5830	33	11	t	t	NOUN
ejpam-5830	33	12	(	(	PUNCT
ejpam-5830	33	13	g	g	NOUN
ejpam-5830	33	14	)	)	PUNCT
ejpam-5830	33	15	:	:	PUNCT
ejpam-5830	33	16	m	m	VERB
ejpam-5830	33	17	→m	→m	PUNCT
ejpam-5830	33	18	by	by	ADP
ejpam-5830	33	19	t	t	PROPN
ejpam-5830	33	20	(	(	PUNCT
ejpam-5830	33	21	g)x	g)x	PROPN
ejpam-5830	33	22	=	=	SYM
ejpam-5830	33	23	t	t	PROPN
ejpam-5830	33	24	(	(	PUNCT
ejpam-5830	33	25	g	g	PROPN
ejpam-5830	33	26	,	,	PUNCT
ejpam-5830	33	27	x	x	NOUN
ejpam-5830	33	28	)	)	PUNCT
ejpam-5830	33	29	.	.	PUNCT
ejpam-5830	34	1	for	for	ADP
ejpam-5830	34	2	each	each	DET
ejpam-5830	34	3	g	g	PROPN
ejpam-5830	34	4	∈	∈	PROPN
ejpam-5830	34	5	g	g	PROPN
ejpam-5830	34	6	,	,	PUNCT
ejpam-5830	34	7	the	the	DET
ejpam-5830	34	8	transformation	transformation	NOUN
ejpam-5830	34	9	t	t	PROPN
ejpam-5830	34	10	(	(	PUNCT
ejpam-5830	34	11	g	g	NOUN
ejpam-5830	34	12	)	)	PUNCT
ejpam-5830	34	13	is	be	AUX
ejpam-5830	34	14	a	a	DET
ejpam-5830	34	15	diffeomorphism	diffeomorphism	NOUN
ejpam-5830	34	16	,	,	PUNCT
ejpam-5830	34	17	t	t	PROPN
ejpam-5830	34	18	(	(	PUNCT
ejpam-5830	34	19	1	1	NUM
ejpam-5830	34	20	)	)	PUNCT
ejpam-5830	34	21	is	be	AUX
ejpam-5830	34	22	the	the	DET
ejpam-5830	34	23	identity	identity	NOUN
ejpam-5830	34	24	transformation	transformation	NOUN
ejpam-5830	34	25	on	on	ADP
ejpam-5830	34	26	m	m	PROPN
ejpam-5830	34	27	(	(	PUNCT
ejpam-5830	34	28	where	where	SCONJ
ejpam-5830	34	29	1	1	NUM
ejpam-5830	34	30	denotes	denote	VERB
ejpam-5830	34	31	the	the	DET
ejpam-5830	34	32	identity	identity	NOUN
ejpam-5830	34	33	of	of	ADP
ejpam-5830	34	34	g	g	NOUN
ejpam-5830	34	35	)	)	PUNCT
ejpam-5830	34	36	,	,	PUNCT
ejpam-5830	34	37	and	and	CCONJ
ejpam-5830	34	38	for	for	ADP
ejpam-5830	34	39	g	g	NOUN
ejpam-5830	34	40	,	,	PUNCT
ejpam-5830	34	41	h	h	NOUN
ejpam-5830	34	42	∈	∈	PROPN
ejpam-5830	34	43	g	g	PROPN
ejpam-5830	34	44	,	,	PUNCT
ejpam-5830	34	45	we	we	PRON
ejpam-5830	34	46	have	have	VERB
ejpam-5830	34	47	t	t	PROPN
ejpam-5830	34	48	(	(	PUNCT
ejpam-5830	34	49	g	g	PROPN
ejpam-5830	34	50	·	·	PUNCT
ejpam-5830	34	51	h	h	NOUN
ejpam-5830	34	52	)	)	PUNCT
ejpam-5830	35	1	=	=	SYM
ejpam-5830	35	2	t	t	PROPN
ejpam-5830	35	3	(	(	PUNCT
ejpam-5830	35	4	g	g	NOUN
ejpam-5830	35	5	)	)	PUNCT
ejpam-5830	35	6	◦	◦	NOUN
ejpam-5830	35	7	t	t	PROPN
ejpam-5830	35	8	(	(	PUNCT
ejpam-5830	35	9	h	h	NOUN
ejpam-5830	35	10	)	)	PUNCT
ejpam-5830	35	11	,	,	PUNCT
ejpam-5830	35	12	denoting	denote	VERB
ejpam-5830	35	13	by	by	ADP
ejpam-5830	35	14	·	·	PUNCT
ejpam-5830	35	15	the	the	DET
ejpam-5830	35	16	group	group	NOUN
ejpam-5830	35	17	operation	operation	NOUN
ejpam-5830	35	18	in	in	ADP
ejpam-5830	35	19	g.	g.	PROPN
ejpam-5830	35	20	now	now	ADV
ejpam-5830	35	21	consider	consider	VERB
ejpam-5830	35	22	cocycles	cocycle	NOUN
ejpam-5830	35	23	with	with	ADP
ejpam-5830	35	24	values	value	NOUN
ejpam-5830	35	25	in	in	ADP
ejpam-5830	35	26	a	a	DET
ejpam-5830	35	27	topological	topological	ADJ
ejpam-5830	35	28	group	group	NOUN
ejpam-5830	35	29	γ	γ	X
ejpam-5830	35	30	(	(	PUNCT
ejpam-5830	35	31	with	with	ADP
ejpam-5830	35	32	an	an	DET
ejpam-5830	35	33	operation	operation	NOUN
ejpam-5830	35	34	denoted	denote	VERB
ejpam-5830	35	35	by	by	ADP
ejpam-5830	35	36	+	+	NOUN
ejpam-5830	35	37	,	,	PUNCT
ejpam-5830	35	38	not	not	PART
ejpam-5830	35	39	necessarily	necessarily	ADV
ejpam-5830	35	40	commutative	commutative	ADJ
ejpam-5830	35	41	)	)	PUNCT
ejpam-5830	35	42	with	with	ADP
ejpam-5830	35	43	identity	identity	NOUN
ejpam-5830	35	44	e.	e.	PROPN
ejpam-5830	35	45	a	a	DET
ejpam-5830	35	46	cocycle	cocycle	PROPN
ejpam-5830	35	47	α	α	PROPN
ejpam-5830	35	48	over	over	ADP
ejpam-5830	35	49	t	t	PROPN
ejpam-5830	35	50	with	with	ADP
ejpam-5830	35	51	values	value	NOUN
ejpam-5830	35	52	in	in	ADP
ejpam-5830	35	53	γ	γ	PROPN
ejpam-5830	35	54	r.	r.	PROPN
ejpam-5830	35	55	d.	d.	PROPN
ejpam-5830	35	56	laureano	laureano	PROPN
ejpam-5830	35	57	/	/	SYM
ejpam-5830	35	58	eur	eur	PROPN
ejpam-5830	35	59	.	.	PUNCT
ejpam-5830	36	1	j.	j.	PROPN
ejpam-5830	36	2	pure	pure	PROPN
ejpam-5830	36	3	appl	appl	PROPN
ejpam-5830	36	4	.	.	PROPN
ejpam-5830	36	5	math	math	PROPN
ejpam-5830	36	6	,	,	PUNCT
ejpam-5830	36	7	18	18	NUM
ejpam-5830	36	8	(	(	PUNCT
ejpam-5830	36	9	2	2	NUM
ejpam-5830	36	10	)	)	PUNCT
ejpam-5830	36	11	(	(	PUNCT
ejpam-5830	36	12	2025	2025	NUM
ejpam-5830	36	13	)	)	PUNCT
ejpam-5830	36	14	,	,	PUNCT
ejpam-5830	36	15	5830	5830	NUM
ejpam-5830	36	16	3	3	NUM
ejpam-5830	36	17	of	of	ADP
ejpam-5830	36	18	11	11	NUM
ejpam-5830	36	19	is	be	AUX
ejpam-5830	36	20	a	a	DET
ejpam-5830	36	21	continuous	continuous	ADJ
ejpam-5830	36	22	transformation	transformation	NOUN
ejpam-5830	36	23	α	α	NOUN
ejpam-5830	36	24	:	:	PUNCT
ejpam-5830	37	1	g×m	g×m	PROPN
ejpam-5830	37	2	→	→	SYM
ejpam-5830	37	3	γ	γ	X
ejpam-5830	37	4	such	such	ADJ
ejpam-5830	37	5	that	that	SCONJ
ejpam-5830	37	6	α	α	PROPN
ejpam-5830	37	7	(	(	PUNCT
ejpam-5830	37	8	g2g1	g2g1	X
ejpam-5830	37	9	,	,	PUNCT
ejpam-5830	37	10	x	x	NOUN
ejpam-5830	37	11	)	)	PUNCT
ejpam-5830	37	12	=	=	SYM
ejpam-5830	37	13	α	α	PROPN
ejpam-5830	37	14	(	(	PUNCT
ejpam-5830	37	15	g2	g2	PROPN
ejpam-5830	37	16	,	,	PUNCT
ejpam-5830	37	17	t	t	PROPN
ejpam-5830	37	18	(	(	PUNCT
ejpam-5830	37	19	g1)x	g1)x	PROPN
ejpam-5830	37	20	)	)	PUNCT
ejpam-5830	37	21	+	+	CCONJ
ejpam-5830	37	22	α	α	PROPN
ejpam-5830	37	23	(	(	PUNCT
ejpam-5830	37	24	g1	g1	PROPN
ejpam-5830	37	25	,	,	PUNCT
ejpam-5830	37	26	x	x	NOUN
ejpam-5830	37	27	)	)	PUNCT
ejpam-5830	37	28	,	,	PUNCT
ejpam-5830	37	29	for	for	ADP
ejpam-5830	37	30	each	each	DET
ejpam-5830	37	31	x	x	SYM
ejpam-5830	37	32	∈m	∈m	NOUN
ejpam-5830	37	33	and	and	CCONJ
ejpam-5830	37	34	g1	g1	NOUN
ejpam-5830	37	35	,	,	PUNCT
ejpam-5830	37	36	g2	g2	PROPN
ejpam-5830	37	37	∈	∈	PROPN
ejpam-5830	37	38	g.	g.	PROPN
ejpam-5830	37	39	similarly	similarly	ADV
ejpam-5830	37	40	,	,	PUNCT
ejpam-5830	37	41	two	two	NUM
ejpam-5830	37	42	cocycles	cocycle	NOUN
ejpam-5830	37	43	α	α	VERB
ejpam-5830	37	44	and	and	CCONJ
ejpam-5830	37	45	β	β	PROPN
ejpam-5830	37	46	over	over	ADP
ejpam-5830	37	47	t	t	PROPN
ejpam-5830	37	48	are	be	AUX
ejpam-5830	37	49	said	say	VERB
ejpam-5830	37	50	to	to	PART
ejpam-5830	37	51	be	be	AUX
ejpam-5830	37	52	cohomologous	cohomologous	ADJ
ejpam-5830	37	53	if	if	SCONJ
ejpam-5830	37	54	there	there	PRON
ejpam-5830	37	55	exists	exist	VERB
ejpam-5830	37	56	a	a	DET
ejpam-5830	37	57	continuous	continuous	ADJ
ejpam-5830	37	58	transformation	transformation	NOUN
ejpam-5830	37	59	φ	φ	NOUN
ejpam-5830	37	60	:	:	PUNCT
ejpam-5830	37	61	m	m	VERB
ejpam-5830	37	62	→	→	SYM
ejpam-5830	37	63	γ	γ	X
ejpam-5830	37	64	such	such	ADJ
ejpam-5830	37	65	that	that	SCONJ
ejpam-5830	37	66	α	α	PROPN
ejpam-5830	37	67	(	(	PUNCT
ejpam-5830	37	68	g	g	NOUN
ejpam-5830	37	69	,	,	PUNCT
ejpam-5830	37	70	x	x	NOUN
ejpam-5830	37	71	)	)	PUNCT
ejpam-5830	37	72	=	=	SYM
ejpam-5830	37	73	φ	φ	PROPN
ejpam-5830	37	74	(	(	PUNCT
ejpam-5830	37	75	t	t	PROPN
ejpam-5830	37	76	(	(	PUNCT
ejpam-5830	37	77	g)x	g)x	ADJ
ejpam-5830	37	78	)	)	PUNCT
ejpam-5830	37	79	+	+	CCONJ
ejpam-5830	37	80	β	β	X
ejpam-5830	37	81	(	(	PUNCT
ejpam-5830	37	82	g	g	PROPN
ejpam-5830	37	83	,	,	PUNCT
ejpam-5830	37	84	x)−	x)−	PROPN
ejpam-5830	37	85	φ(x	φ(x	PROPN
ejpam-5830	37	86	)	)	PUNCT
ejpam-5830	37	87	,	,	PUNCT
ejpam-5830	37	88	(	(	PUNCT
ejpam-5830	37	89	2	2	X
ejpam-5830	37	90	)	)	PUNCT
ejpam-5830	37	91	for	for	ADP
ejpam-5830	37	92	each	each	DET
ejpam-5830	37	93	x	x	SYM
ejpam-5830	37	94	∈m	∈m	NOUN
ejpam-5830	37	95	and	and	CCONJ
ejpam-5830	37	96	g	g	PROPN
ejpam-5830	37	97	∈	∈	PROPN
ejpam-5830	37	98	g	g	PROPN
ejpam-5830	37	99	,	,	PUNCT
ejpam-5830	37	100	where	where	SCONJ
ejpam-5830	37	101	−	−	PROPN
ejpam-5830	37	102	represents	represent	VERB
ejpam-5830	37	103	the	the	DET
ejpam-5830	37	104	inverse	inverse	NOUN
ejpam-5830	37	105	in	in	ADP
ejpam-5830	37	106	γ	γ	PROPN
ejpam-5830	37	107	.	.	PUNCT
ejpam-5830	37	108	a	a	DET
ejpam-5830	37	109	cocycle	cocycle	NOUN
ejpam-5830	37	110	α	α	NOUN
ejpam-5830	37	111	:	:	PUNCT
ejpam-5830	37	112	g	g	PROPN
ejpam-5830	37	113	×	×	PROPN
ejpam-5830	37	114	m	m	VERB
ejpam-5830	37	115	→	→	SYM
ejpam-5830	37	116	γ	γ	X
ejpam-5830	37	117	is	be	AUX
ejpam-5830	37	118	called	call	VERB
ejpam-5830	37	119	a	a	DET
ejpam-5830	37	120	coboundary	coboundary	ADJ
ejpam-5830	37	121	or	or	CCONJ
ejpam-5830	37	122	cohomologically	cohomologically	ADV
ejpam-5830	37	123	trivial	trivial	ADJ
ejpam-5830	37	124	,	,	PUNCT
ejpam-5830	37	125	if	if	SCONJ
ejpam-5830	37	126	the	the	DET
ejpam-5830	37	127	equation	equation	NOUN
ejpam-5830	37	128	α	α	X
ejpam-5830	37	129	(	(	PUNCT
ejpam-5830	37	130	g	g	NOUN
ejpam-5830	37	131	,	,	PUNCT
ejpam-5830	37	132	x	x	NOUN
ejpam-5830	37	133	)	)	PUNCT
ejpam-5830	37	134	=	=	SYM
ejpam-5830	37	135	φ	φ	PROPN
ejpam-5830	37	136	(	(	PUNCT
ejpam-5830	37	137	t	t	PROPN
ejpam-5830	37	138	(	(	PUNCT
ejpam-5830	37	139	g)x)−	g)x)−	PROPN
ejpam-5830	37	140	φ(x	φ(x	PROPN
ejpam-5830	37	141	)	)	PUNCT
ejpam-5830	37	142	(	(	PUNCT
ejpam-5830	37	143	3	3	X
ejpam-5830	37	144	)	)	PUNCT
ejpam-5830	37	145	has	have	VERB
ejpam-5830	37	146	a	a	DET
ejpam-5830	37	147	continuous	continuous	ADJ
ejpam-5830	37	148	solution	solution	NOUN
ejpam-5830	37	149	φ	φ	X
ejpam-5830	37	150	:	:	PUNCT
ejpam-5830	37	151	m	m	PROPN
ejpam-5830	37	152	→	→	SYM
ejpam-5830	37	153	γ	γ	X
ejpam-5830	37	154	.	.	PUNCT
ejpam-5830	38	1	this	this	PRON
ejpam-5830	38	2	corresponds	correspond	VERB
ejpam-5830	38	3	to	to	ADP
ejpam-5830	38	4	the	the	DET
ejpam-5830	38	5	case	case	NOUN
ejpam-5830	38	6	where	where	SCONJ
ejpam-5830	38	7	α	α	NOUN
ejpam-5830	38	8	is	be	AUX
ejpam-5830	38	9	cohomologous	cohomologous	ADJ
ejpam-5830	38	10	to	to	ADP
ejpam-5830	38	11	the	the	DET
ejpam-5830	38	12	trivial	trivial	ADJ
ejpam-5830	38	13	cocycle	cocycle	NOUN
ejpam-5830	38	14	β(g	β(g	PROPN
ejpam-5830	38	15	,	,	PUNCT
ejpam-5830	38	16	x	x	NOUN
ejpam-5830	38	17	)	)	PUNCT
ejpam-5830	39	1	=	=	VERB
ejpam-5830	39	2	e.	e.	PROPN
ejpam-5830	40	1	the	the	DET
ejpam-5830	40	2	transformation	transformation	NOUN
ejpam-5830	40	3	φ	φ	PROPN
ejpam-5830	40	4	is	be	AUX
ejpam-5830	40	5	then	then	ADV
ejpam-5830	40	6	called	call	VERB
ejpam-5830	40	7	a	a	DET
ejpam-5830	40	8	trivialisation	trivialisation	NOUN
ejpam-5830	40	9	of	of	ADP
ejpam-5830	40	10	the	the	DET
ejpam-5830	40	11	cocycle	cocycle	PROPN
ejpam-5830	40	12	α	α	PROPN
ejpam-5830	40	13	.	.	PUNCT
ejpam-5830	41	1	for	for	SCONJ
ejpam-5830	41	2	a	a	DET
ejpam-5830	41	3	cocycle	cocycle	NOUN
ejpam-5830	41	4	α	α	NOUN
ejpam-5830	41	5	to	to	PART
ejpam-5830	41	6	be	be	AUX
ejpam-5830	41	7	cohomologically	cohomologically	ADV
ejpam-5830	41	8	trivial	trivial	ADJ
ejpam-5830	41	9	,	,	PUNCT
ejpam-5830	41	10	it	it	PRON
ejpam-5830	41	11	must	must	AUX
ejpam-5830	41	12	satisfy	satisfy	VERB
ejpam-5830	41	13	the	the	DET
ejpam-5830	41	14	identity	identity	NOUN
ejpam-5830	41	15	α(g	α(g	NUM
ejpam-5830	41	16	,	,	PUNCT
ejpam-5830	41	17	x	x	X
ejpam-5830	41	18	)	)	PUNCT
ejpam-5830	41	19	=	=	SYM
ejpam-5830	41	20	e	e	NOUN
ejpam-5830	41	21	for	for	ADP
ejpam-5830	41	22	each	each	DET
ejpam-5830	41	23	x	x	SYM
ejpam-5830	41	24	∈m	∈m	NOUN
ejpam-5830	41	25	and	and	CCONJ
ejpam-5830	41	26	g	g	PROPN
ejpam-5830	41	27	∈	∈	PROPN
ejpam-5830	41	28	g	g	PROPN
ejpam-5830	41	29	such	such	ADJ
ejpam-5830	41	30	that	that	DET
ejpam-5830	41	31	t	t	PROPN
ejpam-5830	41	32	(	(	PUNCT
ejpam-5830	41	33	g)x	g)x	NOUN
ejpam-5830	41	34	=	=	PUNCT
ejpam-5830	41	35	x.	x.	NOUN
ejpam-5830	41	36	(	(	PUNCT
ejpam-5830	41	37	4	4	X
ejpam-5830	41	38	)	)	PUNCT
ejpam-5830	41	39	note	note	VERB
ejpam-5830	41	40	that	that	SCONJ
ejpam-5830	41	41	for	for	ADP
ejpam-5830	41	42	an	an	DET
ejpam-5830	41	43	abelian	abelian	ADJ
ejpam-5830	41	44	group	group	NOUN
ejpam-5830	41	45	γ	γ	PROPN
ejpam-5830	41	46	,	,	PUNCT
ejpam-5830	41	47	equation	equation	NOUN
ejpam-5830	41	48	(	(	PUNCT
ejpam-5830	41	49	2	2	X
ejpam-5830	41	50	)	)	PUNCT
ejpam-5830	41	51	is	be	AUX
ejpam-5830	41	52	equivalent	equivalent	ADJ
ejpam-5830	41	53	to	to	ADP
ejpam-5830	41	54	α	α	PRON
ejpam-5830	41	55	(	(	PUNCT
ejpam-5830	41	56	g	g	PROPN
ejpam-5830	41	57	,	,	PUNCT
ejpam-5830	41	58	x)−	x)−	PROPN
ejpam-5830	41	59	β	β	X
ejpam-5830	41	60	(	(	PUNCT
ejpam-5830	41	61	g	g	PROPN
ejpam-5830	41	62	,	,	PUNCT
ejpam-5830	41	63	x	x	NOUN
ejpam-5830	41	64	)	)	PUNCT
ejpam-5830	42	1	=	=	SYM
ejpam-5830	42	2	φ	φ	PROPN
ejpam-5830	42	3	(	(	PUNCT
ejpam-5830	42	4	t	t	PROPN
ejpam-5830	42	5	(	(	PUNCT
ejpam-5830	42	6	g)x)−	g)x)−	PROPN
ejpam-5830	42	7	φ(x	φ(x	PROPN
ejpam-5830	42	8	)	)	PUNCT
ejpam-5830	42	9	.	.	PUNCT
ejpam-5830	43	1	the	the	DET
ejpam-5830	43	2	study	study	NOUN
ejpam-5830	43	3	of	of	ADP
ejpam-5830	43	4	cocycle	cocycle	PROPN
ejpam-5830	43	5	cohomology	cohomology	NOUN
ejpam-5830	43	6	has	have	AUX
ejpam-5830	43	7	proven	prove	VERB
ejpam-5830	43	8	advantageous	advantageous	ADJ
ejpam-5830	43	9	when	when	SCONJ
ejpam-5830	43	10	considering	consider	VERB
ejpam-5830	43	11	groups	group	NOUN
ejpam-5830	43	12	with	with	ADP
ejpam-5830	43	13	invariant	invariant	ADJ
ejpam-5830	43	14	metrics	metric	NOUN
ejpam-5830	43	15	,	,	PUNCT
ejpam-5830	43	16	the	the	DET
ejpam-5830	43	17	main	main	ADJ
ejpam-5830	43	18	examples	example	NOUN
ejpam-5830	43	19	being	be	AUX
ejpam-5830	43	20	lie	lie	NOUN
ejpam-5830	43	21	groups	group	NOUN
ejpam-5830	43	22	.	.	PUNCT
ejpam-5830	44	1	let	let	VERB
ejpam-5830	44	2	us	we	PRON
ejpam-5830	44	3	now	now	ADV
ejpam-5830	44	4	briefly	briefly	ADV
ejpam-5830	44	5	recall	recall	VERB
ejpam-5830	44	6	some	some	DET
ejpam-5830	44	7	basic	basic	ADJ
ejpam-5830	44	8	definitions	definition	NOUN
ejpam-5830	44	9	from	from	ADP
ejpam-5830	44	10	the	the	DET
ejpam-5830	44	11	theory	theory	NOUN
ejpam-5830	44	12	of	of	ADP
ejpam-5830	44	13	lie	lie	NOUN
ejpam-5830	44	14	groups	group	NOUN
ejpam-5830	44	15	.	.	PUNCT
ejpam-5830	45	1	a	a	DET
ejpam-5830	45	2	lie	lie	NOUN
ejpam-5830	45	3	group	group	NOUN
ejpam-5830	45	4	γ	γ	PROPN
ejpam-5830	45	5	is	be	AUX
ejpam-5830	45	6	a	a	DET
ejpam-5830	45	7	differentiable	differentiable	ADJ
ejpam-5830	45	8	manifold	manifold	NOUN
ejpam-5830	45	9	with	with	ADP
ejpam-5830	45	10	a	a	DET
ejpam-5830	45	11	group	group	NOUN
ejpam-5830	45	12	structure	structure	NOUN
ejpam-5830	45	13	such	such	ADJ
ejpam-5830	45	14	that	that	SCONJ
ejpam-5830	45	15	,	,	PUNCT
ejpam-5830	45	16	for	for	ADP
ejpam-5830	45	17	every	every	DET
ejpam-5830	45	18	g0	g0	PROPN
ejpam-5830	45	19	∈	∈	PROPN
ejpam-5830	45	20	γ	γ	PROPN
ejpam-5830	45	21	,	,	PUNCT
ejpam-5830	45	22	the	the	DET
ejpam-5830	45	23	transformations	transformation	NOUN
ejpam-5830	45	24	lg0	lg0	NOUN
ejpam-5830	45	25	:	:	PUNCT
ejpam-5830	45	26	γ	γ	X
ejpam-5830	45	27	→	→	SYM
ejpam-5830	45	28	γ	γ	NOUN
ejpam-5830	45	29	and	and	CCONJ
ejpam-5830	45	30	rg0	rg0	NOUN
ejpam-5830	45	31	:	:	PUNCT
ejpam-5830	45	32	γ	γ	X
ejpam-5830	45	33	→	→	SYM
ejpam-5830	45	34	γ	γ	PROPN
ejpam-5830	45	35	,	,	PUNCT
ejpam-5830	45	36	defined	define	VERB
ejpam-5830	45	37	by	by	ADP
ejpam-5830	45	38	lg0(g	lg0(g	NOUN
ejpam-5830	45	39	)	)	PUNCT
ejpam-5830	45	40	=	=	SYM
ejpam-5830	45	41	g0	g0	NOUN
ejpam-5830	45	42	+	+	CCONJ
ejpam-5830	45	43	g	g	PROPN
ejpam-5830	45	44	and	and	CCONJ
ejpam-5830	45	45	rg0(g	rg0(g	PROPN
ejpam-5830	45	46	)	)	PUNCT
ejpam-5830	46	1	=	=	SYM
ejpam-5830	46	2	g	g	PROPN
ejpam-5830	46	3	+	+	CCONJ
ejpam-5830	46	4	g0	g0	PROPN
ejpam-5830	46	5	,	,	PUNCT
ejpam-5830	46	6	called	call	VERB
ejpam-5830	46	7	left	left	ADJ
ejpam-5830	46	8	and	and	CCONJ
ejpam-5830	46	9	right	right	ADJ
ejpam-5830	46	10	translations	translation	NOUN
ejpam-5830	46	11	,	,	PUNCT
ejpam-5830	46	12	respectively	respectively	ADV
ejpam-5830	46	13	,	,	PUNCT
ejpam-5830	46	14	are	be	AUX
ejpam-5830	46	15	differentiable	differentiable	ADJ
ejpam-5830	46	16	,	,	PUNCT
ejpam-5830	46	17	as	as	SCONJ
ejpam-5830	46	18	is	be	AUX
ejpam-5830	46	19	the	the	DET
ejpam-5830	46	20	map	map	NOUN
ejpam-5830	46	21	g	g	PROPN
ejpam-5830	46	22	7→	7→	NUM
ejpam-5830	46	23	−g	−g	NOUN
ejpam-5830	46	24	.	.	PUNCT
ejpam-5830	47	1	the	the	DET
ejpam-5830	47	2	left	left	ADJ
ejpam-5830	47	3	and	and	CCONJ
ejpam-5830	47	4	right	right	ADJ
ejpam-5830	47	5	translations	translation	NOUN
ejpam-5830	47	6	naturally	naturally	ADV
ejpam-5830	47	7	induce	induce	VERB
ejpam-5830	47	8	,	,	PUNCT
ejpam-5830	47	9	at	at	ADP
ejpam-5830	47	10	each	each	DET
ejpam-5830	47	11	point	point	NOUN
ejpam-5830	47	12	g	g	PROPN
ejpam-5830	47	13	∈	∈	PROPN
ejpam-5830	47	14	γ	γ	X
ejpam-5830	47	15	,	,	PUNCT
ejpam-5830	47	16	linear	linear	ADJ
ejpam-5830	47	17	transformations	transformation	NOUN
ejpam-5830	47	18	dg0l(g	dg0l(g	NOUN
ejpam-5830	47	19	)	)	PUNCT
ejpam-5830	47	20	:	:	PUNCT
ejpam-5830	47	21	tgγ	tgγ	NOUN
ejpam-5830	47	22	→	→	PUNCT
ejpam-5830	47	23	tg0+gγ	tg0+gγ	NOUN
ejpam-5830	47	24	and	and	CCONJ
ejpam-5830	47	25	dg0r(g	dg0r(g	PROPN
ejpam-5830	47	26	)	)	PUNCT
ejpam-5830	47	27	:	:	PUNCT
ejpam-5830	47	28	tgγ	tgγ	NOUN
ejpam-5830	47	29	→	→	PUNCT
ejpam-5830	47	30	tg+g0γ	tg+g0γ	PROPN
ejpam-5830	47	31	on	on	ADP
ejpam-5830	47	32	tangent	tangent	NOUN
ejpam-5830	47	33	spaces	space	NOUN
ejpam-5830	47	34	.	.	PUNCT
ejpam-5830	48	1	a	a	DET
ejpam-5830	48	2	vector	vector	NOUN
ejpam-5830	48	3	field	field	NOUN
ejpam-5830	48	4	x	x	PUNCT
ejpam-5830	48	5	on	on	ADP
ejpam-5830	48	6	γ	γ	PROPN
ejpam-5830	48	7	is	be	AUX
ejpam-5830	48	8	said	say	VERB
ejpam-5830	48	9	to	to	PART
ejpam-5830	48	10	be	be	AUX
ejpam-5830	48	11	left	leave	VERB
ejpam-5830	48	12	-	-	PUNCT
ejpam-5830	48	13	invariant	invariant	ADJ
ejpam-5830	48	14	if	if	SCONJ
ejpam-5830	48	15	dg0l(g)x(g	dg0l(g)x(g	NOUN
ejpam-5830	48	16	)	)	PUNCT
ejpam-5830	48	17	=	=	PUNCT
ejpam-5830	48	18	x(g0	x(g0	NOUN
ejpam-5830	49	1	+	+	CCONJ
ejpam-5830	49	2	g	g	NOUN
ejpam-5830	49	3	)	)	PUNCT
ejpam-5830	49	4	,	,	PUNCT
ejpam-5830	49	5	and	and	CCONJ
ejpam-5830	49	6	right	right	ADV
ejpam-5830	49	7	-	-	PUNCT
ejpam-5830	49	8	invariant	invariant	ADJ
ejpam-5830	49	9	if	if	SCONJ
ejpam-5830	49	10	dg0r(g)x(g	dg0r(g)x(g	NOUN
ejpam-5830	49	11	)	)	PUNCT
ejpam-5830	49	12	=	=	SYM
ejpam-5830	50	1	x(g	x(g	PROPN
ejpam-5830	50	2	+	+	CCONJ
ejpam-5830	50	3	g0	g0	NOUN
ejpam-5830	50	4	)	)	PUNCT
ejpam-5830	50	5	.	.	PUNCT
ejpam-5830	51	1	the	the	DET
ejpam-5830	51	2	vector	vector	NOUN
ejpam-5830	51	3	space	space	NOUN
ejpam-5830	51	4	g	g	NOUN
ejpam-5830	51	5	of	of	ADP
ejpam-5830	51	6	left	left	ADJ
ejpam-5830	51	7	-	-	PUNCT
ejpam-5830	51	8	invariant	invariant	ADJ
ejpam-5830	51	9	vector	vector	NOUN
ejpam-5830	51	10	fields	field	NOUN
ejpam-5830	51	11	on	on	ADP
ejpam-5830	51	12	γ	γ	NOUN
ejpam-5830	51	13	,	,	PUNCT
ejpam-5830	51	14	equipped	equip	VERB
ejpam-5830	51	15	with	with	ADP
ejpam-5830	51	16	a	a	DET
ejpam-5830	51	17	bilinear	bilinear	NOUN
ejpam-5830	51	18	,	,	PUNCT
ejpam-5830	51	19	anti	anti	ADJ
ejpam-5830	51	20	-	-	ADJ
ejpam-5830	51	21	symmetric	symmetric	ADJ
ejpam-5830	51	22	operation	operation	NOUN
ejpam-5830	51	23	[	[	X
ejpam-5830	51	24	·	·	PUNCT
ejpam-5830	51	25	,	,	PUNCT
ejpam-5830	51	26	·	·	PUNCT
ejpam-5830	51	27	]	]	X
ejpam-5830	51	28	:	:	PUNCT
ejpam-5830	51	29	g	g	PROPN
ejpam-5830	51	30	×g	×g	NOUN
ejpam-5830	51	31	→	→	PUNCT
ejpam-5830	51	32	g	g	NOUN
ejpam-5830	51	33	satisfying	satisfy	VERB
ejpam-5830	51	34	[	[	X
ejpam-5830	51	35	x	x	X
ejpam-5830	51	36	,	,	PUNCT
ejpam-5830	51	37	[	[	X
ejpam-5830	51	38	y	y	NOUN
ejpam-5830	51	39	,	,	PUNCT
ejpam-5830	51	40	z	z	X
ejpam-5830	51	41	]	]	X
ejpam-5830	51	42	]	]	PUNCT
ejpam-5830	52	1	+	+	CCONJ
ejpam-5830	52	2	[	[	X
ejpam-5830	52	3	y	y	X
ejpam-5830	52	4	,	,	PUNCT
ejpam-5830	52	5	[	[	X
ejpam-5830	52	6	z	z	X
ejpam-5830	52	7	,	,	PUNCT
ejpam-5830	52	8	x	x	X
ejpam-5830	52	9	]	]	X
ejpam-5830	52	10	]	]	PUNCT
ejpam-5830	53	1	+	+	CCONJ
ejpam-5830	54	1	[	[	X
ejpam-5830	54	2	z	z	X
ejpam-5830	54	3	,	,	PUNCT
ejpam-5830	54	4	[	[	X
ejpam-5830	54	5	x	x	X
ejpam-5830	54	6	,	,	PUNCT
ejpam-5830	54	7	y	y	PROPN
ejpam-5830	54	8	]	]	X
ejpam-5830	54	9	]	]	X
ejpam-5830	54	10	=	=	SYM
ejpam-5830	54	11	0	0	NUM
ejpam-5830	54	12	is	be	AUX
ejpam-5830	54	13	called	call	VERB
ejpam-5830	54	14	the	the	DET
ejpam-5830	54	15	lie	lie	NOUN
ejpam-5830	54	16	algebra	algebra	NOUN
ejpam-5830	54	17	of	of	ADP
ejpam-5830	54	18	γ	γ	PROPN
ejpam-5830	54	19	.	.	PUNCT
ejpam-5830	55	1	a	a	DET
ejpam-5830	55	2	riemannian	riemannian	ADJ
ejpam-5830	55	3	metric	metric	NOUN
ejpam-5830	55	4	on	on	ADP
ejpam-5830	55	5	γ	γ	X
ejpam-5830	55	6	is	be	AUX
ejpam-5830	55	7	called	call	VERB
ejpam-5830	55	8	left	left	ADJ
ejpam-5830	55	9	-	-	PUNCT
ejpam-5830	55	10	invariant	invariant	ADJ
ejpam-5830	55	11	if	if	SCONJ
ejpam-5830	55	12	lg0	lg0	NOUN
ejpam-5830	55	13	is	be	AUX
ejpam-5830	55	14	an	an	DET
ejpam-5830	55	15	isometry	isometry	NOUN
ejpam-5830	55	16	for	for	ADP
ejpam-5830	55	17	all	all	DET
ejpam-5830	55	18	g0	g0	PROPN
ejpam-5830	55	19	∈	∈	PROPN
ejpam-5830	55	20	γ	γ	PROPN
ejpam-5830	55	21	,	,	PUNCT
ejpam-5830	55	22	that	that	ADV
ejpam-5830	55	23	is	is	ADV
ejpam-5830	55	24	,	,	PUNCT
ejpam-5830	55	25	⟨g0	⟨g0	ADJ
ejpam-5830	55	26	+	+	CCONJ
ejpam-5830	55	27	g1	g1	NOUN
ejpam-5830	55	28	,	,	PUNCT
ejpam-5830	55	29	g0	g0	NOUN
ejpam-5830	55	30	+	+	CCONJ
ejpam-5830	55	31	g2⟩	g2⟩	PROPN
ejpam-5830	56	1	=	=	SYM
ejpam-5830	56	2	⟨g1	⟨g1	PROPN
ejpam-5830	56	3	,	,	PUNCT
ejpam-5830	56	4	g2⟩.	g2⟩.	VERB
ejpam-5830	56	5	a	a	DET
ejpam-5830	56	6	right	right	ADJ
ejpam-5830	56	7	-	-	PUNCT
ejpam-5830	56	8	invariant	invariant	ADJ
ejpam-5830	56	9	metric	metric	NOUN
ejpam-5830	56	10	can	can	AUX
ejpam-5830	56	11	be	be	AUX
ejpam-5830	56	12	defined	define	VERB
ejpam-5830	56	13	similarly	similarly	ADV
ejpam-5830	56	14	by	by	ADP
ejpam-5830	56	15	replacing	replace	VERB
ejpam-5830	56	16	lg0	lg0	NOUN
ejpam-5830	56	17	with	with	ADP
ejpam-5830	56	18	rg0	rg0	NOUN
ejpam-5830	56	19	.	.	PUNCT
ejpam-5830	57	1	in	in	ADP
ejpam-5830	57	2	any	any	DET
ejpam-5830	57	3	lie	lie	NOUN
ejpam-5830	57	4	group	group	NOUN
ejpam-5830	57	5	γ	γ	PROPN
ejpam-5830	57	6	,	,	PUNCT
ejpam-5830	57	7	the	the	DET
ejpam-5830	57	8	choice	choice	NOUN
ejpam-5830	57	9	of	of	ADP
ejpam-5830	57	10	a	a	DET
ejpam-5830	57	11	symmetric	symmetric	ADJ
ejpam-5830	57	12	,	,	PUNCT
ejpam-5830	57	13	non	non	ADJ
ejpam-5830	57	14	-	-	ADJ
ejpam-5830	57	15	degenerate	degenerate	ADJ
ejpam-5830	57	16	bilinear	bilinear	NOUN
ejpam-5830	57	17	form	form	NOUN
ejpam-5830	57	18	⟨	⟨	VERB
ejpam-5830	57	19	·	·	PUNCT
ejpam-5830	57	20	,	,	PUNCT
ejpam-5830	57	21	·	·	PUNCT
ejpam-5830	57	22	⟩	⟩	NOUN
ejpam-5830	57	23	on	on	ADP
ejpam-5830	57	24	the	the	DET
ejpam-5830	57	25	tangent	tangent	ADJ
ejpam-5830	57	26	space	space	NOUN
ejpam-5830	57	27	at	at	ADP
ejpam-5830	57	28	the	the	DET
ejpam-5830	57	29	identity	identity	NOUN
ejpam-5830	57	30	,	,	PUNCT
ejpam-5830	57	31	teγ	teγ	CCONJ
ejpam-5830	57	32	,	,	PUNCT
ejpam-5830	57	33	defines	define	VERB
ejpam-5830	57	34	a	a	DET
ejpam-5830	57	35	left	left	ADJ
ejpam-5830	57	36	-	-	PUNCT
ejpam-5830	57	37	invariant	invariant	ADJ
ejpam-5830	57	38	riemannian	riemannian	ADJ
ejpam-5830	57	39	metric	metric	NOUN
ejpam-5830	57	40	on	on	ADP
ejpam-5830	57	41	γ	γ	NOUN
ejpam-5830	57	42	via	via	ADP
ejpam-5830	57	43	⟨u	⟨u	NOUN
ejpam-5830	57	44	,	,	PUNCT
ejpam-5830	57	45	v	v	ADP
ejpam-5830	57	46	⟩g0	⟩g0	NOUN
ejpam-5830	57	47	=	=	SYM
ejpam-5830	58	1	⟨d−g0l(g0)u	⟨d−g0l(g0)u	PROPN
ejpam-5830	58	2	,	,	PUNCT
ejpam-5830	58	3	d−g0l(g0)v	d−g0l(g0)v	VERB
ejpam-5830	58	4	⟩	⟩	PROPN
ejpam-5830	58	5	,	,	PUNCT
ejpam-5830	58	6	r.	r.	PROPN
ejpam-5830	58	7	d.	d.	PROPN
ejpam-5830	58	8	laureano	laureano	PROPN
ejpam-5830	58	9	/	/	SYM
ejpam-5830	58	10	eur	eur	PROPN
ejpam-5830	58	11	.	.	PUNCT
ejpam-5830	59	1	j.	j.	PROPN
ejpam-5830	59	2	pure	pure	PROPN
ejpam-5830	59	3	appl	appl	PROPN
ejpam-5830	59	4	.	.	PROPN
ejpam-5830	59	5	math	math	PROPN
ejpam-5830	59	6	,	,	PUNCT
ejpam-5830	59	7	18	18	NUM
ejpam-5830	59	8	(	(	PUNCT
ejpam-5830	59	9	2	2	NUM
ejpam-5830	59	10	)	)	PUNCT
ejpam-5830	59	11	(	(	PUNCT
ejpam-5830	59	12	2025	2025	NUM
ejpam-5830	59	13	)	)	PUNCT
ejpam-5830	59	14	,	,	PUNCT
ejpam-5830	59	15	5830	5830	NUM
ejpam-5830	59	16	4	4	NUM
ejpam-5830	59	17	of	of	ADP
ejpam-5830	59	18	11	11	NUM
ejpam-5830	59	19	for	for	ADP
ejpam-5830	59	20	all	all	DET
ejpam-5830	59	21	u	u	NOUN
ejpam-5830	59	22	,	,	PUNCT
ejpam-5830	59	23	v	v	NOUN
ejpam-5830	59	24	∈	∈	PROPN
ejpam-5830	59	25	tg0γ	tg0γ	NOUN
ejpam-5830	59	26	.	.	PUNCT
ejpam-5830	60	1	if	if	SCONJ
ejpam-5830	60	2	the	the	DET
ejpam-5830	60	3	metric	metric	NOUN
ejpam-5830	60	4	is	be	AUX
ejpam-5830	60	5	also	also	ADV
ejpam-5830	60	6	right	right	ADV
ejpam-5830	60	7	-	-	PUNCT
ejpam-5830	60	8	invariant	invariant	ADJ
ejpam-5830	60	9	,	,	PUNCT
ejpam-5830	60	10	it	it	PRON
ejpam-5830	60	11	is	be	AUX
ejpam-5830	60	12	called	call	VERB
ejpam-5830	60	13	bi	bi	ADJ
ejpam-5830	60	14	-	-	ADJ
ejpam-5830	60	15	invariant	invariant	ADJ
ejpam-5830	60	16	.	.	PUNCT
ejpam-5830	61	1	given	give	VERB
ejpam-5830	61	2	g	g	PROPN
ejpam-5830	61	3	∈	∈	PROPN
ejpam-5830	61	4	γ	γ	NOUN
ejpam-5830	61	5	,	,	PUNCT
ejpam-5830	61	6	consider	consider	VERB
ejpam-5830	61	7	the	the	DET
ejpam-5830	61	8	conjugation	conjugation	NOUN
ejpam-5830	61	9	map	map	NOUN
ejpam-5830	61	10	defined	define	VERB
ejpam-5830	61	11	by	by	ADP
ejpam-5830	61	12	a	a	DET
ejpam-5830	61	13	7→	7→	NUM
ejpam-5830	61	14	−g	−g	NOUN
ejpam-5830	61	15	+	+	CCONJ
ejpam-5830	61	16	a	a	DET
ejpam-5830	61	17	+	+	NOUN
ejpam-5830	61	18	g	g	NOUN
ejpam-5830	61	19	for	for	ADP
ejpam-5830	61	20	all	all	DET
ejpam-5830	61	21	a	a	DET
ejpam-5830	61	22	∈	∈	PROPN
ejpam-5830	61	23	γ	γ	X
ejpam-5830	61	24	,	,	PUNCT
ejpam-5830	61	25	and	and	CCONJ
ejpam-5830	61	26	the	the	DET
ejpam-5830	61	27	transformation	transformation	NOUN
ejpam-5830	61	28	ad	ad	NOUN
ejpam-5830	61	29	:	:	PUNCT
ejpam-5830	61	30	γ	γ	X
ejpam-5830	61	31	→	→	SYM
ejpam-5830	61	32	aut(g	aut(g	PROPN
ejpam-5830	61	33	)	)	PUNCT
ejpam-5830	61	34	given	give	VERB
ejpam-5830	61	35	by	by	ADP
ejpam-5830	61	36	the	the	DET
ejpam-5830	61	37	derivative	derivative	NOUN
ejpam-5830	61	38	of	of	ADP
ejpam-5830	61	39	conjugation	conjugation	NOUN
ejpam-5830	61	40	by	by	ADP
ejpam-5830	61	41	g	g	PROPN
ejpam-5830	61	42	,	,	PUNCT
ejpam-5830	61	43	defined	define	VERB
ejpam-5830	61	44	as	as	ADP
ejpam-5830	61	45	ad(g)x	ad(g)x	PROPN
ejpam-5830	61	46	=	=	SYM
ejpam-5830	61	47	(	(	PUNCT
ejpam-5830	61	48	d−gr(g	d−gr(g	ADJ
ejpam-5830	61	49	)	)	PUNCT
ejpam-5830	61	50	◦	◦	NOUN
ejpam-5830	61	51	dgl(e))x	dgl(e))x	PROPN
ejpam-5830	61	52	,	,	PUNCT
ejpam-5830	61	53	for	for	ADP
ejpam-5830	61	54	x	x	PROPN
ejpam-5830	61	55	∈	∈	PROPN
ejpam-5830	61	56	γ	γ	X
ejpam-5830	61	57	.	.	PUNCT
ejpam-5830	62	1	the	the	DET
ejpam-5830	62	2	study	study	NOUN
ejpam-5830	62	3	of	of	ADP
ejpam-5830	62	4	cohomology	cohomology	NOUN
ejpam-5830	62	5	of	of	ADP
ejpam-5830	62	6	cocycles	cocycle	NOUN
ejpam-5830	62	7	over	over	ADP
ejpam-5830	62	8	anosov	anosov	NOUN
ejpam-5830	62	9	diffeomorphisms	diffeomorphism	NOUN
ejpam-5830	62	10	and	and	CCONJ
ejpam-5830	62	11	flows	flow	NOUN
ejpam-5830	62	12	(	(	PUNCT
ejpam-5830	62	13	that	that	PRON
ejpam-5830	62	14	is	be	AUX
ejpam-5830	62	15	,	,	PUNCT
ejpam-5830	62	16	hyperbolic	hyperbolic	ADJ
ejpam-5830	62	17	actions	action	NOUN
ejpam-5830	62	18	of	of	ADP
ejpam-5830	62	19	g	g	PROPN
ejpam-5830	62	20	=	=	PROPN
ejpam-5830	62	21	z	z	PROPN
ejpam-5830	62	22	and	and	CCONJ
ejpam-5830	62	23	g	g	NOUN
ejpam-5830	62	24	=	=	SYM
ejpam-5830	62	25	r	r	NOUN
ejpam-5830	62	26	,	,	PUNCT
ejpam-5830	62	27	respectively	respectively	ADV
ejpam-5830	62	28	)	)	PUNCT
ejpam-5830	62	29	was	be	AUX
ejpam-5830	62	30	initiated	initiate	VERB
ejpam-5830	62	31	by	by	ADP
ejpam-5830	62	32	livschitz	livschitz	PROPN
ejpam-5830	62	33	.	.	PUNCT
ejpam-5830	63	1	in	in	ADP
ejpam-5830	63	2	[	[	X
ejpam-5830	63	3	1	1	NUM
ejpam-5830	63	4	]	]	PUNCT
ejpam-5830	63	5	,	,	PUNCT
ejpam-5830	63	6	as	as	SCONJ
ejpam-5830	63	7	discussed	discuss	VERB
ejpam-5830	63	8	in	in	ADP
ejpam-5830	63	9	[	[	X
ejpam-5830	63	10	4	4	NUM
ejpam-5830	63	11	]	]	PUNCT
ejpam-5830	63	12	,	,	PUNCT
ejpam-5830	63	13	it	it	PRON
ejpam-5830	63	14	was	be	AUX
ejpam-5830	63	15	proven	prove	VERB
ejpam-5830	63	16	that	that	SCONJ
ejpam-5830	63	17	a	a	DET
ejpam-5830	63	18	hölder	hölder	NOUN
ejpam-5830	63	19	cocycle	cocycle	NOUN
ejpam-5830	63	20	with	with	ADP
ejpam-5830	63	21	values	value	NOUN
ejpam-5830	63	22	in	in	ADP
ejpam-5830	63	23	γ	γ	X
ejpam-5830	63	24	=	=	NOUN
ejpam-5830	63	25	r	r	NOUN
ejpam-5830	63	26	satisfying	satisfy	VERB
ejpam-5830	63	27	the	the	DET
ejpam-5830	63	28	conditions	condition	NOUN
ejpam-5830	63	29	in	in	ADP
ejpam-5830	63	30	(	(	PUNCT
ejpam-5830	63	31	4	4	NUM
ejpam-5830	63	32	)	)	PUNCT
ejpam-5830	63	33	is	be	AUX
ejpam-5830	63	34	cohomologous	cohomologous	ADJ
ejpam-5830	63	35	to	to	ADP
ejpam-5830	63	36	the	the	DET
ejpam-5830	63	37	trivial	trivial	ADJ
ejpam-5830	63	38	cocycle	cocycle	NOUN
ejpam-5830	63	39	via	via	ADP
ejpam-5830	63	40	a	a	DET
ejpam-5830	63	41	hölder	hölder	NOUN
ejpam-5830	63	42	solution	solution	NOUN
ejpam-5830	63	43	φ	φ	X
ejpam-5830	63	44	.	.	PUNCT
ejpam-5830	64	1	the	the	DET
ejpam-5830	64	2	same	same	ADJ
ejpam-5830	64	3	result	result	NOUN
ejpam-5830	64	4	was	be	AUX
ejpam-5830	64	5	extended	extend	VERB
ejpam-5830	64	6	to	to	ADP
ejpam-5830	64	7	γ	γ	PROPN
ejpam-5830	64	8	as	as	ADP
ejpam-5830	64	9	a	a	DET
ejpam-5830	64	10	connected	connected	ADJ
ejpam-5830	64	11	lie	lie	NOUN
ejpam-5830	64	12	group	group	NOUN
ejpam-5830	64	13	admitting	admit	VERB
ejpam-5830	64	14	a	a	DET
ejpam-5830	64	15	bi	bi	ADJ
ejpam-5830	64	16	-	-	ADJ
ejpam-5830	64	17	invariant	invariant	ADJ
ejpam-5830	64	18	metric	metric	NOUN
ejpam-5830	64	19	.	.	PUNCT
ejpam-5830	65	1	the	the	DET
ejpam-5830	65	2	search	search	NOUN
ejpam-5830	65	3	for	for	ADP
ejpam-5830	65	4	hölder	hölder	NOUN
ejpam-5830	65	5	solutions	solution	NOUN
ejpam-5830	65	6	to	to	ADP
ejpam-5830	65	7	equation	equation	NOUN
ejpam-5830	65	8	(	(	PUNCT
ejpam-5830	65	9	2	2	X
ejpam-5830	65	10	)	)	PUNCT
ejpam-5830	65	11	is	be	AUX
ejpam-5830	65	12	discussed	discuss	VERB
ejpam-5830	65	13	in	in	ADP
ejpam-5830	65	14	[	[	X
ejpam-5830	65	15	11	11	NUM
ejpam-5830	65	16	]	]	PUNCT
ejpam-5830	65	17	and	and	CCONJ
ejpam-5830	65	18	[	[	X
ejpam-5830	65	19	12	12	NUM
ejpam-5830	65	20	]	]	PUNCT
ejpam-5830	65	21	.	.	PUNCT
ejpam-5830	66	1	now	now	ADV
ejpam-5830	66	2	,	,	PUNCT
ejpam-5830	66	3	let	let	VERB
ejpam-5830	66	4	us	we	PRON
ejpam-5830	66	5	consider	consider	VERB
ejpam-5830	66	6	the	the	DET
ejpam-5830	66	7	measurable	measurable	ADJ
ejpam-5830	66	8	case	case	NOUN
ejpam-5830	66	9	.	.	PUNCT
ejpam-5830	67	1	let	let	VERB
ejpam-5830	67	2	t	t	NOUN
ejpam-5830	67	3	be	be	AUX
ejpam-5830	67	4	an	an	DET
ejpam-5830	67	5	anosov	anosov	NOUN
ejpam-5830	67	6	diffeomorphism	diffeomorphism	NOUN
ejpam-5830	67	7	and	and	CCONJ
ejpam-5830	67	8	µ	µ	PRON
ejpam-5830	67	9	a	a	DET
ejpam-5830	67	10	t	t	NOUN
ejpam-5830	67	11	invariant	invariant	ADJ
ejpam-5830	67	12	measure	measure	NOUN
ejpam-5830	67	13	equivalent	equivalent	ADJ
ejpam-5830	67	14	to	to	ADP
ejpam-5830	67	15	the	the	DET
ejpam-5830	67	16	lebesgue	lebesgue	ADJ
ejpam-5830	67	17	measure	measure	NOUN
ejpam-5830	67	18	.	.	PUNCT
ejpam-5830	68	1	livschitz	livschitz	PROPN
ejpam-5830	68	2	showed	show	VERB
ejpam-5830	68	3	in	in	ADP
ejpam-5830	68	4	[	[	X
ejpam-5830	68	5	2	2	X
ejpam-5830	68	6	]	]	PUNCT
ejpam-5830	68	7	that	that	SCONJ
ejpam-5830	68	8	,	,	PUNCT
ejpam-5830	68	9	for	for	ADP
ejpam-5830	68	10	any	any	DET
ejpam-5830	68	11	hölder	hölder	NOUN
ejpam-5830	68	12	cocycle	cocycle	NOUN
ejpam-5830	68	13	α	α	PROPN
ejpam-5830	68	14	with	with	ADP
ejpam-5830	68	15	real	real	ADJ
ejpam-5830	68	16	values	value	NOUN
ejpam-5830	68	17	,	,	PUNCT
ejpam-5830	68	18	a	a	DET
ejpam-5830	68	19	measurable	measurable	ADJ
ejpam-5830	68	20	function	function	NOUN
ejpam-5830	68	21	φ	φ	NOUN
ejpam-5830	68	22	:	:	PUNCT
ejpam-5830	68	23	m	m	VERB
ejpam-5830	68	24	→	→	SYM
ejpam-5830	68	25	r	r	NOUN
ejpam-5830	68	26	satisfying	satisfying	NOUN
ejpam-5830	68	27	(	(	PUNCT
ejpam-5830	68	28	3	3	NUM
ejpam-5830	68	29	)	)	PUNCT
ejpam-5830	68	30	almost	almost	ADV
ejpam-5830	68	31	everywhere	everywhere	ADV
ejpam-5830	68	32	is	be	AUX
ejpam-5830	68	33	almost	almost	ADV
ejpam-5830	68	34	everywhere	everywhere	ADV
ejpam-5830	68	35	equal	equal	ADJ
ejpam-5830	68	36	to	to	ADP
ejpam-5830	68	37	a	a	DET
ejpam-5830	68	38	hölder	hölder	NOUN
ejpam-5830	68	39	function	function	NOUN
ejpam-5830	68	40	φ̃	φ̃	PROPN
ejpam-5830	68	41	,	,	PUNCT
ejpam-5830	68	42	for	for	ADP
ejpam-5830	68	43	which	which	PRON
ejpam-5830	68	44	α	α	X
ejpam-5830	68	45	(	(	PUNCT
ejpam-5830	68	46	g	g	PROPN
ejpam-5830	68	47	,	,	PUNCT
ejpam-5830	68	48	x	x	NOUN
ejpam-5830	68	49	)	)	PUNCT
ejpam-5830	68	50	=	=	SYM
ejpam-5830	69	1	φ̃	φ̃	PROPN
ejpam-5830	69	2	(	(	PUNCT
ejpam-5830	69	3	t	t	PROPN
ejpam-5830	69	4	(	(	PUNCT
ejpam-5830	69	5	g)x)−	g)x)−	PROPN
ejpam-5830	69	6	φ̃(x	φ̃(x	PROPN
ejpam-5830	69	7	)	)	PUNCT
ejpam-5830	69	8	everywhere	everywhere	ADV
ejpam-5830	69	9	.	.	PUNCT
ejpam-5830	70	1	the	the	DET
ejpam-5830	70	2	same	same	ADJ
ejpam-5830	70	3	applies	apply	VERB
ejpam-5830	70	4	to	to	ADP
ejpam-5830	70	5	anosov	anosov	PROPN
ejpam-5830	70	6	flows	flow	NOUN
ejpam-5830	70	7	.	.	PUNCT
ejpam-5830	71	1	pollicott	pollicott	ADJ
ejpam-5830	71	2	and	and	CCONJ
ejpam-5830	71	3	walkden	walkden	ADJ
ejpam-5830	71	4	state	state	NOUN
ejpam-5830	71	5	in	in	ADP
ejpam-5830	71	6	[	[	X
ejpam-5830	71	7	13	13	NUM
ejpam-5830	71	8	]	]	PUNCT
ejpam-5830	71	9	that	that	SCONJ
ejpam-5830	71	10	the	the	DET
ejpam-5830	71	11	proof	proof	NOUN
ejpam-5830	71	12	presented	present	VERB
ejpam-5830	71	13	by	by	ADP
ejpam-5830	71	14	livschitz	livschitz	PROPN
ejpam-5830	71	15	extends	extend	VERB
ejpam-5830	71	16	to	to	ADP
ejpam-5830	71	17	any	any	DET
ejpam-5830	71	18	connected	connected	ADJ
ejpam-5830	71	19	lie	lie	NOUN
ejpam-5830	71	20	group	group	NOUN
ejpam-5830	71	21	with	with	ADP
ejpam-5830	71	22	a	a	DET
ejpam-5830	71	23	bi	bi	ADJ
ejpam-5830	71	24	-	-	ADJ
ejpam-5830	71	25	invariant	invariant	ADJ
ejpam-5830	71	26	metric	metric	NOUN
ejpam-5830	71	27	.	.	PUNCT
ejpam-5830	72	1	an	an	DET
ejpam-5830	72	2	analogous	analogous	ADJ
ejpam-5830	72	3	result	result	NOUN
ejpam-5830	72	4	for	for	ADP
ejpam-5830	72	5	equation	equation	NOUN
ejpam-5830	72	6	(	(	PUNCT
ejpam-5830	72	7	2	2	NUM
ejpam-5830	72	8	)	)	PUNCT
ejpam-5830	72	9	for	for	ADP
ejpam-5830	72	10	compact	compact	ADJ
ejpam-5830	72	11	lie	lie	NOUN
ejpam-5830	72	12	groups	group	NOUN
ejpam-5830	72	13	was	be	AUX
ejpam-5830	72	14	proven	prove	VERB
ejpam-5830	72	15	by	by	ADP
ejpam-5830	72	16	parry	parry	PROPN
ejpam-5830	72	17	and	and	CCONJ
ejpam-5830	72	18	pollicott	pollicott	ADJ
ejpam-5830	72	19	in	in	ADP
ejpam-5830	72	20	[	[	X
ejpam-5830	72	21	14	14	NUM
ejpam-5830	72	22	]	]	PUNCT
ejpam-5830	72	23	.	.	PUNCT
ejpam-5830	73	1	we	we	PRON
ejpam-5830	73	2	now	now	ADV
ejpam-5830	73	3	describe	describe	VERB
ejpam-5830	73	4	recent	recent	ADJ
ejpam-5830	73	5	work	work	NOUN
ejpam-5830	73	6	by	by	ADP
ejpam-5830	73	7	pollicott	pollicott	ADJ
ejpam-5830	73	8	and	and	CCONJ
ejpam-5830	73	9	walkden	walkden	PROPN
ejpam-5830	73	10	,	,	PUNCT
ejpam-5830	73	11	which	which	PRON
ejpam-5830	73	12	considers	consider	VERB
ejpam-5830	73	13	lie	lie	NOUN
ejpam-5830	73	14	groups	group	NOUN
ejpam-5830	73	15	that	that	PRON
ejpam-5830	73	16	do	do	AUX
ejpam-5830	73	17	not	not	PART
ejpam-5830	73	18	necessarily	necessarily	ADV
ejpam-5830	73	19	have	have	VERB
ejpam-5830	73	20	a	a	DET
ejpam-5830	73	21	bi	bi	ADJ
ejpam-5830	73	22	-	-	ADJ
ejpam-5830	73	23	invariant	invariant	ADJ
ejpam-5830	73	24	metric	metric	NOUN
ejpam-5830	73	25	.	.	PUNCT
ejpam-5830	74	1	let	let	VERB
ejpam-5830	74	2	f	f	NOUN
ejpam-5830	74	3	:	:	PUNCT
ejpam-5830	74	4	m	m	AUX
ejpam-5830	74	5	→m	→m	PUNCT
ejpam-5830	74	6	be	be	AUX
ejpam-5830	74	7	a	a	DET
ejpam-5830	74	8	c1	c1	NOUN
ejpam-5830	74	9	diffeomorphism	diffeomorphism	NOUN
ejpam-5830	74	10	and	and	CCONJ
ejpam-5830	74	11	let	let	VERB
ejpam-5830	74	12	λ	λ	NOUN
ejpam-5830	74	13	be	be	AUX
ejpam-5830	74	14	a	a	DET
ejpam-5830	74	15	locally	locally	ADV
ejpam-5830	74	16	maximal	maximal	ADJ
ejpam-5830	74	17	hyperbolic	hyperbolic	ADJ
ejpam-5830	74	18	set	set	NOUN
ejpam-5830	74	19	for	for	ADP
ejpam-5830	74	20	f	f	PROPN
ejpam-5830	74	21	.	.	PUNCT
ejpam-5830	75	1	for	for	ADP
ejpam-5830	75	2	a	a	DET
ejpam-5830	75	3	continuous	continuous	ADJ
ejpam-5830	75	4	function	function	NOUN
ejpam-5830	75	5	g	g	NOUN
ejpam-5830	75	6	:	:	PUNCT
ejpam-5830	75	7	λ	λ	X
ejpam-5830	75	8	→	→	SYM
ejpam-5830	75	9	γ	γ	X
ejpam-5830	75	10	,	,	PUNCT
ejpam-5830	75	11	consider	consider	VERB
ejpam-5830	75	12	the	the	DET
ejpam-5830	75	13	supremum	supremum	ADJ
ejpam-5830	75	14	sup	sup	NOUN
ejpam-5830	75	15	{	{	PUNCT
ejpam-5830	75	16	hm(f	hm(f	NOUN
ejpam-5830	75	17	)	)	PUNCT
ejpam-5830	76	1	+	+	CCONJ
ejpam-5830	76	2	∫	∫	PROPN
ejpam-5830	76	3	λ	λ	X
ejpam-5830	76	4	g	g	PROPN
ejpam-5830	76	5	,	,	PUNCT
ejpam-5830	76	6	dm	dm	X
ejpam-5830	76	7	:	:	PUNCT
ejpam-5830	76	8	m	m	VERB
ejpam-5830	76	9	is	be	AUX
ejpam-5830	76	10	an	an	DET
ejpam-5830	76	11	f	f	PROPN
ejpam-5830	76	12	-invariant	-invariant	PROPN
ejpam-5830	76	13	probability	probability	NOUN
ejpam-5830	76	14	measure	measure	NOUN
ejpam-5830	76	15	}	}	PUNCT
ejpam-5830	76	16	,	,	PUNCT
ejpam-5830	76	17	where	where	SCONJ
ejpam-5830	76	18	hm(f	hm(f	NOUN
ejpam-5830	76	19	)	)	PUNCT
ejpam-5830	76	20	is	be	AUX
ejpam-5830	76	21	the	the	DET
ejpam-5830	76	22	entropy	entropy	NOUN
ejpam-5830	76	23	of	of	ADP
ejpam-5830	76	24	f	f	PROPN
ejpam-5830	76	25	relative	relative	ADJ
ejpam-5830	76	26	to	to	ADP
ejpam-5830	76	27	m.	m.	NOUN
ejpam-5830	76	28	if	if	SCONJ
ejpam-5830	76	29	g	g	PROPN
ejpam-5830	76	30	is	be	AUX
ejpam-5830	76	31	hölder	hölder	NOUN
ejpam-5830	76	32	,	,	PUNCT
ejpam-5830	76	33	then	then	ADV
ejpam-5830	76	34	this	this	DET
ejpam-5830	76	35	supremum	supremum	NOUN
ejpam-5830	76	36	is	be	AUX
ejpam-5830	76	37	attained	attain	VERB
ejpam-5830	76	38	by	by	ADP
ejpam-5830	76	39	some	some	DET
ejpam-5830	76	40	f	f	PROPN
ejpam-5830	76	41	-invariant	-invariant	ADJ
ejpam-5830	76	42	probability	probability	NOUN
ejpam-5830	76	43	measure	measure	NOUN
ejpam-5830	76	44	,	,	PUNCT
ejpam-5830	76	45	which	which	PRON
ejpam-5830	76	46	we	we	PRON
ejpam-5830	76	47	call	call	VERB
ejpam-5830	76	48	the	the	DET
ejpam-5830	76	49	equilibrium	equilibrium	NOUN
ejpam-5830	76	50	measure	measure	NOUN
ejpam-5830	76	51	of	of	ADP
ejpam-5830	76	52	g	g	PROPN
ejpam-5830	76	53	(	(	PUNCT
ejpam-5830	76	54	see	see	VERB
ejpam-5830	76	55	,	,	PUNCT
ejpam-5830	76	56	for	for	ADP
ejpam-5830	76	57	example	example	NOUN
ejpam-5830	76	58	,	,	PUNCT
ejpam-5830	76	59	[	[	X
ejpam-5830	76	60	5	5	NUM
ejpam-5830	76	61	]	]	NUM
ejpam-5830	76	62	)	)	PUNCT
ejpam-5830	76	63	.	.	PUNCT
ejpam-5830	77	1	the	the	DET
ejpam-5830	77	2	hyperbolicity	hyperbolicity	NOUN
ejpam-5830	77	3	of	of	ADP
ejpam-5830	77	4	f	f	PROPN
ejpam-5830	77	5	|λ	|λ	ADV
ejpam-5830	77	6	can	can	AUX
ejpam-5830	77	7	be	be	AUX
ejpam-5830	77	8	characterized	characterize	VERB
ejpam-5830	77	9	in	in	ADP
ejpam-5830	77	10	terms	term	NOUN
ejpam-5830	77	11	of	of	ADP
ejpam-5830	77	12	the	the	DET
ejpam-5830	77	13	mather	mather	ADJ
ejpam-5830	77	14	spectrum	spectrum	NOUN
ejpam-5830	77	15	of	of	ADP
ejpam-5830	77	16	f	f	PROPN
ejpam-5830	77	17	.	.	PUNCT
ejpam-5830	78	1	let	let	VERB
ejpam-5830	78	2	χ(λ	χ(λ	PROPN
ejpam-5830	78	3	)	)	PUNCT
ejpam-5830	78	4	denote	denote	VERB
ejpam-5830	78	5	the	the	DET
ejpam-5830	78	6	banach	banach	NOUN
ejpam-5830	78	7	space	space	NOUN
ejpam-5830	78	8	of	of	ADP
ejpam-5830	78	9	continuous	continuous	ADJ
ejpam-5830	78	10	vector	vector	NOUN
ejpam-5830	78	11	fields	field	NOUN
ejpam-5830	78	12	in	in	ADP
ejpam-5830	78	13	λ	λ	PROPN
ejpam-5830	78	14	.	.	PUNCT
ejpam-5830	79	1	define	define	VERB
ejpam-5830	79	2	the	the	DET
ejpam-5830	79	3	transformation	transformation	NOUN
ejpam-5830	79	4	f∗	f∗	NOUN
ejpam-5830	79	5	:	:	PUNCT
ejpam-5830	79	6	χ(λ	χ(λ	PROPN
ejpam-5830	79	7	)	)	PUNCT
ejpam-5830	79	8	→	→	SYM
ejpam-5830	79	9	χ(λ	χ(λ	PROPN
ejpam-5830	79	10	)	)	PUNCT
ejpam-5830	79	11	by	by	ADP
ejpam-5830	79	12	(	(	PUNCT
ejpam-5830	79	13	f∗v	f∗v	NUM
ejpam-5830	79	14	)	)	PUNCT
ejpam-5830	79	15	(	(	PUNCT
ejpam-5830	79	16	x	x	X
ejpam-5830	79	17	)	)	PUNCT
ejpam-5830	79	18	=	=	SYM
ejpam-5830	79	19	df(v(f−1x	df(v(f−1x	NOUN
ejpam-5830	79	20	)	)	PUNCT
ejpam-5830	79	21	)	)	PUNCT
ejpam-5830	79	22	.	.	PUNCT
ejpam-5830	80	1	the	the	DET
ejpam-5830	80	2	mather	mather	PROPN
ejpam-5830	80	3	spectrum	spectrum	NOUN
ejpam-5830	80	4	of	of	ADP
ejpam-5830	80	5	f	f	PROPN
ejpam-5830	80	6	is	be	AUX
ejpam-5830	80	7	the	the	DET
ejpam-5830	80	8	spectrum	spectrum	NOUN
ejpam-5830	80	9	of	of	ADP
ejpam-5830	80	10	f∗	f∗	NOUN
ejpam-5830	80	11	acting	act	VERB
ejpam-5830	80	12	on	on	ADP
ejpam-5830	80	13	the	the	DET
ejpam-5830	80	14	complexification	complexification	NOUN
ejpam-5830	80	15	of	of	ADP
ejpam-5830	80	16	χ(λ	χ(λ	PROPN
ejpam-5830	80	17	)	)	PUNCT
ejpam-5830	80	18	.	.	PUNCT
ejpam-5830	81	1	if	if	SCONJ
ejpam-5830	81	2	the	the	DET
ejpam-5830	81	3	mather	mather	PROPN
ejpam-5830	81	4	spectrum	spectrum	NOUN
ejpam-5830	81	5	of	of	ADP
ejpam-5830	81	6	f	f	PROPN
ejpam-5830	81	7	|λ	|λ	PROPN
ejpam-5830	81	8	is	be	AUX
ejpam-5830	81	9	contained	contain	VERB
ejpam-5830	81	10	in	in	ADP
ejpam-5830	81	11	the	the	DET
ejpam-5830	81	12	set	set	NOUN
ejpam-5830	81	13	{	{	PUNCT
ejpam-5830	81	14	z	z	NOUN
ejpam-5830	81	15	∈	∈	PROPN
ejpam-5830	81	16	c	c	NOUN
ejpam-5830	81	17	:	:	PUNCT
ejpam-5830	81	18	0	0	PUNCT
ejpam-5830	81	19	<	<	X
ejpam-5830	81	20	|z|	|z|	X
ejpam-5830	81	21	<	<	X
ejpam-5830	81	22	λs	λs	NOUN
ejpam-5830	81	23	}	}	PUNCT
ejpam-5830	81	24	∪	∪	X
ejpam-5830	81	25	{	{	PUNCT
ejpam-5830	81	26	z	z	NOUN
ejpam-5830	81	27	∈	∈	PROPN
ejpam-5830	81	28	c	c	NOUN
ejpam-5830	81	29	:	:	PUNCT
ejpam-5830	81	30	λu	λu	X
ejpam-5830	81	31	<	<	X
ejpam-5830	81	32	|z|	|z|	NOUN
ejpam-5830	81	33	<	<	X
ejpam-5830	81	34	∞	∞	NUM
ejpam-5830	81	35	}	}	PUNCT
ejpam-5830	81	36	,	,	PUNCT
ejpam-5830	81	37	for	for	ADP
ejpam-5830	81	38	λs	λs	NOUN
ejpam-5830	81	39	<	<	X
ejpam-5830	81	40	1	1	NUM
ejpam-5830	81	41	<	<	X
ejpam-5830	81	42	λu	λu	PROPN
ejpam-5830	81	43	,	,	PUNCT
ejpam-5830	81	44	then	then	ADV
ejpam-5830	81	45	we	we	PRON
ejpam-5830	81	46	say	say	VERB
ejpam-5830	81	47	that	that	SCONJ
ejpam-5830	81	48	the	the	DET
ejpam-5830	81	49	function	function	NOUN
ejpam-5830	81	50	φ	φ	NOUN
ejpam-5830	81	51	:	:	PUNCT
ejpam-5830	82	1	λ	λ	X
ejpam-5830	82	2	→	→	PUNCT
ejpam-5830	82	3	γ	γ	X
ejpam-5830	82	4	satisfies	satisfy	VERB
ejpam-5830	82	5	a	a	DET
ejpam-5830	82	6	partial	partial	ADJ
ejpam-5830	82	7	hyperbolicity	hyperbolicity	NOUN
ejpam-5830	82	8	hypothesis	hypothesis	NOUN
ejpam-5830	82	9	if	if	SCONJ
ejpam-5830	82	10	we	we	PRON
ejpam-5830	82	11	can	can	AUX
ejpam-5830	82	12	choose	choose	VERB
ejpam-5830	82	13	λs	λs	ADP
ejpam-5830	82	14	and	and	CCONJ
ejpam-5830	82	15	λu	λu	X
ejpam-5830	82	16	such	such	ADJ
ejpam-5830	82	17	that	that	DET
ejpam-5830	82	18	λs	λs	NOUN
ejpam-5830	82	19	<	<	X
ejpam-5830	82	20	µs	µs	X
ejpam-5830	82	21	≤	≤	NUM
ejpam-5830	82	22	1	1	NUM
ejpam-5830	82	23	≤	≤	NUM
ejpam-5830	82	24	µu	µu	ADP
ejpam-5830	82	25	<	<	X
ejpam-5830	82	26	λu	λu	X
ejpam-5830	82	27	,	,	PUNCT
ejpam-5830	82	28	where	where	SCONJ
ejpam-5830	82	29	µs	µs	X
ejpam-5830	82	30	=	=	SYM
ejpam-5830	82	31	lim	lim	PROPN
ejpam-5830	82	32	sup	sup	PROPN
ejpam-5830	82	33	n→∞	n→∞	NUM
ejpam-5830	82	34	(	(	PUNCT
ejpam-5830	82	35	sup	sup	NOUN
ejpam-5830	82	36	x∈λ	x∈λ	ADJ
ejpam-5830	82	37	|ad(φ(fn−1x	|ad(φ(fn−1x	NOUN
ejpam-5830	82	38	)	)	PUNCT
ejpam-5830	82	39	·	·	PUNCT
ejpam-5830	82	40	·	·	PUNCT
ejpam-5830	83	1	·	·	PUNCT
ejpam-5830	83	2	φ(fx)φ(x))|	φ(fx)φ(x))|	PRON
ejpam-5830	83	3	)	)	PUNCT
ejpam-5830	83	4	1	1	NUM
ejpam-5830	83	5	n	n	PROPN
ejpam-5830	83	6	r.	r.	PROPN
ejpam-5830	83	7	d.	d.	PROPN
ejpam-5830	83	8	laureano	laureano	PROPN
ejpam-5830	83	9	/	/	SYM
ejpam-5830	83	10	eur	eur	PROPN
ejpam-5830	83	11	.	.	PUNCT
ejpam-5830	84	1	j.	j.	PROPN
ejpam-5830	84	2	pure	pure	PROPN
ejpam-5830	84	3	appl	appl	PROPN
ejpam-5830	84	4	.	.	PROPN
ejpam-5830	84	5	math	math	PROPN
ejpam-5830	84	6	,	,	PUNCT
ejpam-5830	84	7	18	18	NUM
ejpam-5830	84	8	(	(	PUNCT
ejpam-5830	84	9	2	2	NUM
ejpam-5830	84	10	)	)	PUNCT
ejpam-5830	84	11	(	(	PUNCT
ejpam-5830	84	12	2025	2025	NUM
ejpam-5830	84	13	)	)	PUNCT
ejpam-5830	84	14	,	,	PUNCT
ejpam-5830	84	15	5830	5830	NUM
ejpam-5830	84	16	5	5	NUM
ejpam-5830	84	17	of	of	ADP
ejpam-5830	84	18	11	11	NUM
ejpam-5830	84	19	and	and	CCONJ
ejpam-5830	84	20	µu	µu	VERB
ejpam-5830	84	21	=	=	SYM
ejpam-5830	84	22	lim	lim	PROPN
ejpam-5830	84	23	inf	inf	PROPN
ejpam-5830	84	24	n→∞	n→∞	X
ejpam-5830	85	1	(	(	PUNCT
ejpam-5830	85	2	sup	sup	NOUN
ejpam-5830	85	3	x∈λ	x∈λ	ADJ
ejpam-5830	85	4	|ad(φ(fn−1x	|ad(φ(fn−1x	NOUN
ejpam-5830	85	5	)	)	PUNCT
ejpam-5830	85	6	·	·	PUNCT
ejpam-5830	85	7	·	·	PUNCT
ejpam-5830	86	1	·	·	PUNCT
ejpam-5830	86	2	φ(fx)φ(x))−1|	φ(fx)φ(x))−1|	X
ejpam-5830	86	3	)	)	PUNCT
ejpam-5830	86	4	−	−	PROPN
ejpam-5830	86	5	1	1	NUM
ejpam-5830	86	6	n	n	NOUN
ejpam-5830	86	7	.	.	PUNCT
ejpam-5830	87	1	let	let	AUX
ejpam-5830	87	2	be	be	AUX
ejpam-5830	87	3	θ̃	θ̃	NOUN
ejpam-5830	87	4	=	=	SYM
ejpam-5830	87	5	max	max	PROPN
ejpam-5830	87	6	{	{	PUNCT
ejpam-5830	87	7	logµs	logµs	PROPN
ejpam-5830	87	8	log	log	NOUN
ejpam-5830	87	9	λs	λs	ADV
ejpam-5830	87	10	,	,	PUNCT
ejpam-5830	87	11	log	log	VERB
ejpam-5830	87	12	λu	λu	PRON
ejpam-5830	87	13	logµu	logµu	VERB
ejpam-5830	87	14	}	}	PUNCT
ejpam-5830	87	15	<	<	X
ejpam-5830	87	16	1	1	X
ejpam-5830	87	17	.	.	PUNCT
ejpam-5830	87	18	assuming	assume	VERB
ejpam-5830	87	19	this	this	DET
ejpam-5830	87	20	partial	partial	ADJ
ejpam-5830	87	21	hyperbolicity	hyperbolicity	NOUN
ejpam-5830	87	22	hypothesis	hypothesis	NOUN
ejpam-5830	87	23	,	,	PUNCT
ejpam-5830	87	24	pollicott	pollicott	ADJ
ejpam-5830	87	25	and	and	CCONJ
ejpam-5830	87	26	walkden	walkden	ADJ
ejpam-5830	87	27	generalized	generalized	ADJ
ejpam-5830	87	28	in	in	ADP
ejpam-5830	87	29	[	[	X
ejpam-5830	87	30	13	13	NUM
ejpam-5830	87	31	]	]	PUNCT
ejpam-5830	87	32	livschitz	livschitz	PROPN
ejpam-5830	87	33	’s	’s	PART
ejpam-5830	87	34	hölder	hölder	NOUN
ejpam-5830	87	35	regularity	regularity	NOUN
ejpam-5830	87	36	result	result	NOUN
ejpam-5830	87	37	to	to	ADP
ejpam-5830	87	38	any	any	DET
ejpam-5830	87	39	connected	connected	ADJ
ejpam-5830	87	40	lie	lie	NOUN
ejpam-5830	87	41	group	group	NOUN
ejpam-5830	87	42	(	(	PUNCT
ejpam-5830	87	43	not	not	PART
ejpam-5830	87	44	necessarily	necessarily	ADV
ejpam-5830	87	45	possessing	possess	VERB
ejpam-5830	87	46	a	a	DET
ejpam-5830	87	47	bi	bi	ADJ
ejpam-5830	87	48	-	-	ADJ
ejpam-5830	87	49	invariant	invariant	ADJ
ejpam-5830	87	50	metric	metric	NOUN
ejpam-5830	87	51	)	)	PUNCT
ejpam-5830	87	52	.	.	PUNCT
ejpam-5830	88	1	theorem	theorem	NOUN
ejpam-5830	88	2	1	1	NUM
ejpam-5830	88	3	.	.	PUNCT
ejpam-5830	89	1	let	let	VERB
ejpam-5830	89	2	λ	λ	PRON
ejpam-5830	89	3	be	be	AUX
ejpam-5830	89	4	a	a	DET
ejpam-5830	89	5	compact	compact	ADJ
ejpam-5830	89	6	locally	locally	ADV
ejpam-5830	89	7	maximal	maximal	ADJ
ejpam-5830	89	8	hyperbolic	hyperbolic	ADJ
ejpam-5830	89	9	set	set	NOUN
ejpam-5830	89	10	of	of	ADP
ejpam-5830	89	11	a	a	DET
ejpam-5830	89	12	c1	c1	PROPN
ejpam-5830	89	13	diffeomorphism	diffeomorphism	NOUN
ejpam-5830	89	14	f	f	X
ejpam-5830	89	15	,	,	PUNCT
ejpam-5830	89	16	and	and	CCONJ
ejpam-5830	89	17	m	m	VERB
ejpam-5830	89	18	an	an	DET
ejpam-5830	89	19	equilibrium	equilibrium	NOUN
ejpam-5830	89	20	measure	measure	NOUN
ejpam-5830	89	21	of	of	ADP
ejpam-5830	89	22	an	an	DET
ejpam-5830	89	23	hölder	hölder	NOUN
ejpam-5830	89	24	function	function	NOUN
ejpam-5830	89	25	.	.	PUNCT
ejpam-5830	90	1	let	let	VERB
ejpam-5830	90	2	γ	γ	NOUN
ejpam-5830	90	3	be	be	AUX
ejpam-5830	90	4	a	a	DET
ejpam-5830	90	5	connected	connected	ADJ
ejpam-5830	90	6	lie	lie	NOUN
ejpam-5830	90	7	group	group	NOUN
ejpam-5830	90	8	and	and	CCONJ
ejpam-5830	90	9	φ	φ	NOUN
ejpam-5830	90	10	:	:	PUNCT
ejpam-5830	91	1	λ	λ	X
ejpam-5830	91	2	→	→	PUNCT
ejpam-5830	91	3	γ	γ	X
ejpam-5830	91	4	be	be	AUX
ejpam-5830	91	5	a	a	DET
ejpam-5830	91	6	hölder	hölder	NOUN
ejpam-5830	91	7	function	function	NOUN
ejpam-5830	91	8	with	with	ADP
ejpam-5830	91	9	exponent	exponent	NOUN
ejpam-5830	91	10	θ	θ	PROPN
ejpam-5830	91	11	∈	∈	PROPN
ejpam-5830	91	12	(	(	PUNCT
ejpam-5830	91	13	θ̃	θ̃	PROPN
ejpam-5830	91	14	,	,	PUNCT
ejpam-5830	91	15	1	1	X
ejpam-5830	91	16	)	)	PUNCT
ejpam-5830	91	17	satisfying	satisfy	VERB
ejpam-5830	91	18	a	a	DET
ejpam-5830	91	19	partial	partial	ADJ
ejpam-5830	91	20	hyperbolicity	hyperbolicity	NOUN
ejpam-5830	91	21	hypothesis	hypothesis	NOUN
ejpam-5830	91	22	.	.	PUNCT
ejpam-5830	92	1	if	if	SCONJ
ejpam-5830	92	2	φ	φ	PROPN
ejpam-5830	92	3	is	be	AUX
ejpam-5830	92	4	a	a	DET
ejpam-5830	92	5	measurable	measurable	ADJ
ejpam-5830	92	6	solution	solution	NOUN
ejpam-5830	92	7	of	of	ADP
ejpam-5830	92	8	the	the	DET
ejpam-5830	92	9	cohomological	cohomological	ADJ
ejpam-5830	92	10	equation	equation	NOUN
ejpam-5830	92	11	φ	φ	PROPN
ejpam-5830	92	12	=	=	SYM
ejpam-5830	92	13	φ	φ	PROPN
ejpam-5830	92	14	◦	◦	NOUN
ejpam-5830	92	15	f	f	PROPN
ejpam-5830	92	16	−	−	PROPN
ejpam-5830	92	17	φ	φ	NUM
ejpam-5830	92	18	m	m	PROPN
ejpam-5830	92	19	-	-	PUNCT
ejpam-5830	92	20	almost	almost	ADV
ejpam-5830	92	21	everywhere	everywhere	ADV
ejpam-5830	92	22	,	,	PUNCT
ejpam-5830	92	23	then	then	ADV
ejpam-5830	92	24	φ	φ	PROPN
ejpam-5830	92	25	is	be	AUX
ejpam-5830	92	26	m	m	NOUN
ejpam-5830	92	27	-	-	PUNCT
ejpam-5830	92	28	almost	almost	ADV
ejpam-5830	92	29	everywhere	everywhere	ADV
ejpam-5830	92	30	equal	equal	ADJ
ejpam-5830	92	31	to	to	ADP
ejpam-5830	92	32	a	a	DET
ejpam-5830	92	33	hölder	hölder	NOUN
ejpam-5830	92	34	transformation	transformation	NOUN
ejpam-5830	92	35	φ̃	φ̃	PROPN
ejpam-5830	92	36	for	for	ADP
ejpam-5830	92	37	which	which	PRON
ejpam-5830	92	38	φ	φ	NOUN
ejpam-5830	92	39	=	=	SYM
ejpam-5830	92	40	φ̃	φ̃	PROPN
ejpam-5830	92	41	◦	◦	NOUN
ejpam-5830	92	42	f	f	X
ejpam-5830	92	43	−	−	PROPN
ejpam-5830	92	44	φ̃	φ̃	PROPN
ejpam-5830	92	45	everywhere	everywhere	ADV
ejpam-5830	92	46	.	.	PUNCT
ejpam-5830	93	1	we	we	PRON
ejpam-5830	93	2	note	note	VERB
ejpam-5830	93	3	that	that	SCONJ
ejpam-5830	93	4	this	this	DET
ejpam-5830	93	5	result	result	NOUN
ejpam-5830	93	6	does	do	AUX
ejpam-5830	93	7	not	not	PART
ejpam-5830	93	8	guarantee	guarantee	VERB
ejpam-5830	93	9	the	the	DET
ejpam-5830	93	10	existence	existence	NOUN
ejpam-5830	93	11	of	of	ADP
ejpam-5830	93	12	solutions	solution	NOUN
ejpam-5830	93	13	to	to	ADP
ejpam-5830	93	14	the	the	DET
ejpam-5830	93	15	cohomological	cohomological	ADJ
ejpam-5830	93	16	equation	equation	NOUN
ejpam-5830	93	17	.	.	PUNCT
ejpam-5830	94	1	we	we	PRON
ejpam-5830	94	2	now	now	ADV
ejpam-5830	94	3	describe	describe	VERB
ejpam-5830	94	4	a	a	DET
ejpam-5830	94	5	sufficiently	sufficiently	ADV
ejpam-5830	94	6	general	general	ADJ
ejpam-5830	94	7	additional	additional	ADJ
ejpam-5830	94	8	condition	condition	NOUN
ejpam-5830	94	9	under	under	ADP
ejpam-5830	94	10	which	which	PRON
ejpam-5830	94	11	existence	existence	NOUN
ejpam-5830	94	12	can	can	AUX
ejpam-5830	94	13	be	be	AUX
ejpam-5830	94	14	ensured	ensure	VERB
ejpam-5830	94	15	.	.	PUNCT
ejpam-5830	95	1	let	let	VERB
ejpam-5830	95	2	φ	φ	NOUN
ejpam-5830	95	3	:	:	PUNCT
ejpam-5830	95	4	λ	λ	X
ejpam-5830	95	5	→	→	PUNCT
ejpam-5830	95	6	γ	γ	X
ejpam-5830	95	7	be	be	AUX
ejpam-5830	95	8	a	a	DET
ejpam-5830	95	9	hölder	hölder	NOUN
ejpam-5830	95	10	function	function	NOUN
ejpam-5830	95	11	satisfying	satisfy	VERB
ejpam-5830	95	12	a	a	DET
ejpam-5830	95	13	partial	partial	ADJ
ejpam-5830	95	14	hyperbolicity	hyperbolicity	NOUN
ejpam-5830	95	15	hypothesis	hypothesis	NOUN
ejpam-5830	95	16	such	such	ADJ
ejpam-5830	95	17	that	that	PRON
ejpam-5830	95	18	λs	λs	NOUN
ejpam-5830	95	19	<	<	X
ejpam-5830	95	20	µ−1	µ−1	PROPN
ejpam-5830	95	21	u	u	NOUN
ejpam-5830	95	22	and	and	CCONJ
ejpam-5830	95	23	µ−1	µ−1	PROPN
ejpam-5830	95	24	s	s	X
ejpam-5830	95	25	<	<	X
ejpam-5830	95	26	λu	λu	X
ejpam-5830	95	27	.	.	PUNCT
ejpam-5830	96	1	we	we	PRON
ejpam-5830	96	2	define	define	VERB
ejpam-5830	96	3	the	the	DET
ejpam-5830	96	4	constant	constant	ADJ
ejpam-5830	96	5	θ̃′	θ̃′	NOUN
ejpam-5830	96	6	=	=	PROPN
ejpam-5830	96	7	max	max	PROPN
ejpam-5830	96	8	{	{	PUNCT
ejpam-5830	96	9	θ̃	θ̃	PROPN
ejpam-5830	96	10	,	,	PUNCT
ejpam-5830	96	11	logµ−1	logµ−1	PROPN
ejpam-5830	96	12	s	s	PART
ejpam-5830	96	13	log	log	NOUN
ejpam-5830	96	14	λu	λu	X
ejpam-5830	96	15	,	,	PUNCT
ejpam-5830	96	16	logµu	logµu	VERB
ejpam-5830	96	17	log	log	NOUN
ejpam-5830	97	1	λ−1	λ−1	PROPN
ejpam-5830	97	2	s	s	PART
ejpam-5830	97	3	}	}	PUNCT
ejpam-5830	97	4	<	<	X
ejpam-5830	97	5	1	1	NUM
ejpam-5830	97	6	.	.	PUNCT
ejpam-5830	98	1	still	still	ADV
ejpam-5830	98	2	in	in	ADP
ejpam-5830	98	3	[	[	X
ejpam-5830	98	4	13	13	NUM
ejpam-5830	98	5	]	]	PUNCT
ejpam-5830	98	6	,	,	PUNCT
ejpam-5830	98	7	pollicott	pollicott	ADJ
ejpam-5830	98	8	and	and	CCONJ
ejpam-5830	98	9	walkden	walkden	PROPN
ejpam-5830	98	10	proved	prove	VERB
ejpam-5830	98	11	the	the	DET
ejpam-5830	98	12	following	follow	VERB
ejpam-5830	98	13	result	result	NOUN
ejpam-5830	98	14	.	.	PUNCT
ejpam-5830	99	1	theorem	theorem	NOUN
ejpam-5830	99	2	2	2	NUM
ejpam-5830	99	3	.	.	PUNCT
ejpam-5830	100	1	let	let	VERB
ejpam-5830	100	2	λ	λ	PRON
ejpam-5830	100	3	be	be	AUX
ejpam-5830	100	4	a	a	DET
ejpam-5830	100	5	compact	compact	ADJ
ejpam-5830	100	6	locally	locally	ADV
ejpam-5830	100	7	maximal	maximal	ADJ
ejpam-5830	100	8	hyperbolic	hyperbolic	ADJ
ejpam-5830	100	9	set	set	NOUN
ejpam-5830	100	10	of	of	ADP
ejpam-5830	100	11	a	a	DET
ejpam-5830	100	12	c1	c1	PROPN
ejpam-5830	100	13	diffeomorphism	diffeomorphism	NOUN
ejpam-5830	101	1	f	f	PROPN
ejpam-5830	101	2	.	.	PUNCT
ejpam-5830	102	1	let	let	VERB
ejpam-5830	102	2	γ	γ	NOUN
ejpam-5830	102	3	be	be	AUX
ejpam-5830	102	4	a	a	DET
ejpam-5830	102	5	connected	connected	ADJ
ejpam-5830	102	6	lie	lie	NOUN
ejpam-5830	102	7	group	group	NOUN
ejpam-5830	102	8	and	and	CCONJ
ejpam-5830	102	9	φ	φ	NOUN
ejpam-5830	102	10	:	:	PUNCT
ejpam-5830	103	1	λ	λ	X
ejpam-5830	103	2	→	→	SYM
ejpam-5830	103	3	γ	γ	X
ejpam-5830	103	4	a	a	DET
ejpam-5830	103	5	hölder	hölder	NOUN
ejpam-5830	103	6	function	function	NOUN
ejpam-5830	103	7	with	with	ADP
ejpam-5830	103	8	exponent	exponent	NOUN
ejpam-5830	103	9	θ	θ	PROPN
ejpam-5830	103	10	∈	∈	PROPN
ejpam-5830	103	11	(	(	PUNCT
ejpam-5830	103	12	θ̃′	θ̃′	PROPN
ejpam-5830	103	13	,	,	PUNCT
ejpam-5830	103	14	1	1	NUM
ejpam-5830	103	15	)	)	PUNCT
ejpam-5830	103	16	satisfying	satisfy	VERB
ejpam-5830	103	17	a	a	DET
ejpam-5830	103	18	partial	partial	ADJ
ejpam-5830	103	19	hyperbolicity	hyperbolicity	NOUN
ejpam-5830	103	20	hypothesis	hypothesis	NOUN
ejpam-5830	103	21	with	with	ADP
ejpam-5830	103	22	λs	λs	NOUN
ejpam-5830	103	23	<	<	X
ejpam-5830	103	24	µ−1	µ−1	PROPN
ejpam-5830	103	25	u	u	NOUN
ejpam-5830	103	26	and	and	CCONJ
ejpam-5830	103	27	µ−1	µ−1	PROPN
ejpam-5830	103	28	s	s	X
ejpam-5830	103	29	<	<	X
ejpam-5830	103	30	λu	λu	X
ejpam-5830	103	31	.	.	PUNCT
ejpam-5830	104	1	if	if	SCONJ
ejpam-5830	104	2	n−1∑	n−1∑	PROPN
ejpam-5830	104	3	i=0	i=0	PROPN
ejpam-5830	104	4	φ(f	φ(f	PROPN
ejpam-5830	104	5	ix	ix	PROPN
ejpam-5830	104	6	)	)	PUNCT
ejpam-5830	104	7	=	=	SYM
ejpam-5830	105	1	0	0	NUM
ejpam-5830	105	2	,	,	PUNCT
ejpam-5830	105	3	whenever	whenever	SCONJ
ejpam-5830	105	4	fnx	fnx	PROPN
ejpam-5830	105	5	=	=	SYM
ejpam-5830	105	6	x	x	PROPN
ejpam-5830	105	7	,	,	PUNCT
ejpam-5830	105	8	then	then	ADV
ejpam-5830	105	9	there	there	PRON
ejpam-5830	105	10	exists	exist	VERB
ejpam-5830	105	11	a	a	DET
ejpam-5830	105	12	hölder	hölder	NOUN
ejpam-5830	105	13	solution	solution	NOUN
ejpam-5830	105	14	φ	φ	X
ejpam-5830	105	15	:	:	PUNCT
ejpam-5830	106	1	λ	λ	X
ejpam-5830	106	2	→	→	SYM
ejpam-5830	106	3	γ	γ	X
ejpam-5830	106	4	for	for	ADP
ejpam-5830	106	5	the	the	DET
ejpam-5830	106	6	cohomological	cohomological	ADJ
ejpam-5830	106	7	equation	equation	NOUN
ejpam-5830	106	8	φ	φ	PROPN
ejpam-5830	106	9	=	=	SYM
ejpam-5830	106	10	φ	φ	PROPN
ejpam-5830	106	11	◦	◦	NOUN
ejpam-5830	106	12	f	f	PROPN
ejpam-5830	107	1	−	−	PROPN
ejpam-5830	107	2	φ	φ	PROPN
ejpam-5830	107	3	.	.	PUNCT
ejpam-5830	108	1	pollicott	pollicott	PROPN
ejpam-5830	108	2	and	and	CCONJ
ejpam-5830	108	3	walkden	walkden	PROPN
ejpam-5830	108	4	initially	initially	ADV
ejpam-5830	108	5	addressed	address	VERB
ejpam-5830	108	6	the	the	DET
ejpam-5830	108	7	case	case	NOUN
ejpam-5830	108	8	where	where	SCONJ
ejpam-5830	108	9	γ	γ	PROPN
ejpam-5830	108	10	is	be	AUX
ejpam-5830	108	11	a	a	DET
ejpam-5830	108	12	connected	connect	VERB
ejpam-5830	108	13	solvable	solvable	ADJ
ejpam-5830	108	14	lie	lie	NOUN
ejpam-5830	108	15	group	group	NOUN
ejpam-5830	108	16	(	(	PUNCT
ejpam-5830	108	17	recall	recall	VERB
ejpam-5830	108	18	that	that	SCONJ
ejpam-5830	108	19	a	a	DET
ejpam-5830	108	20	group	group	NOUN
ejpam-5830	108	21	is	be	AUX
ejpam-5830	108	22	solvable	solvable	ADJ
ejpam-5830	108	23	if	if	SCONJ
ejpam-5830	108	24	there	there	PRON
ejpam-5830	108	25	exist	exist	VERB
ejpam-5830	108	26	subgroups	subgroup	NOUN
ejpam-5830	108	27	γ	γ	X
ejpam-5830	108	28	=	=	SYM
ejpam-5830	108	29	γ0	γ0	PROPN
ejpam-5830	108	30	>	>	X
ejpam-5830	108	31	γ1	γ1	PROPN
ejpam-5830	108	32	>	>	X
ejpam-5830	108	33	·	·	PUNCT
ejpam-5830	108	34	·	·	PUNCT
ejpam-5830	108	35	·	·	PUNCT
ejpam-5830	108	36	>	>	X
ejpam-5830	109	1	γn	γn	X
ejpam-5830	109	2	=	=	PUNCT
ejpam-5830	109	3	{	{	PUNCT
ejpam-5830	109	4	e	e	NOUN
ejpam-5830	109	5	}	}	PUNCT
ejpam-5830	109	6	such	such	ADJ
ejpam-5830	109	7	that	that	SCONJ
ejpam-5830	109	8	the	the	DET
ejpam-5830	109	9	quotients	quotient	NOUN
ejpam-5830	109	10	γi	γi	X
ejpam-5830	109	11	/	/	SYM
ejpam-5830	109	12	γi+1	γi+1	NOUN
ejpam-5830	109	13	are	be	AUX
ejpam-5830	109	14	abelian	abelian	ADJ
ejpam-5830	109	15	,	,	PUNCT
ejpam-5830	109	16	0	0	NUM
ejpam-5830	109	17	≤	≤	NUM
ejpam-5830	109	18	i	i	PRON
ejpam-5830	109	19	≤	≤	ADJ
ejpam-5830	109	20	n	n	CCONJ
ejpam-5830	109	21	−	−	PROPN
ejpam-5830	109	22	1	1	NUM
ejpam-5830	109	23	)	)	PUNCT
ejpam-5830	109	24	and	and	CCONJ
ejpam-5830	109	25	then	then	ADV
ejpam-5830	109	26	considered	consider	VERB
ejpam-5830	109	27	the	the	DET
ejpam-5830	109	28	more	more	ADV
ejpam-5830	109	29	general	general	ADJ
ejpam-5830	109	30	case	case	NOUN
ejpam-5830	109	31	.	.	PUNCT
ejpam-5830	110	1	specifically	specifically	ADV
ejpam-5830	110	2	,	,	PUNCT
ejpam-5830	110	3	they	they	PRON
ejpam-5830	110	4	showed	show	VERB
ejpam-5830	110	5	that	that	SCONJ
ejpam-5830	110	6	for	for	ADP
ejpam-5830	110	7	solvable	solvable	ADJ
ejpam-5830	110	8	groups	group	NOUN
ejpam-5830	110	9	it	it	PRON
ejpam-5830	110	10	is	be	AUX
ejpam-5830	110	11	not	not	PART
ejpam-5830	110	12	necessary	necessary	ADJ
ejpam-5830	110	13	to	to	PART
ejpam-5830	110	14	assume	assume	VERB
ejpam-5830	110	15	any	any	DET
ejpam-5830	110	16	partial	partial	ADJ
ejpam-5830	110	17	hyperbolicity	hyperbolicity	NOUN
ejpam-5830	110	18	hypothesis	hypothesis	NOUN
ejpam-5830	110	19	.	.	PUNCT
ejpam-5830	111	1	to	to	PART
ejpam-5830	111	2	prove	prove	VERB
ejpam-5830	111	3	the	the	DET
ejpam-5830	111	4	results	result	NOUN
ejpam-5830	111	5	,	,	PUNCT
ejpam-5830	111	6	cohomological	cohomological	ADJ
ejpam-5830	111	7	equations	equation	NOUN
ejpam-5830	111	8	over	over	ADP
ejpam-5830	111	9	topological	topological	ADJ
ejpam-5830	111	10	markov	markov	NOUN
ejpam-5830	111	11	chains	chain	NOUN
ejpam-5830	111	12	and	and	CCONJ
ejpam-5830	111	13	their	their	PRON
ejpam-5830	111	14	suspensions	suspension	NOUN
ejpam-5830	111	15	are	be	AUX
ejpam-5830	111	16	considered	consider	VERB
ejpam-5830	111	17	(	(	PUNCT
ejpam-5830	111	18	see	see	VERB
ejpam-5830	111	19	[	[	X
ejpam-5830	111	20	3	3	NUM
ejpam-5830	111	21	]	]	NUM
ejpam-5830	111	22	)	)	PUNCT
ejpam-5830	111	23	,	,	PUNCT
ejpam-5830	111	24	which	which	PRON
ejpam-5830	111	25	allows	allow	VERB
ejpam-5830	111	26	the	the	DET
ejpam-5830	111	27	equation	equation	NOUN
ejpam-5830	111	28	to	to	PART
ejpam-5830	111	29	be	be	AUX
ejpam-5830	111	30	solved	solve	VERB
ejpam-5830	111	31	first	first	ADV
ejpam-5830	111	32	in	in	ADP
ejpam-5830	111	33	symbolic	symbolic	ADJ
ejpam-5830	111	34	dynamics	dynamic	NOUN
ejpam-5830	111	35	.	.	PUNCT
ejpam-5830	112	1	it	it	PRON
ejpam-5830	112	2	should	should	AUX
ejpam-5830	112	3	be	be	AUX
ejpam-5830	112	4	noted	note	VERB
ejpam-5830	112	5	that	that	SCONJ
ejpam-5830	112	6	the	the	DET
ejpam-5830	112	7	work	work	NOUN
ejpam-5830	112	8	of	of	ADP
ejpam-5830	112	9	pollicott	pollicott	ADJ
ejpam-5830	112	10	and	and	CCONJ
ejpam-5830	112	11	walkden	walkden	NOUN
ejpam-5830	112	12	is	be	AUX
ejpam-5830	112	13	based	base	VERB
ejpam-5830	112	14	on	on	ADP
ejpam-5830	112	15	articles	article	NOUN
ejpam-5830	112	16	[	[	X
ejpam-5830	112	17	15	15	NUM
ejpam-5830	112	18	]	]	PUNCT
ejpam-5830	112	19	and	and	CCONJ
ejpam-5830	112	20	[	[	X
ejpam-5830	112	21	14	14	NUM
ejpam-5830	112	22	]	]	X
ejpam-5830	112	23	,	,	PUNCT
ejpam-5830	112	24	where	where	SCONJ
ejpam-5830	112	25	cocycles	cocycle	NOUN
ejpam-5830	112	26	taking	take	VERB
ejpam-5830	112	27	values	value	NOUN
ejpam-5830	112	28	in	in	ADP
ejpam-5830	112	29	a	a	DET
ejpam-5830	112	30	r.	r.	PROPN
ejpam-5830	112	31	d.	d.	PROPN
ejpam-5830	112	32	laureano	laureano	PROPN
ejpam-5830	112	33	/	/	SYM
ejpam-5830	112	34	eur	eur	PROPN
ejpam-5830	112	35	.	.	PUNCT
ejpam-5830	113	1	j.	j.	PROPN
ejpam-5830	113	2	pure	pure	PROPN
ejpam-5830	113	3	appl	appl	PROPN
ejpam-5830	113	4	.	.	PROPN
ejpam-5830	113	5	math	math	PROPN
ejpam-5830	113	6	,	,	PUNCT
ejpam-5830	113	7	18	18	NUM
ejpam-5830	113	8	(	(	PUNCT
ejpam-5830	113	9	2	2	NUM
ejpam-5830	113	10	)	)	PUNCT
ejpam-5830	113	11	(	(	PUNCT
ejpam-5830	113	12	2025	2025	NUM
ejpam-5830	113	13	)	)	PUNCT
ejpam-5830	113	14	,	,	PUNCT
ejpam-5830	113	15	5830	5830	NUM
ejpam-5830	113	16	6	6	NUM
ejpam-5830	113	17	of	of	ADP
ejpam-5830	113	18	11	11	NUM
ejpam-5830	113	19	compact	compact	ADJ
ejpam-5830	113	20	lie	lie	NOUN
ejpam-5830	113	21	group	group	NOUN
ejpam-5830	113	22	over	over	ADP
ejpam-5830	113	23	anosov	anosov	NOUN
ejpam-5830	113	24	diffeomorphisms	diffeomorphism	NOUN
ejpam-5830	113	25	were	be	AUX
ejpam-5830	113	26	studied	study	VERB
ejpam-5830	113	27	.	.	PUNCT
ejpam-5830	114	1	this	this	DET
ejpam-5830	114	2	problem	problem	NOUN
ejpam-5830	114	3	was	be	AUX
ejpam-5830	114	4	also	also	ADV
ejpam-5830	114	5	the	the	DET
ejpam-5830	114	6	subject	subject	NOUN
ejpam-5830	114	7	of	of	ADP
ejpam-5830	114	8	several	several	ADJ
ejpam-5830	114	9	earlier	early	ADJ
ejpam-5830	114	10	articles	article	NOUN
ejpam-5830	114	11	preceding	precede	VERB
ejpam-5830	114	12	[	[	X
ejpam-5830	114	13	13	13	NUM
ejpam-5830	114	14	]	]	PUNCT
ejpam-5830	114	15	,	,	PUNCT
ejpam-5830	114	16	namely	namely	ADV
ejpam-5830	114	17	,	,	PUNCT
ejpam-5830	114	18	[	[	X
ejpam-5830	114	19	16	16	NUM
ejpam-5830	114	20	]	]	PUNCT
ejpam-5830	114	21	by	by	ADP
ejpam-5830	114	22	niţică	niţică	ADJ
ejpam-5830	114	23	and	and	CCONJ
ejpam-5830	114	24	török	török	NOUN
ejpam-5830	114	25	,	,	PUNCT
ejpam-5830	114	26	[	[	X
ejpam-5830	114	27	11	11	NUM
ejpam-5830	114	28	]	]	PUNCT
ejpam-5830	114	29	by	by	ADP
ejpam-5830	114	30	parry	parry	NOUN
ejpam-5830	114	31	,	,	PUNCT
ejpam-5830	114	32	and	and	CCONJ
ejpam-5830	114	33	[	[	X
ejpam-5830	114	34	17	17	NUM
ejpam-5830	114	35	]	]	PUNCT
ejpam-5830	114	36	and	and	CCONJ
ejpam-5830	114	37	[	[	X
ejpam-5830	114	38	18	18	NUM
ejpam-5830	114	39	]	]	PUNCT
ejpam-5830	114	40	by	by	ADP
ejpam-5830	114	41	walkden	walkden	PROPN
ejpam-5830	114	42	.	.	PUNCT
ejpam-5830	115	1	another	another	DET
ejpam-5830	115	2	generalization	generalization	NOUN
ejpam-5830	115	3	of	of	ADP
ejpam-5830	115	4	the	the	DET
ejpam-5830	115	5	hölder	hölder	PROPN
ejpam-5830	115	6	livschitz	livschitz	PROPN
ejpam-5830	115	7	’s	’s	PART
ejpam-5830	115	8	results	result	NOUN
ejpam-5830	115	9	was	be	AUX
ejpam-5830	115	10	obtained	obtain	VERB
ejpam-5830	115	11	by	by	ADP
ejpam-5830	115	12	niţică	niţică	ADJ
ejpam-5830	115	13	and	and	CCONJ
ejpam-5830	115	14	török	török	NOUN
ejpam-5830	115	15	for	for	ADP
ejpam-5830	115	16	cocycles	cocycle	NOUN
ejpam-5830	115	17	taking	take	VERB
ejpam-5830	115	18	values	value	NOUN
ejpam-5830	115	19	in	in	ADP
ejpam-5830	115	20	diffeomorphism	diffeomorphism	NOUN
ejpam-5830	115	21	groups	group	NOUN
ejpam-5830	115	22	of	of	ADP
ejpam-5830	115	23	class	class	NOUN
ejpam-5830	115	24	ck	ck	PROPN
ejpam-5830	115	25	,	,	PUNCT
ejpam-5830	115	26	k	k	PROPN
ejpam-5830	116	1	=	=	SYM
ejpam-5830	116	2	1	1	NUM
ejpam-5830	116	3	,	,	PUNCT
ejpam-5830	116	4	2	2	NUM
ejpam-5830	116	5	,	,	PUNCT
ejpam-5830	116	6	.	.	PUNCT
ejpam-5830	116	7	.	.	PUNCT
ejpam-5830	117	1	.	.	PUNCT
ejpam-5830	118	1	,	,	PUNCT
ejpam-5830	118	2	∞	∞	PROPN
ejpam-5830	118	3	,	,	PUNCT
ejpam-5830	118	4	ω	ω	NOUN
ejpam-5830	118	5	.	.	PUNCT
ejpam-5830	118	6	given	give	VERB
ejpam-5830	118	7	a	a	DET
ejpam-5830	118	8	differentiable	differentiable	ADJ
ejpam-5830	118	9	manifold	manifold	ADJ
ejpam-5830	118	10	n	n	NOUN
ejpam-5830	118	11	,	,	PUNCT
ejpam-5830	118	12	a	a	DET
ejpam-5830	118	13	cocycle	cocycle	NOUN
ejpam-5830	118	14	α	α	NOUN
ejpam-5830	118	15	:	:	PUNCT
ejpam-5830	118	16	z	z	NOUN
ejpam-5830	118	17	×m	×m	PROPN
ejpam-5830	118	18	→	→	SYM
ejpam-5830	118	19	diffk(n	diffk(n	PROPN
ejpam-5830	118	20	)	)	PUNCT
ejpam-5830	118	21	is	be	AUX
ejpam-5830	118	22	said	say	VERB
ejpam-5830	118	23	to	to	PART
ejpam-5830	118	24	be	be	AUX
ejpam-5830	118	25	of	of	ADP
ejpam-5830	118	26	class	class	NOUN
ejpam-5830	118	27	ck	ck	NOUN
ejpam-5830	119	1	(	(	PUNCT
ejpam-5830	119	2	k	k	NOUN
ejpam-5830	119	3	=	=	SYM
ejpam-5830	119	4	1	1	NUM
ejpam-5830	119	5	,	,	PUNCT
ejpam-5830	119	6	2	2	NUM
ejpam-5830	119	7	,	,	PUNCT
ejpam-5830	119	8	.	.	PUNCT
ejpam-5830	119	9	.	.	PUNCT
ejpam-5830	120	1	.	.	PUNCT
ejpam-5830	121	1	,	,	PUNCT
ejpam-5830	121	2	∞	∞	NOUN
ejpam-5830	121	3	)	)	PUNCT
ejpam-5830	121	4	if	if	SCONJ
ejpam-5830	121	5	the	the	DET
ejpam-5830	121	6	function	function	NOUN
ejpam-5830	121	7	φ	φ	NOUN
ejpam-5830	121	8	=	=	SYM
ejpam-5830	121	9	α(1	α(1	PROPN
ejpam-5830	121	10	,	,	PUNCT
ejpam-5830	121	11	·	·	PUNCT
ejpam-5830	121	12	)	)	PUNCT
ejpam-5830	121	13	:	:	PUNCT
ejpam-5830	121	14	m	m	VERB
ejpam-5830	121	15	→	→	SYM
ejpam-5830	121	16	diffk(n	diffk(n	NOUN
ejpam-5830	121	17	)	)	PUNCT
ejpam-5830	121	18	is	be	AUX
ejpam-5830	121	19	a	a	DET
ejpam-5830	121	20	function	function	NOUN
ejpam-5830	121	21	of	of	ADP
ejpam-5830	121	22	class	class	NOUN
ejpam-5830	121	23	ck	ck	PROPN
ejpam-5830	121	24	.	.	PUNCT
ejpam-5830	122	1	for	for	ADP
ejpam-5830	122	2	γ	γ	PROPN
ejpam-5830	122	3	=	=	SYM
ejpam-5830	122	4	diffk(n	diffk(n	PROPN
ejpam-5830	122	5	)	)	PUNCT
ejpam-5830	122	6	,	,	PUNCT
ejpam-5830	122	7	these	these	DET
ejpam-5830	122	8	authors	author	NOUN
ejpam-5830	122	9	proved	prove	VERB
ejpam-5830	122	10	in	in	ADP
ejpam-5830	122	11	[	[	X
ejpam-5830	122	12	19	19	NUM
ejpam-5830	122	13	]	]	PUNCT
ejpam-5830	122	14	and	and	CCONJ
ejpam-5830	123	1	[	[	X
ejpam-5830	123	2	20	20	NUM
ejpam-5830	123	3	]	]	PUNCT
ejpam-5830	123	4	that	that	SCONJ
ejpam-5830	123	5	a	a	DET
ejpam-5830	123	6	cocycle	cocycle	NOUN
ejpam-5830	123	7	with	with	ADP
ejpam-5830	123	8	values	value	NOUN
ejpam-5830	123	9	close	close	ADJ
ejpam-5830	123	10	to	to	ADP
ejpam-5830	123	11	the	the	DET
ejpam-5830	123	12	identity	identity	NOUN
ejpam-5830	123	13	over	over	ADP
ejpam-5830	123	14	a	a	DET
ejpam-5830	123	15	diffeomorphism	diffeomorphism	NOUN
ejpam-5830	123	16	f	f	NOUN
ejpam-5830	123	17	with	with	ADP
ejpam-5830	123	18	a	a	DET
ejpam-5830	123	19	hyperbolic	hyperbolic	ADJ
ejpam-5830	123	20	set	set	NOUN
ejpam-5830	123	21	is	be	AUX
ejpam-5830	123	22	cohomologous	cohomologous	ADJ
ejpam-5830	123	23	to	to	ADP
ejpam-5830	123	24	the	the	DET
ejpam-5830	123	25	trivial	trivial	ADJ
ejpam-5830	123	26	cocycle	cocycle	NOUN
ejpam-5830	123	27	provided	provide	VERB
ejpam-5830	123	28	that	that	SCONJ
ejpam-5830	123	29	the	the	DET
ejpam-5830	123	30	conditions	condition	NOUN
ejpam-5830	123	31	in	in	ADP
ejpam-5830	123	32	(	(	PUNCT
ejpam-5830	123	33	4	4	X
ejpam-5830	123	34	)	)	PUNCT
ejpam-5830	123	35	are	be	AUX
ejpam-5830	123	36	satisfied	satisfied	ADJ
ejpam-5830	123	37	.	.	PUNCT
ejpam-5830	124	1	the	the	DET
ejpam-5830	124	2	proof	proof	ADJ
ejpam-5830	124	3	strategy	strategy	NOUN
ejpam-5830	124	4	is	be	AUX
ejpam-5830	124	5	analogous	analogous	ADJ
ejpam-5830	124	6	to	to	ADP
ejpam-5830	124	7	the	the	DET
ejpam-5830	124	8	one	one	NOUN
ejpam-5830	124	9	used	use	VERB
ejpam-5830	124	10	by	by	ADP
ejpam-5830	124	11	livschitz	livschitz	PROPN
ejpam-5830	124	12	.	.	PUNCT
ejpam-5830	125	1	the	the	DET
ejpam-5830	125	2	main	main	ADJ
ejpam-5830	125	3	difference	difference	NOUN
ejpam-5830	125	4	is	be	AUX
ejpam-5830	125	5	that	that	SCONJ
ejpam-5830	125	6	in	in	ADP
ejpam-5830	125	7	the	the	DET
ejpam-5830	125	8	group	group	NOUN
ejpam-5830	125	9	diffk(n	diffk(n	PROPN
ejpam-5830	125	10	)	)	PUNCT
ejpam-5830	125	11	,	,	PUNCT
ejpam-5830	125	12	the	the	DET
ejpam-5830	125	13	natural	natural	ADJ
ejpam-5830	125	14	metric	metric	NOUN
ejpam-5830	125	15	is	be	AUX
ejpam-5830	125	16	neither	neither	CCONJ
ejpam-5830	125	17	left	left	ADJ
ejpam-5830	125	18	-	-	PUNCT
ejpam-5830	125	19	invariant	invariant	ADJ
ejpam-5830	125	20	nor	nor	CCONJ
ejpam-5830	125	21	right	right	ADV
ejpam-5830	125	22	-	-	PUNCT
ejpam-5830	125	23	invariant	invariant	ADJ
ejpam-5830	125	24	.	.	PUNCT
ejpam-5830	126	1	however	however	ADV
ejpam-5830	126	2	,	,	PUNCT
ejpam-5830	126	3	in	in	ADP
ejpam-5830	126	4	a	a	DET
ejpam-5830	126	5	sufficiently	sufficiently	ADV
ejpam-5830	126	6	small	small	ADJ
ejpam-5830	126	7	neighborhood	neighborhood	NOUN
ejpam-5830	126	8	of	of	ADP
ejpam-5830	126	9	the	the	DET
ejpam-5830	126	10	identity	identity	NOUN
ejpam-5830	126	11	,	,	PUNCT
ejpam-5830	126	12	it	it	PRON
ejpam-5830	126	13	can	can	AUX
ejpam-5830	126	14	be	be	AUX
ejpam-5830	126	15	shown	show	VERB
ejpam-5830	126	16	that	that	SCONJ
ejpam-5830	126	17	this	this	DET
ejpam-5830	126	18	metric	metric	NOUN
ejpam-5830	126	19	is	be	AUX
ejpam-5830	126	20	“	"	PUNCT
ejpam-5830	126	21	almost	almost	ADV
ejpam-5830	126	22	invariant	invariant	ADJ
ejpam-5830	126	23	”	"	PUNCT
ejpam-5830	126	24	,	,	PUNCT
ejpam-5830	126	25	which	which	PRON
ejpam-5830	126	26	is	be	AUX
ejpam-5830	126	27	sufficient	sufficient	ADJ
ejpam-5830	126	28	for	for	ADP
ejpam-5830	126	29	the	the	DET
ejpam-5830	126	30	proof	proof	NOUN
ejpam-5830	126	31	.	.	PUNCT
ejpam-5830	127	1	3	3	X
ejpam-5830	127	2	.	.	X
ejpam-5830	127	3	the	the	DET
ejpam-5830	127	4	regularity	regularity	NOUN
ejpam-5830	127	5	problem	problem	NOUN
ejpam-5830	127	6	another	another	DET
ejpam-5830	127	7	important	important	ADJ
ejpam-5830	127	8	question	question	NOUN
ejpam-5830	127	9	is	be	AUX
ejpam-5830	127	10	what	what	PRON
ejpam-5830	127	11	can	can	AUX
ejpam-5830	127	12	be	be	AUX
ejpam-5830	127	13	said	say	VERB
ejpam-5830	127	14	about	about	ADP
ejpam-5830	127	15	the	the	DET
ejpam-5830	127	16	regularity	regularity	NOUN
ejpam-5830	127	17	of	of	ADP
ejpam-5830	127	18	the	the	DET
ejpam-5830	127	19	solution	solution	NOUN
ejpam-5830	127	20	φ	φ	NUM
ejpam-5830	127	21	of	of	ADP
ejpam-5830	127	22	the	the	DET
ejpam-5830	127	23	cohomological	cohomological	ADJ
ejpam-5830	127	24	equation	equation	NOUN
ejpam-5830	127	25	when	when	SCONJ
ejpam-5830	127	26	the	the	DET
ejpam-5830	127	27	cocycle	cocycle	NOUN
ejpam-5830	127	28	α	α	PROPN
ejpam-5830	127	29	and	and	CCONJ
ejpam-5830	127	30	the	the	DET
ejpam-5830	127	31	action	action	NOUN
ejpam-5830	127	32	t	t	NOUN
ejpam-5830	127	33	are	be	AUX
ejpam-5830	127	34	of	of	ADP
ejpam-5830	127	35	class	class	NOUN
ejpam-5830	127	36	ck	ck	PROPN
ejpam-5830	127	37	,	,	PUNCT
ejpam-5830	127	38	k	k	PROPN
ejpam-5830	127	39	=	=	SYM
ejpam-5830	127	40	1	1	NUM
ejpam-5830	127	41	,	,	PUNCT
ejpam-5830	127	42	2	2	NUM
ejpam-5830	127	43	,	,	PUNCT
ejpam-5830	127	44	.	.	PUNCT
ejpam-5830	127	45	.	.	PUNCT
ejpam-5830	128	1	.	.	PUNCT
ejpam-5830	129	1	,	,	PUNCT
ejpam-5830	129	2	∞	∞	PROPN
ejpam-5830	129	3	,	,	PUNCT
ejpam-5830	129	4	ω	ω	NOUN
ejpam-5830	129	5	.	.	PUNCT
ejpam-5830	130	1	this	this	DET
ejpam-5830	130	2	question	question	NOUN
ejpam-5830	130	3	was	be	AUX
ejpam-5830	130	4	also	also	ADV
ejpam-5830	130	5	first	first	ADV
ejpam-5830	130	6	studied	study	VERB
ejpam-5830	130	7	by	by	ADP
ejpam-5830	130	8	livschitz	livschitz	PROPN
ejpam-5830	130	9	.	.	PUNCT
ejpam-5830	131	1	he	he	PRON
ejpam-5830	131	2	showed	show	VERB
ejpam-5830	131	3	in	in	ADP
ejpam-5830	131	4	[	[	X
ejpam-5830	131	5	1	1	X
ejpam-5830	131	6	]	]	PUNCT
ejpam-5830	131	7	that	that	SCONJ
ejpam-5830	131	8	for	for	ADP
ejpam-5830	131	9	c1	c1	PROPN
ejpam-5830	131	10	cocycles	cocycle	NOUN
ejpam-5830	131	11	α	α	PRON
ejpam-5830	131	12	,	,	PUNCT
ejpam-5830	131	13	the	the	DET
ejpam-5830	131	14	solution	solution	NOUN
ejpam-5830	131	15	φ	φ	PROPN
ejpam-5830	131	16	is	be	AUX
ejpam-5830	131	17	still	still	ADV
ejpam-5830	131	18	of	of	ADP
ejpam-5830	131	19	class	class	NOUN
ejpam-5830	131	20	c1	c1	PROPN
ejpam-5830	131	21	.	.	PUNCT
ejpam-5830	132	1	livschitz	livschitz	PROPN
ejpam-5830	132	2	also	also	ADV
ejpam-5830	132	3	showed	show	VERB
ejpam-5830	132	4	,	,	PUNCT
ejpam-5830	132	5	using	use	VERB
ejpam-5830	132	6	the	the	DET
ejpam-5830	132	7	decay	decay	NOUN
ejpam-5830	132	8	of	of	ADP
ejpam-5830	132	9	fourier	fourier	ADJ
ejpam-5830	132	10	coefficients	coefficient	NOUN
ejpam-5830	132	11	,	,	PUNCT
ejpam-5830	132	12	that	that	SCONJ
ejpam-5830	132	13	if	if	SCONJ
ejpam-5830	132	14	α	α	PRON
ejpam-5830	132	15	is	be	AUX
ejpam-5830	132	16	a	a	DET
ejpam-5830	132	17	c∞	c∞	PROPN
ejpam-5830	132	18	cocycle	cocycle	NOUN
ejpam-5830	132	19	(	(	PUNCT
ejpam-5830	132	20	respectively	respectively	ADV
ejpam-5830	132	21	cω	cω	NOUN
ejpam-5830	132	22	)	)	PUNCT
ejpam-5830	132	23	over	over	ADP
ejpam-5830	132	24	certain	certain	ADJ
ejpam-5830	132	25	linear	linear	ADJ
ejpam-5830	132	26	actions	action	NOUN
ejpam-5830	132	27	in	in	ADP
ejpam-5830	132	28	the	the	DET
ejpam-5830	132	29	torus	torus	NOUN
ejpam-5830	132	30	,	,	PUNCT
ejpam-5830	132	31	then	then	ADV
ejpam-5830	132	32	the	the	DET
ejpam-5830	132	33	same	same	ADJ
ejpam-5830	132	34	holds	hold	VERB
ejpam-5830	132	35	for	for	ADP
ejpam-5830	132	36	the	the	DET
ejpam-5830	132	37	solution	solution	NOUN
ejpam-5830	132	38	φ	φ	PROPN
ejpam-5830	132	39	(	(	PUNCT
ejpam-5830	132	40	see	see	VERB
ejpam-5830	132	41	[	[	X
ejpam-5830	132	42	2	2	NUM
ejpam-5830	132	43	]	]	NUM
ejpam-5830	132	44	)	)	PUNCT
ejpam-5830	132	45	.	.	PUNCT
ejpam-5830	133	1	subsequently	subsequently	ADV
ejpam-5830	133	2	,	,	PUNCT
ejpam-5830	133	3	guillemin	guillemin	NOUN
ejpam-5830	133	4	and	and	CCONJ
ejpam-5830	133	5	kazhdan	kazhdan	PROPN
ejpam-5830	133	6	found	find	VERB
ejpam-5830	133	7	c∞	c∞	PROPN
ejpam-5830	133	8	solutions	solution	NOUN
ejpam-5830	133	9	φ	φ	X
ejpam-5830	133	10	for	for	ADP
ejpam-5830	133	11	the	the	DET
ejpam-5830	133	12	case	case	NOUN
ejpam-5830	133	13	of	of	ADP
ejpam-5830	133	14	c∞	c∞	PROPN
ejpam-5830	133	15	geodesic	geodesic	NOUN
ejpam-5830	133	16	flows	flow	VERB
ejpam-5830	133	17	on	on	ADP
ejpam-5830	133	18	surfaces	surface	NOUN
ejpam-5830	133	19	with	with	ADP
ejpam-5830	133	20	negative	negative	ADJ
ejpam-5830	133	21	curvature	curvature	NOUN
ejpam-5830	133	22	[	[	X
ejpam-5830	133	23	21	21	NUM
ejpam-5830	133	24	,	,	PUNCT
ejpam-5830	133	25	22	22	NUM
ejpam-5830	133	26	]	]	PUNCT
ejpam-5830	133	27	.	.	PUNCT
ejpam-5830	134	1	in	in	ADP
ejpam-5830	134	2	turn	turn	NOUN
ejpam-5830	134	3	,	,	PUNCT
ejpam-5830	134	4	collet	collet	NOUN
ejpam-5830	134	5	,	,	PUNCT
ejpam-5830	134	6	epstein	epstein	NOUN
ejpam-5830	134	7	and	and	CCONJ
ejpam-5830	134	8	gallavotti	gallavotti	VERB
ejpam-5830	134	9	in	in	ADP
ejpam-5830	134	10	[	[	X
ejpam-5830	134	11	23	23	NUM
ejpam-5830	134	12	]	]	PUNCT
ejpam-5830	134	13	proved	prove	VERB
ejpam-5830	134	14	an	an	DET
ejpam-5830	134	15	analytic	analytic	ADJ
ejpam-5830	134	16	version	version	NOUN
ejpam-5830	134	17	also	also	ADV
ejpam-5830	134	18	for	for	ADP
ejpam-5830	134	19	geodesic	geodesic	ADJ
ejpam-5830	134	20	flows	flow	NOUN
ejpam-5830	134	21	but	but	CCONJ
ejpam-5830	134	22	only	only	ADV
ejpam-5830	134	23	on	on	ADP
ejpam-5830	134	24	surfaces	surface	NOUN
ejpam-5830	134	25	with	with	ADP
ejpam-5830	134	26	constant	constant	ADJ
ejpam-5830	134	27	negative	negative	ADJ
ejpam-5830	134	28	curvature	curvature	NOUN
ejpam-5830	134	29	.	.	PUNCT
ejpam-5830	135	1	all	all	DET
ejpam-5830	135	2	the	the	DET
ejpam-5830	135	3	aforementioned	aforementioned	ADJ
ejpam-5830	135	4	c∞	c∞	PROPN
ejpam-5830	135	5	and	and	CCONJ
ejpam-5830	135	6	cω	cω	PROPN
ejpam-5830	135	7	regularity	regularity	NOUN
ejpam-5830	135	8	results	result	NOUN
ejpam-5830	135	9	were	be	AUX
ejpam-5830	135	10	obtained	obtain	VERB
ejpam-5830	135	11	through	through	ADP
ejpam-5830	135	12	some	some	DET
ejpam-5830	135	13	form	form	NOUN
ejpam-5830	135	14	of	of	ADP
ejpam-5830	135	15	generalized	generalized	ADJ
ejpam-5830	135	16	harmonic	harmonic	ADJ
ejpam-5830	135	17	analysis	analysis	NOUN
ejpam-5830	135	18	,	,	PUNCT
ejpam-5830	135	19	and	and	CCONJ
ejpam-5830	135	20	as	as	ADP
ejpam-5830	135	21	such	such	ADJ
ejpam-5830	135	22	require	require	VERB
ejpam-5830	135	23	a	a	DET
ejpam-5830	135	24	special	special	ADJ
ejpam-5830	135	25	structure	structure	NOUN
ejpam-5830	135	26	on	on	ADP
ejpam-5830	135	27	the	the	DET
ejpam-5830	135	28	manifold	manifold	NOUN
ejpam-5830	135	29	.	.	PUNCT
ejpam-5830	136	1	only	only	ADV
ejpam-5830	136	2	in	in	ADP
ejpam-5830	136	3	1986	1986	NUM
ejpam-5830	136	4	,	,	PUNCT
ejpam-5830	136	5	using	use	VERB
ejpam-5830	136	6	a	a	DET
ejpam-5830	136	7	geometric	geometric	ADJ
ejpam-5830	136	8	argument	argument	NOUN
ejpam-5830	136	9	,	,	PUNCT
ejpam-5830	136	10	was	be	AUX
ejpam-5830	136	11	a	a	DET
ejpam-5830	136	12	general	general	ADJ
ejpam-5830	136	13	result	result	NOUN
ejpam-5830	136	14	for	for	ADP
ejpam-5830	136	15	c∞	c∞	PROPN
ejpam-5830	136	16	regularity	regularity	NOUN
ejpam-5830	136	17	presented	present	VERB
ejpam-5830	136	18	by	by	ADP
ejpam-5830	136	19	de	de	PROPN
ejpam-5830	136	20	la	la	PROPN
ejpam-5830	136	21	llave	llave	PROPN
ejpam-5830	136	22	,	,	PUNCT
ejpam-5830	136	23	marco	marco	PROPN
ejpam-5830	136	24	,	,	PUNCT
ejpam-5830	136	25	and	and	CCONJ
ejpam-5830	136	26	moriyón	moriyón	PROPN
ejpam-5830	136	27	[	[	X
ejpam-5830	136	28	24	24	NUM
ejpam-5830	136	29	]	]	PUNCT
ejpam-5830	136	30	.	.	PUNCT
ejpam-5830	137	1	theorem	theorem	NOUN
ejpam-5830	137	2	3	3	X
ejpam-5830	137	3	.	.	PUNCT
ejpam-5830	138	1	let	let	VERB
ejpam-5830	138	2	m	m	PRON
ejpam-5830	138	3	be	be	AUX
ejpam-5830	138	4	a	a	DET
ejpam-5830	138	5	compact	compact	ADJ
ejpam-5830	138	6	manifold	manifold	NOUN
ejpam-5830	138	7	,	,	PUNCT
ejpam-5830	138	8	f	f	X
ejpam-5830	138	9	:	:	PUNCT
ejpam-5830	138	10	m	m	VERB
ejpam-5830	138	11	→	→	SYM
ejpam-5830	138	12	m	m	VERB
ejpam-5830	138	13	a	a	DET
ejpam-5830	138	14	topologically	topologically	ADV
ejpam-5830	138	15	transitive	transitive	ADJ
ejpam-5830	138	16	c∞	c∞	PROPN
ejpam-5830	138	17	anosov	anosov	NOUN
ejpam-5830	138	18	diffeomorphism	diffeomorphism	NOUN
ejpam-5830	138	19	,	,	PUNCT
ejpam-5830	138	20	and	and	CCONJ
ejpam-5830	138	21	φ	φ	NOUN
ejpam-5830	138	22	:	:	PUNCT
ejpam-5830	139	1	m	m	VERB
ejpam-5830	139	2	→	→	SYM
ejpam-5830	139	3	r	r	VERB
ejpam-5830	139	4	a	a	DET
ejpam-5830	139	5	c∞	c∞	PROPN
ejpam-5830	139	6	function	function	NOUN
ejpam-5830	139	7	.	.	PUNCT
ejpam-5830	140	1	then	then	ADV
ejpam-5830	140	2	,	,	PUNCT
ejpam-5830	140	3	the	the	DET
ejpam-5830	140	4	following	follow	VERB
ejpam-5830	140	5	statements	statement	NOUN
ejpam-5830	140	6	are	be	AUX
ejpam-5830	140	7	equivalent	equivalent	ADJ
ejpam-5830	140	8	:	:	PUNCT
ejpam-5830	140	9	(	(	PUNCT
ejpam-5830	140	10	i	i	NOUN
ejpam-5830	140	11	)	)	PUNCT
ejpam-5830	140	12	there	there	PRON
ejpam-5830	140	13	exists	exist	VERB
ejpam-5830	140	14	a	a	DET
ejpam-5830	140	15	c∞	c∞	PROPN
ejpam-5830	140	16	function	function	NOUN
ejpam-5830	140	17	φ	φ	NOUN
ejpam-5830	140	18	:	:	PUNCT
ejpam-5830	140	19	m	m	VERB
ejpam-5830	140	20	→	→	SYM
ejpam-5830	140	21	r	r	NOUN
ejpam-5830	140	22	satisfying	satisfy	VERB
ejpam-5830	140	23	φ	φ	PROPN
ejpam-5830	140	24	=	=	SYM
ejpam-5830	140	25	φ	φ	PROPN
ejpam-5830	140	26	◦	◦	NOUN
ejpam-5830	140	27	f	f	PROPN
ejpam-5830	141	1	−	−	PROPN
ejpam-5830	141	2	φ	φ	PROPN
ejpam-5830	141	3	;	;	PUNCT
ejpam-5830	141	4	(	(	PUNCT
ejpam-5830	141	5	ii	ii	NOUN
ejpam-5830	141	6	)	)	PUNCT
ejpam-5830	141	7	for	for	ADP
ejpam-5830	141	8	any	any	DET
ejpam-5830	141	9	periodic	periodic	ADJ
ejpam-5830	141	10	point	point	NOUN
ejpam-5830	141	11	x	x	PUNCT
ejpam-5830	141	12	of	of	ADP
ejpam-5830	141	13	period	period	NOUN
ejpam-5830	141	14	n	n	CCONJ
ejpam-5830	141	15	,	,	PUNCT
ejpam-5830	141	16	n−1∑	n−1∑	PROPN
ejpam-5830	141	17	i=0	i=0	PROPN
ejpam-5830	141	18	φ(f	φ(f	PROPN
ejpam-5830	141	19	ix	ix	PROPN
ejpam-5830	141	20	)	)	PUNCT
ejpam-5830	141	21	=	=	SYM
ejpam-5830	141	22	0	0	X
ejpam-5830	141	23	.	.	PUNCT
ejpam-5830	141	24	r.	r.	PROPN
ejpam-5830	141	25	d.	d.	PROPN
ejpam-5830	141	26	laureano	laureano	PROPN
ejpam-5830	141	27	/	/	SYM
ejpam-5830	141	28	eur	eur	PROPN
ejpam-5830	141	29	.	.	PUNCT
ejpam-5830	142	1	j.	j.	PROPN
ejpam-5830	142	2	pure	pure	PROPN
ejpam-5830	142	3	appl	appl	PROPN
ejpam-5830	142	4	.	.	PROPN
ejpam-5830	142	5	math	math	PROPN
ejpam-5830	142	6	,	,	PUNCT
ejpam-5830	142	7	18	18	NUM
ejpam-5830	142	8	(	(	PUNCT
ejpam-5830	142	9	2	2	NUM
ejpam-5830	142	10	)	)	PUNCT
ejpam-5830	142	11	(	(	PUNCT
ejpam-5830	142	12	2025	2025	NUM
ejpam-5830	142	13	)	)	PUNCT
ejpam-5830	142	14	,	,	PUNCT
ejpam-5830	142	15	5830	5830	NUM
ejpam-5830	142	16	7	7	NUM
ejpam-5830	142	17	of	of	ADP
ejpam-5830	142	18	11	11	NUM
ejpam-5830	142	19	moreover	moreover	ADV
ejpam-5830	142	20	,	,	PUNCT
ejpam-5830	142	21	if	if	SCONJ
ejpam-5830	142	22	f	f	PROPN
ejpam-5830	142	23	is	be	AUX
ejpam-5830	142	24	analytic	analytic	ADJ
ejpam-5830	142	25	,	,	PUNCT
ejpam-5830	142	26	as	as	ADV
ejpam-5830	142	27	well	well	ADV
ejpam-5830	142	28	as	as	ADP
ejpam-5830	142	29	the	the	DET
ejpam-5830	142	30	stable	stable	ADJ
ejpam-5830	142	31	and	and	CCONJ
ejpam-5830	142	32	unstable	unstable	ADJ
ejpam-5830	142	33	bundles	bundle	NOUN
ejpam-5830	142	34	and	and	CCONJ
ejpam-5830	142	35	the	the	DET
ejpam-5830	142	36	function	function	NOUN
ejpam-5830	142	37	φ	φ	PROPN
ejpam-5830	142	38	,	,	PUNCT
ejpam-5830	142	39	then	then	ADV
ejpam-5830	142	40	φ	φ	PROPN
ejpam-5830	142	41	is	be	AUX
ejpam-5830	142	42	analytic	analytic	ADJ
ejpam-5830	142	43	.	.	PUNCT
ejpam-5830	143	1	these	these	DET
ejpam-5830	143	2	authors	author	NOUN
ejpam-5830	143	3	also	also	ADV
ejpam-5830	143	4	established	establish	VERB
ejpam-5830	143	5	a	a	DET
ejpam-5830	143	6	corresponding	corresponding	ADJ
ejpam-5830	143	7	result	result	NOUN
ejpam-5830	143	8	for	for	ADP
ejpam-5830	143	9	flows	flow	NOUN
ejpam-5830	143	10	.	.	PUNCT
ejpam-5830	144	1	theorem	theorem	ADJ
ejpam-5830	144	2	4	4	NUM
ejpam-5830	144	3	.	.	PUNCT
ejpam-5830	145	1	let	let	VERB
ejpam-5830	145	2	m	m	PRON
ejpam-5830	145	3	be	be	AUX
ejpam-5830	145	4	a	a	DET
ejpam-5830	145	5	compact	compact	ADJ
ejpam-5830	145	6	manifold	manifold	NOUN
ejpam-5830	145	7	,	,	PUNCT
ejpam-5830	145	8	ψ	ψ	X
ejpam-5830	145	9	=	=	X
ejpam-5830	145	10	{	{	PUNCT
ejpam-5830	145	11	ψt	ψt	NOUN
ejpam-5830	145	12	}	}	PUNCT
ejpam-5830	145	13	t∈r	t∈r	NOUN
ejpam-5830	145	14	a	a	DET
ejpam-5830	145	15	topologically	topologically	ADV
ejpam-5830	145	16	transitive	transitive	ADJ
ejpam-5830	145	17	c∞	c∞	PROPN
ejpam-5830	145	18	anosov	anosov	NOUN
ejpam-5830	145	19	flow	flow	NOUN
ejpam-5830	145	20	,	,	PUNCT
ejpam-5830	145	21	and	and	CCONJ
ejpam-5830	145	22	φ	φ	NOUN
ejpam-5830	145	23	:	:	PUNCT
ejpam-5830	146	1	m	m	VERB
ejpam-5830	146	2	→	→	SYM
ejpam-5830	146	3	r	r	VERB
ejpam-5830	146	4	a	a	DET
ejpam-5830	146	5	c∞	c∞	PROPN
ejpam-5830	146	6	function	function	NOUN
ejpam-5830	146	7	.	.	PUNCT
ejpam-5830	147	1	then	then	ADV
ejpam-5830	147	2	,	,	PUNCT
ejpam-5830	147	3	the	the	DET
ejpam-5830	147	4	following	follow	VERB
ejpam-5830	147	5	statements	statement	NOUN
ejpam-5830	147	6	are	be	AUX
ejpam-5830	147	7	equivalent	equivalent	ADJ
ejpam-5830	147	8	:	:	PUNCT
ejpam-5830	147	9	(	(	PUNCT
ejpam-5830	147	10	i	i	NOUN
ejpam-5830	147	11	)	)	PUNCT
ejpam-5830	147	12	there	there	PRON
ejpam-5830	147	13	exists	exist	VERB
ejpam-5830	147	14	a	a	DET
ejpam-5830	147	15	c∞	c∞	PROPN
ejpam-5830	147	16	function	function	NOUN
ejpam-5830	147	17	φ	φ	NOUN
ejpam-5830	147	18	:	:	PUNCT
ejpam-5830	147	19	m	m	AUX
ejpam-5830	147	20	→	→	SYM
ejpam-5830	147	21	r	r	NOUN
ejpam-5830	147	22	satisfying	satisfy	VERB
ejpam-5830	147	23	φ(x	φ(x	NOUN
ejpam-5830	147	24	)	)	PUNCT
ejpam-5830	147	25	=	=	SYM
ejpam-5830	148	1	d	d	NOUN
ejpam-5830	148	2	dt	dt	X
ejpam-5830	148	3	φ(ψtx)|t=0	φ(ψtx)|t=0	PUNCT
ejpam-5830	148	4	;	;	PUNCT
ejpam-5830	148	5	(	(	PUNCT
ejpam-5830	148	6	ii	ii	NOUN
ejpam-5830	148	7	)	)	PUNCT
ejpam-5830	148	8	for	for	ADP
ejpam-5830	148	9	any	any	DET
ejpam-5830	148	10	periodic	periodic	ADJ
ejpam-5830	148	11	orbit	orbit	NOUN
ejpam-5830	148	12	{	{	PUNCT
ejpam-5830	148	13	ψtx	ψtx	NOUN
ejpam-5830	148	14	}	}	PUNCT
ejpam-5830	148	15	t∈r	t∈r	NOUN
ejpam-5830	148	16	of	of	ADP
ejpam-5830	148	17	period	period	NOUN
ejpam-5830	148	18	t	t	NOUN
ejpam-5830	148	19	,	,	PUNCT
ejpam-5830	148	20	we	we	PRON
ejpam-5830	148	21	have∫	have∫	VERB
ejpam-5830	148	22	t	t	NOUN
ejpam-5830	148	23	0	0	PUNCT
ejpam-5830	148	24	φ(ψtx	φ(ψtx	NOUN
ejpam-5830	148	25	)	)	PUNCT
ejpam-5830	148	26	dt	dt	NOUN
ejpam-5830	149	1	=	=	PUNCT
ejpam-5830	149	2	0	0	X
ejpam-5830	149	3	.	.	PUNCT
ejpam-5830	150	1	moreover	moreover	ADV
ejpam-5830	150	2	,	,	PUNCT
ejpam-5830	150	3	if	if	SCONJ
ejpam-5830	150	4	ψ	ψ	NOUN
ejpam-5830	150	5	is	be	AUX
ejpam-5830	150	6	analytic	analytic	ADJ
ejpam-5830	150	7	,	,	PUNCT
ejpam-5830	150	8	as	as	ADV
ejpam-5830	150	9	well	well	ADV
ejpam-5830	150	10	as	as	ADP
ejpam-5830	150	11	the	the	DET
ejpam-5830	150	12	stable	stable	ADJ
ejpam-5830	150	13	and	and	CCONJ
ejpam-5830	150	14	unstable	unstable	ADJ
ejpam-5830	150	15	bundles	bundle	NOUN
ejpam-5830	150	16	and	and	CCONJ
ejpam-5830	150	17	the	the	DET
ejpam-5830	150	18	function	function	NOUN
ejpam-5830	150	19	φ	φ	PROPN
ejpam-5830	150	20	,	,	PUNCT
ejpam-5830	150	21	then	then	ADV
ejpam-5830	150	22	φ	φ	PROPN
ejpam-5830	150	23	is	be	AUX
ejpam-5830	150	24	analytic	analytic	ADJ
ejpam-5830	150	25	.	.	PUNCT
ejpam-5830	151	1	in	in	ADP
ejpam-5830	151	2	the	the	DET
ejpam-5830	151	3	proof	proof	NOUN
ejpam-5830	151	4	,	,	PUNCT
ejpam-5830	151	5	an	an	DET
ejpam-5830	151	6	important	important	ADJ
ejpam-5830	151	7	general	general	ADJ
ejpam-5830	151	8	result	result	NOUN
ejpam-5830	151	9	of	of	ADP
ejpam-5830	151	10	harmonic	harmonic	ADJ
ejpam-5830	151	11	analysis	analysis	NOUN
ejpam-5830	151	12	is	be	AUX
ejpam-5830	151	13	used	use	VERB
ejpam-5830	151	14	,	,	PUNCT
ejpam-5830	151	15	which	which	PRON
ejpam-5830	151	16	states	state	VERB
ejpam-5830	151	17	that	that	SCONJ
ejpam-5830	151	18	if	if	SCONJ
ejpam-5830	151	19	a	a	DET
ejpam-5830	151	20	function	function	NOUN
ejpam-5830	151	21	is	be	AUX
ejpam-5830	151	22	of	of	ADP
ejpam-5830	151	23	class	class	NOUN
ejpam-5830	151	24	c∞	c∞	PROPN
ejpam-5830	151	25	along	along	ADP
ejpam-5830	151	26	two	two	NUM
ejpam-5830	151	27	absolutely	absolutely	ADV
ejpam-5830	151	28	continuous	continuous	ADJ
ejpam-5830	151	29	foliations	foliation	NOUN
ejpam-5830	151	30	of	of	ADP
ejpam-5830	151	31	class	class	NOUN
ejpam-5830	151	32	c∞	c∞	PROPN
ejpam-5830	151	33	with	with	ADP
ejpam-5830	151	34	jacobians	jacobian	NOUN
ejpam-5830	151	35	having	have	VERB
ejpam-5830	151	36	certain	certain	ADJ
ejpam-5830	151	37	regularity	regularity	NOUN
ejpam-5830	151	38	properties	property	NOUN
ejpam-5830	151	39	,	,	PUNCT
ejpam-5830	151	40	then	then	ADV
ejpam-5830	151	41	the	the	DET
ejpam-5830	151	42	function	function	NOUN
ejpam-5830	151	43	is	be	AUX
ejpam-5830	151	44	globally	globally	ADV
ejpam-5830	151	45	of	of	ADP
ejpam-5830	151	46	class	class	NOUN
ejpam-5830	151	47	c∞.	c∞.	PROPN
ejpam-5830	151	48	this	this	DET
ejpam-5830	151	49	result	result	NOUN
ejpam-5830	151	50	is	be	AUX
ejpam-5830	151	51	proved	prove	VERB
ejpam-5830	151	52	in	in	ADP
ejpam-5830	151	53	the	the	DET
ejpam-5830	151	54	article	article	NOUN
ejpam-5830	151	55	using	use	VERB
ejpam-5830	151	56	the	the	DET
ejpam-5830	151	57	theory	theory	NOUN
ejpam-5830	151	58	of	of	ADP
ejpam-5830	151	59	elliptic	elliptic	ADJ
ejpam-5830	151	60	operators	operator	NOUN
ejpam-5830	151	61	and	and	CCONJ
ejpam-5830	151	62	the	the	DET
ejpam-5830	151	63	absolute	absolute	ADJ
ejpam-5830	151	64	continuity	continuity	NOUN
ejpam-5830	151	65	of	of	ADP
ejpam-5830	151	66	the	the	DET
ejpam-5830	151	67	jacobian	jacobian	PROPN
ejpam-5830	151	68	along	along	ADP
ejpam-5830	151	69	the	the	DET
ejpam-5830	151	70	stable	stable	ADJ
ejpam-5830	151	71	and	and	CCONJ
ejpam-5830	151	72	unstable	unstable	ADJ
ejpam-5830	151	73	foliations	foliation	NOUN
ejpam-5830	151	74	.	.	PUNCT
ejpam-5830	152	1	since	since	SCONJ
ejpam-5830	152	2	then	then	ADV
ejpam-5830	152	3	,	,	PUNCT
ejpam-5830	152	4	two	two	NUM
ejpam-5830	152	5	new	new	ADJ
ejpam-5830	152	6	proofs	proof	NOUN
ejpam-5830	152	7	for	for	ADP
ejpam-5830	152	8	c∞	c∞	PROPN
ejpam-5830	152	9	anosov	anosov	NOUN
ejpam-5830	152	10	systems	system	NOUN
ejpam-5830	152	11	have	have	AUX
ejpam-5830	152	12	emerged	emerge	VERB
ejpam-5830	152	13	.	.	PUNCT
ejpam-5830	153	1	one	one	NUM
ejpam-5830	153	2	is	be	AUX
ejpam-5830	153	3	due	due	ADJ
ejpam-5830	153	4	to	to	ADP
ejpam-5830	153	5	journé	journé	NOUN
ejpam-5830	153	6	in	in	ADP
ejpam-5830	153	7	[	[	X
ejpam-5830	153	8	25	25	NUM
ejpam-5830	153	9	]	]	PUNCT
ejpam-5830	153	10	.	.	PUNCT
ejpam-5830	154	1	an	an	DET
ejpam-5830	154	2	alternative	alternative	ADJ
ejpam-5830	154	3	approach	approach	NOUN
ejpam-5830	154	4	was	be	AUX
ejpam-5830	154	5	proposed	propose	VERB
ejpam-5830	154	6	by	by	ADP
ejpam-5830	154	7	hurder	hurder	NOUN
ejpam-5830	154	8	and	and	CCONJ
ejpam-5830	154	9	katok	katok	NOUN
ejpam-5830	154	10	in	in	ADP
ejpam-5830	154	11	[	[	X
ejpam-5830	154	12	26	26	NUM
ejpam-5830	154	13	]	]	PUNCT
ejpam-5830	154	14	,	,	PUNCT
ejpam-5830	154	15	based	base	VERB
ejpam-5830	154	16	on	on	ADP
ejpam-5830	154	17	an	an	DET
ejpam-5830	154	18	unpublished	unpublished	ADJ
ejpam-5830	154	19	idea	idea	NOUN
ejpam-5830	154	20	by	by	ADP
ejpam-5830	154	21	toll	toll	NOUN
ejpam-5830	154	22	.	.	PUNCT
ejpam-5830	155	1	building	build	VERB
ejpam-5830	155	2	on	on	ADP
ejpam-5830	155	3	the	the	DET
ejpam-5830	155	4	approach	approach	NOUN
ejpam-5830	155	5	presented	present	VERB
ejpam-5830	155	6	in	in	ADP
ejpam-5830	155	7	[	[	X
ejpam-5830	155	8	26	26	NUM
ejpam-5830	155	9	]	]	PUNCT
ejpam-5830	155	10	,	,	PUNCT
ejpam-5830	155	11	de	de	X
ejpam-5830	155	12	la	la	X
ejpam-5830	155	13	llave	llave	PROPN
ejpam-5830	155	14	later	later	ADV
ejpam-5830	155	15	established	establish	VERB
ejpam-5830	155	16	the	the	DET
ejpam-5830	155	17	analytic	analytic	ADJ
ejpam-5830	155	18	case	case	NOUN
ejpam-5830	155	19	in	in	ADP
ejpam-5830	155	20	1997	1997	NUM
ejpam-5830	155	21	[	[	X
ejpam-5830	155	22	27	27	NUM
ejpam-5830	155	23	]	]	PUNCT
ejpam-5830	155	24	.	.	PUNCT
ejpam-5830	156	1	on	on	ADP
ejpam-5830	156	2	the	the	DET
ejpam-5830	156	3	other	other	ADJ
ejpam-5830	156	4	hand	hand	NOUN
ejpam-5830	156	5	,	,	PUNCT
ejpam-5830	156	6	continuing	continue	VERB
ejpam-5830	156	7	the	the	DET
ejpam-5830	156	8	work	work	NOUN
ejpam-5830	156	9	developed	develop	VERB
ejpam-5830	156	10	by	by	ADP
ejpam-5830	156	11	niţică	niţică	ADJ
ejpam-5830	156	12	and	and	CCONJ
ejpam-5830	156	13	török	török	NOUN
ejpam-5830	156	14	in	in	ADP
ejpam-5830	156	15	[	[	X
ejpam-5830	156	16	16	16	NUM
ejpam-5830	156	17	,	,	PUNCT
ejpam-5830	156	18	20	20	NUM
ejpam-5830	156	19	]	]	PUNCT
ejpam-5830	156	20	,	,	PUNCT
ejpam-5830	156	21	katok	katok	NOUN
ejpam-5830	156	22	,	,	PUNCT
ejpam-5830	156	23	niţică	niţică	NOUN
ejpam-5830	156	24	,	,	PUNCT
ejpam-5830	156	25	and	and	CCONJ
ejpam-5830	156	26	török	török	NOUN
ejpam-5830	156	27	extended	extend	VERB
ejpam-5830	156	28	in	in	ADP
ejpam-5830	156	29	[	[	X
ejpam-5830	156	30	28	28	NUM
ejpam-5830	156	31	]	]	PUNCT
ejpam-5830	156	32	the	the	DET
ejpam-5830	156	33	regularity	regularity	NOUN
ejpam-5830	156	34	results	result	VERB
ejpam-5830	156	35	in	in	ADP
ejpam-5830	156	36	cocycles	cocycle	NOUN
ejpam-5830	156	37	taking	take	VERB
ejpam-5830	156	38	values	value	NOUN
ejpam-5830	156	39	in	in	ADP
ejpam-5830	156	40	lie	lie	NOUN
ejpam-5830	156	41	groups	group	NOUN
ejpam-5830	156	42	and	and	CCONJ
ejpam-5830	156	43	diffeomorphism	diffeomorphism	NOUN
ejpam-5830	156	44	groups	group	NOUN
ejpam-5830	156	45	.	.	PUNCT
ejpam-5830	157	1	4	4	X
ejpam-5830	157	2	.	.	X
ejpam-5830	157	3	cohomology	cohomology	NOUN
ejpam-5830	157	4	in	in	ADP
ejpam-5830	157	5	higher	high	ADJ
ejpam-5830	157	6	dimensions	dimension	NOUN
ejpam-5830	157	7	another	another	DET
ejpam-5830	157	8	direction	direction	NOUN
ejpam-5830	157	9	of	of	ADP
ejpam-5830	157	10	research	research	NOUN
ejpam-5830	157	11	is	be	AUX
ejpam-5830	157	12	the	the	DET
ejpam-5830	157	13	study	study	NOUN
ejpam-5830	157	14	of	of	ADP
ejpam-5830	157	15	cohomology	cohomology	NOUN
ejpam-5830	157	16	in	in	ADP
ejpam-5830	157	17	higher	high	ADJ
ejpam-5830	157	18	dimensions	dimension	NOUN
ejpam-5830	157	19	for	for	ADP
ejpam-5830	157	20	group	group	NOUN
ejpam-5830	157	21	actions	action	NOUN
ejpam-5830	157	22	such	such	ADJ
ejpam-5830	157	23	as	as	ADP
ejpam-5830	157	24	zk	zk	PROPN
ejpam-5830	157	25	and	and	CCONJ
ejpam-5830	157	26	rk	rk	PROPN
ejpam-5830	157	27	for	for	ADP
ejpam-5830	157	28	k	k	PROPN
ejpam-5830	157	29	≥	≥	NUM
ejpam-5830	157	30	2	2	NUM
ejpam-5830	157	31	,	,	PUNCT
ejpam-5830	157	32	as	as	ADV
ejpam-5830	157	33	well	well	ADV
ejpam-5830	157	34	as	as	ADP
ejpam-5830	157	35	their	their	PRON
ejpam-5830	157	36	”	"	PUNCT
ejpam-5830	157	37	non	non	ADJ
ejpam-5830	157	38	-	-	ADJ
ejpam-5830	157	39	invertible	invertible	ADJ
ejpam-5830	157	40	”	"	PUNCT
ejpam-5830	157	41	versions	version	NOUN
ejpam-5830	157	42	zk	zk	PROPN
ejpam-5830	158	1	+	+	NOUN
ejpam-5830	158	2	=	=	PRON
ejpam-5830	158	3	{	{	PUNCT
ejpam-5830	158	4	(	(	PUNCT
ejpam-5830	158	5	n1	n1	NOUN
ejpam-5830	158	6	,	,	PUNCT
ejpam-5830	158	7	.	.	PUNCT
ejpam-5830	158	8	.	.	PUNCT
ejpam-5830	158	9	.	.	PUNCT
ejpam-5830	159	1	,	,	PUNCT
ejpam-5830	159	2	nk	nk	PROPN
ejpam-5830	159	3	)	)	PUNCT
ejpam-5830	159	4	:	:	PUNCT
ejpam-5830	159	5	n1	n1	NOUN
ejpam-5830	159	6	,	,	PUNCT
ejpam-5830	159	7	.	.	PUNCT
ejpam-5830	159	8	.	.	PUNCT
ejpam-5830	159	9	.	.	PUNCT
ejpam-5830	160	1	,	,	PUNCT
ejpam-5830	160	2	nk	nk	PROPN
ejpam-5830	160	3	∈	∈	PROPN
ejpam-5830	160	4	n	n	CCONJ
ejpam-5830	160	5	}	}	PUNCT
ejpam-5830	160	6	and	and	CCONJ
ejpam-5830	160	7	rk	rk	PRON
ejpam-5830	160	8	+	+	NOUN
ejpam-5830	160	9	=	=	PRON
ejpam-5830	160	10	{	{	PUNCT
ejpam-5830	160	11	(	(	PUNCT
ejpam-5830	160	12	x1	x1	PROPN
ejpam-5830	160	13	,	,	PUNCT
ejpam-5830	160	14	.	.	PUNCT
ejpam-5830	160	15	.	.	PUNCT
ejpam-5830	160	16	.	.	PUNCT
ejpam-5830	161	1	,	,	PUNCT
ejpam-5830	161	2	xk	xk	PROPN
ejpam-5830	161	3	)	)	PUNCT
ejpam-5830	161	4	:	:	PUNCT
ejpam-5830	162	1	x1	x1	NUM
ejpam-5830	162	2	,	,	PUNCT
ejpam-5830	162	3	.	.	PUNCT
ejpam-5830	162	4	.	.	PUNCT
ejpam-5830	162	5	.	.	PUNCT
ejpam-5830	163	1	,	,	PUNCT
ejpam-5830	163	2	xk	xk	PROPN
ejpam-5830	163	3	∈	∈	PROPN
ejpam-5830	163	4	r+	r+	PRON
ejpam-5830	163	5	}	}	PUNCT
ejpam-5830	163	6	.	.	PUNCT
ejpam-5830	164	1	let	let	VERB
ejpam-5830	164	2	m	m	PRON
ejpam-5830	164	3	be	be	AUX
ejpam-5830	164	4	a	a	DET
ejpam-5830	164	5	compact	compact	ADJ
ejpam-5830	164	6	manifold	manifold	NOUN
ejpam-5830	164	7	and	and	CCONJ
ejpam-5830	164	8	let	let	VERB
ejpam-5830	164	9	t	t	PROPN
ejpam-5830	164	10	be	be	AUX
ejpam-5830	164	11	an	an	DET
ejpam-5830	164	12	action	action	NOUN
ejpam-5830	164	13	of	of	ADP
ejpam-5830	164	14	zk	zk	PROPN
ejpam-5830	164	15	+	+	X
ejpam-5830	164	16	on	on	SCONJ
ejpam-5830	164	17	m	m	AUX
ejpam-5830	164	18	generated	generate	VERB
ejpam-5830	164	19	by	by	ADP
ejpam-5830	164	20	(	(	PUNCT
ejpam-5830	164	21	not	not	PART
ejpam-5830	164	22	necessarily	necessarily	ADV
ejpam-5830	164	23	invertible	invertible	ADJ
ejpam-5830	164	24	)	)	PUNCT
ejpam-5830	164	25	transformations	transformation	NOUN
ejpam-5830	164	26	f1	f1	NOUN
ejpam-5830	164	27	,	,	PUNCT
ejpam-5830	164	28	.	.	PUNCT
ejpam-5830	164	29	.	.	PUNCT
ejpam-5830	165	1	.	.	PUNCT
ejpam-5830	166	1	,	,	PUNCT
ejpam-5830	166	2	fk	fk	INTJ
ejpam-5830	166	3	:	:	PUNCT
ejpam-5830	166	4	m	m	VERB
ejpam-5830	166	5	→	→	NOUN
ejpam-5830	166	6	m	m	NOUN
ejpam-5830	166	7	of	of	ADP
ejpam-5830	166	8	class	class	NOUN
ejpam-5830	166	9	c∞	c∞	PROPN
ejpam-5830	166	10	that	that	PRON
ejpam-5830	166	11	commute	commute	VERB
ejpam-5830	166	12	with	with	ADP
ejpam-5830	166	13	each	each	DET
ejpam-5830	166	14	other	other	ADJ
ejpam-5830	166	15	,	,	PUNCT
ejpam-5830	166	16	that	that	ADV
ejpam-5830	166	17	is	is	ADV
ejpam-5830	166	18	,	,	PUNCT
ejpam-5830	166	19	fi	fi	NOUN
ejpam-5830	166	20	◦	◦	NOUN
ejpam-5830	166	21	fj	fj	X
ejpam-5830	166	22	=	=	PUNCT
ejpam-5830	166	23	fj	fj	PROPN
ejpam-5830	167	1	◦	◦	NOUN
ejpam-5830	167	2	fi	fi	NOUN
ejpam-5830	167	3	for	for	ADP
ejpam-5830	167	4	all	all	DET
ejpam-5830	167	5	i	i	PRON
ejpam-5830	167	6	and	and	CCONJ
ejpam-5830	167	7	j.	j.	PROPN
ejpam-5830	167	8	for	for	ADP
ejpam-5830	167	9	each	each	DET
ejpam-5830	167	10	n	n	PRON
ejpam-5830	167	11	∈	∈	PROPN
ejpam-5830	167	12	{	{	PUNCT
ejpam-5830	167	13	1	1	NUM
ejpam-5830	167	14	,	,	PUNCT
ejpam-5830	167	15	.	.	PUNCT
ejpam-5830	167	16	.	.	PUNCT
ejpam-5830	168	1	.	.	PUNCT
ejpam-5830	169	1	,	,	PUNCT
ejpam-5830	169	2	k	k	X
ejpam-5830	169	3	}	}	PUNCT
ejpam-5830	169	4	,	,	PUNCT
ejpam-5830	169	5	an	an	DET
ejpam-5830	169	6	n	n	NOUN
ejpam-5830	169	7	-	-	PUNCT
ejpam-5830	169	8	cochain	cochain	NOUN
ejpam-5830	169	9	t	t	NOUN
ejpam-5830	169	10	on	on	ADP
ejpam-5830	169	11	m	m	PROPN
ejpam-5830	169	12	with	with	ADP
ejpam-5830	169	13	values	value	NOUN
ejpam-5830	169	14	in	in	ADP
ejpam-5830	169	15	rl	rl	PROPN
ejpam-5830	169	16	(	(	PUNCT
ejpam-5830	169	17	l	l	X
ejpam-5830	169	18	≥	≥	NUM
ejpam-5830	169	19	1	1	NUM
ejpam-5830	169	20	)	)	PUNCT
ejpam-5830	169	21	is	be	AUX
ejpam-5830	169	22	any	any	DET
ejpam-5830	169	23	function	function	NOUN
ejpam-5830	169	24	α	α	NOUN
ejpam-5830	169	25	:	:	PUNCT
ejpam-5830	169	26	(	(	PUNCT
ejpam-5830	169	27	zk	zk	X
ejpam-5830	170	1	+	+	NOUN
ejpam-5830	170	2	)	)	PUNCT
ejpam-5830	170	3	n	n	PRON
ejpam-5830	170	4	×m	×m	NOUN
ejpam-5830	170	5	→	→	SYM
ejpam-5830	170	6	rl	rl	PROPN
ejpam-5830	170	7	r.	r.	PROPN
ejpam-5830	170	8	d.	d.	PROPN
ejpam-5830	170	9	laureano	laureano	PROPN
ejpam-5830	170	10	/	/	SYM
ejpam-5830	170	11	eur	eur	PROPN
ejpam-5830	170	12	.	.	PUNCT
ejpam-5830	171	1	j.	j.	PROPN
ejpam-5830	171	2	pure	pure	PROPN
ejpam-5830	171	3	appl	appl	PROPN
ejpam-5830	171	4	.	.	PROPN
ejpam-5830	171	5	math	math	PROPN
ejpam-5830	171	6	,	,	PUNCT
ejpam-5830	171	7	18	18	NUM
ejpam-5830	171	8	(	(	PUNCT
ejpam-5830	171	9	2	2	NUM
ejpam-5830	171	10	)	)	PUNCT
ejpam-5830	171	11	(	(	PUNCT
ejpam-5830	171	12	2025	2025	NUM
ejpam-5830	171	13	)	)	PUNCT
ejpam-5830	171	14	,	,	PUNCT
ejpam-5830	171	15	5830	5830	NUM
ejpam-5830	171	16	8	8	NUM
ejpam-5830	171	17	of	of	ADP
ejpam-5830	171	18	11	11	NUM
ejpam-5830	171	19	that	that	PRON
ejpam-5830	171	20	is	be	AUX
ejpam-5830	171	21	multi	multi	ADJ
ejpam-5830	171	22	-	-	ADJ
ejpam-5830	171	23	linear	linear	ADJ
ejpam-5830	171	24	and	and	CCONJ
ejpam-5830	171	25	antisymmetric	antisymmetric	VERB
ejpam-5830	171	26	in	in	ADP
ejpam-5830	171	27	the	the	DET
ejpam-5830	171	28	first	first	ADJ
ejpam-5830	171	29	n	n	ADJ
ejpam-5830	171	30	variables	variable	NOUN
ejpam-5830	171	31	and	and	CCONJ
ejpam-5830	171	32	of	of	ADP
ejpam-5830	171	33	class	class	NOUN
ejpam-5830	171	34	c∞	c∞	PROPN
ejpam-5830	171	35	in	in	ADP
ejpam-5830	171	36	the	the	DET
ejpam-5830	171	37	last	last	ADJ
ejpam-5830	171	38	variable	variable	NOUN
ejpam-5830	171	39	.	.	PUNCT
ejpam-5830	172	1	since	since	SCONJ
ejpam-5830	172	2	a	a	DET
ejpam-5830	172	3	multi	multi	ADJ
ejpam-5830	172	4	-	-	ADJ
ejpam-5830	172	5	linear	linear	ADJ
ejpam-5830	172	6	function	function	NOUN
ejpam-5830	172	7	is	be	AUX
ejpam-5830	172	8	determined	determine	VERB
ejpam-5830	172	9	by	by	ADP
ejpam-5830	172	10	its	its	PRON
ejpam-5830	172	11	coefficients	coefficient	NOUN
ejpam-5830	172	12	,	,	PUNCT
ejpam-5830	172	13	the	the	DET
ejpam-5830	172	14	function	function	NOUN
ejpam-5830	172	15	α	α	NOUN
ejpam-5830	172	16	can	can	AUX
ejpam-5830	172	17	be	be	AUX
ejpam-5830	172	18	viewed	view	VERB
ejpam-5830	172	19	as	as	ADP
ejpam-5830	172	20	a	a	DET
ejpam-5830	172	21	c∞	c∞	PROPN
ejpam-5830	172	22	function	function	NOUN
ejpam-5830	172	23	α	α	NOUN
ejpam-5830	172	24	:	:	PUNCT
ejpam-5830	172	25	m	m	VERB
ejpam-5830	172	26	→	→	PUNCT
ejpam-5830	172	27	(	(	PUNCT
ejpam-5830	172	28	rl	rl	NOUN
ejpam-5830	172	29	)	)	PUNCT
ejpam-5830	172	30	(	(	PUNCT
ejpam-5830	172	31	n	n	X
ejpam-5830	172	32	k	k	NOUN
ejpam-5830	172	33	)	)	PUNCT
ejpam-5830	172	34	with	with	ADP
ejpam-5830	172	35	components	component	NOUN
ejpam-5830	172	36	indexed	index	VERB
ejpam-5830	172	37	by	by	ADP
ejpam-5830	172	38	i1	i1	PROPN
ejpam-5830	172	39	<	<	X
ejpam-5830	172	40	·	·	PUNCT
ejpam-5830	172	41	·	·	PUNCT
ejpam-5830	172	42	·	·	PUNCT
ejpam-5830	173	1	<	<	X
ejpam-5830	173	2	in	in	ADP
ejpam-5830	173	3	,	,	PUNCT
ejpam-5830	173	4	i1	i1	PROPN
ejpam-5830	173	5	,	,	PUNCT
ejpam-5830	173	6	.	.	PUNCT
ejpam-5830	173	7	.	.	PUNCT
ejpam-5830	173	8	.	.	PUNCT
ejpam-5830	174	1	,	,	PUNCT
ejpam-5830	174	2	in	in	ADP
ejpam-5830	174	3	∈	∈	PROPN
ejpam-5830	174	4	{	{	PUNCT
ejpam-5830	174	5	1	1	NUM
ejpam-5830	174	6	,	,	PUNCT
ejpam-5830	174	7	.	.	PUNCT
ejpam-5830	174	8	.	.	PUNCT
ejpam-5830	175	1	.	.	PUNCT
ejpam-5830	176	1	,	,	PUNCT
ejpam-5830	176	2	k	k	X
ejpam-5830	176	3	}	}	PUNCT
ejpam-5830	176	4	.	.	PUNCT
ejpam-5830	177	1	consider	consider	VERB
ejpam-5830	177	2	an	an	DET
ejpam-5830	177	3	operator	operator	NOUN
ejpam-5830	177	4	d	d	NOUN
ejpam-5830	177	5	,	,	PUNCT
ejpam-5830	177	6	referred	refer	VERB
ejpam-5830	177	7	to	to	ADP
ejpam-5830	177	8	as	as	ADP
ejpam-5830	177	9	the	the	DET
ejpam-5830	177	10	coboundary	coboundary	ADJ
ejpam-5830	177	11	operator	operator	NOUN
ejpam-5830	177	12	,	,	PUNCT
ejpam-5830	177	13	which	which	PRON
ejpam-5830	177	14	acts	act	VERB
ejpam-5830	177	15	on	on	ADP
ejpam-5830	177	16	each	each	DET
ejpam-5830	177	17	n	n	NOUN
ejpam-5830	177	18	-	-	PUNCT
ejpam-5830	177	19	cochain	cochain	NOUN
ejpam-5830	177	20	α	α	NOUN
ejpam-5830	177	21	to	to	PART
ejpam-5830	177	22	produce	produce	VERB
ejpam-5830	177	23	an	an	DET
ejpam-5830	177	24	(	(	PUNCT
ejpam-5830	177	25	n+	n+	NUM
ejpam-5830	177	26	1)-cochain	1)-cochain	NUM
ejpam-5830	177	27	dα	dα	X
ejpam-5830	177	28	whose	whose	DET
ejpam-5830	177	29	(	(	PUNCT
ejpam-5830	177	30	k	k	NOUN
ejpam-5830	177	31	n+1	n+1	X
ejpam-5830	177	32	)	)	PUNCT
ejpam-5830	177	33	components	component	NOUN
ejpam-5830	177	34	are	be	AUX
ejpam-5830	177	35	given	give	VERB
ejpam-5830	177	36	by	by	ADP
ejpam-5830	177	37	(	(	PUNCT
ejpam-5830	177	38	dα)i1···in+1	dα)i1···in+1	PROPN
ejpam-5830	177	39	(	(	PUNCT
ejpam-5830	177	40	x	x	NOUN
ejpam-5830	177	41	)	)	PUNCT
ejpam-5830	177	42	=	=	SYM
ejpam-5830	178	1	n+1∑	n+1∑	PROPN
ejpam-5830	178	2	j=1	j=1	NOUN
ejpam-5830	178	3	(	(	PUNCT
ejpam-5830	178	4	−1)j+1	−1)j+1	ADP
ejpam-5830	178	5	[	[	X
ejpam-5830	178	6	αi1···îj	αi1···îj	X
ejpam-5830	178	7	·	·	SYM
ejpam-5830	178	8	·	·	PUNCT
ejpam-5830	178	9	·	·	SYM
ejpam-5830	178	10	in+1	in+1	PROPN
ejpam-5830	178	11	(	(	PUNCT
ejpam-5830	178	12	fijx)−	fijx)−	PROPN
ejpam-5830	178	13	αi1···îj	αi1···îj	PROPN
ejpam-5830	178	14	·	·	SYM
ejpam-5830	178	15	·	·	PUNCT
ejpam-5830	178	16	·	·	SYM
ejpam-5830	178	17	in+1	in+1	PROPN
ejpam-5830	178	18	(	(	PUNCT
ejpam-5830	178	19	x	x	NOUN
ejpam-5830	178	20	)	)	PUNCT
ejpam-5830	178	21	]	]	PUNCT
ejpam-5830	178	22	.	.	PUNCT
ejpam-5830	179	1	here	here	ADV
ejpam-5830	179	2	,	,	PUNCT
ejpam-5830	179	3	the	the	DET
ejpam-5830	179	4	notation	notation	NOUN
ejpam-5830	179	5	îj	îj	NOUN
ejpam-5830	179	6	indicates	indicate	VERB
ejpam-5830	179	7	that	that	SCONJ
ejpam-5830	179	8	the	the	DET
ejpam-5830	179	9	index	index	NOUN
ejpam-5830	179	10	ij	ij	NOUN
ejpam-5830	179	11	is	be	AUX
ejpam-5830	179	12	omitted	omit	VERB
ejpam-5830	179	13	.	.	PUNCT
ejpam-5830	180	1	it	it	PRON
ejpam-5830	180	2	is	be	AUX
ejpam-5830	180	3	straightforward	straightforward	ADJ
ejpam-5830	180	4	to	to	PART
ejpam-5830	180	5	verify	verify	VERB
ejpam-5830	180	6	that	that	DET
ejpam-5830	180	7	d2	d2	NOUN
ejpam-5830	180	8	=	=	SYM
ejpam-5830	180	9	0	0	PROPN
ejpam-5830	180	10	,	,	PUNCT
ejpam-5830	180	11	which	which	PRON
ejpam-5830	180	12	allows	allow	VERB
ejpam-5830	180	13	the	the	DET
ejpam-5830	180	14	introduction	introduction	NOUN
ejpam-5830	180	15	of	of	ADP
ejpam-5830	180	16	a	a	DET
ejpam-5830	180	17	notion	notion	NOUN
ejpam-5830	180	18	of	of	ADP
ejpam-5830	180	19	cohomology	cohomology	NOUN
ejpam-5830	180	20	associated	associate	VERB
ejpam-5830	180	21	with	with	ADP
ejpam-5830	180	22	the	the	DET
ejpam-5830	180	23	coboundary	coboundary	ADJ
ejpam-5830	180	24	operator	operator	NOUN
ejpam-5830	180	25	.	.	PUNCT
ejpam-5830	181	1	the	the	DET
ejpam-5830	181	2	cohomology	cohomology	NOUN
ejpam-5830	181	3	of	of	ADP
ejpam-5830	181	4	the	the	DET
ejpam-5830	181	5	n	n	NOUN
ejpam-5830	181	6	-	-	PUNCT
ejpam-5830	181	7	cochain	cochain	NOUN
ejpam-5830	181	8	is	be	AUX
ejpam-5830	181	9	known	know	VERB
ejpam-5830	181	10	as	as	ADP
ejpam-5830	181	11	n	n	NOUN
ejpam-5830	181	12	-	-	PUNCT
ejpam-5830	181	13	th	th	X
ejpam-5830	181	14	cohomology	cohomology	NOUN
ejpam-5830	181	15	c∞	c∞	PROPN
ejpam-5830	181	16	of	of	ADP
ejpam-5830	181	17	the	the	DET
ejpam-5830	181	18	action	action	NOUN
ejpam-5830	181	19	t	t	NOUN
ejpam-5830	181	20	.	.	PUNCT
ejpam-5830	182	1	the	the	DET
ejpam-5830	182	2	action	action	NOUN
ejpam-5830	182	3	t	t	PROPN
ejpam-5830	182	4	of	of	ADP
ejpam-5830	182	5	zk	zk	PROPN
ejpam-5830	182	6	+	+	X
ejpam-5830	182	7	on	on	ADP
ejpam-5830	182	8	m	m	NOUN
ejpam-5830	182	9	naturally	naturally	ADV
ejpam-5830	182	10	induces	induce	VERB
ejpam-5830	182	11	orbits	orbit	NOUN
ejpam-5830	182	12	in	in	ADP
ejpam-5830	182	13	m	m	PROPN
ejpam-5830	182	14	.	.	PUNCT
ejpam-5830	183	1	let	let	VERB
ejpam-5830	183	2	pt	pt	PROPN
ejpam-5830	183	3	denote	denote	VERB
ejpam-5830	183	4	the	the	DET
ejpam-5830	183	5	set	set	NOUN
ejpam-5830	183	6	of	of	ADP
ejpam-5830	183	7	all	all	DET
ejpam-5830	183	8	periodic	periodic	ADJ
ejpam-5830	183	9	orbits	orbit	NOUN
ejpam-5830	183	10	of	of	ADP
ejpam-5830	183	11	the	the	DET
ejpam-5830	183	12	action	action	NOUN
ejpam-5830	183	13	t	t	NOUN
ejpam-5830	183	14	,	,	PUNCT
ejpam-5830	183	15	that	that	ADV
ejpam-5830	183	16	is	is	ADV
ejpam-5830	183	17	,	,	PUNCT
ejpam-5830	183	18	the	the	DET
ejpam-5830	183	19	finite	finite	ADJ
ejpam-5830	183	20	orbits	orbit	NOUN
ejpam-5830	183	21	of	of	ADP
ejpam-5830	183	22	t	t	PROPN
ejpam-5830	183	23	.	.	PUNCT
ejpam-5830	184	1	for	for	ADP
ejpam-5830	184	2	a	a	DET
ejpam-5830	184	3	periodic	periodic	ADJ
ejpam-5830	184	4	orbit	orbit	NOUN
ejpam-5830	184	5	o	o	X
ejpam-5830	184	6	∈	∈	PROPN
ejpam-5830	184	7	pt	pt	NOUN
ejpam-5830	184	8	,	,	PUNCT
ejpam-5830	184	9	let	let	VERB
ejpam-5830	184	10	µo	µo	PART
ejpam-5830	184	11	be	be	AUX
ejpam-5830	184	12	the	the	DET
ejpam-5830	184	13	unique	unique	ADJ
ejpam-5830	184	14	normalized	normalize	VERB
ejpam-5830	184	15	t	t	NOUN
ejpam-5830	184	16	-invariant	-invariant	PROPN
ejpam-5830	184	17	measure	measure	NOUN
ejpam-5830	184	18	associated	associate	VERB
ejpam-5830	184	19	with	with	ADP
ejpam-5830	184	20	o.	o.	NOUN
ejpam-5830	184	21	integrating	integrate	VERB
ejpam-5830	184	22	α	α	NOUN
ejpam-5830	184	23	with	with	ADP
ejpam-5830	184	24	respect	respect	NOUN
ejpam-5830	184	25	to	to	ADP
ejpam-5830	184	26	this	this	DET
ejpam-5830	184	27	measure	measure	NOUN
ejpam-5830	184	28	produces	produce	VERB
ejpam-5830	184	29	a	a	DET
ejpam-5830	184	30	n	n	NOUN
ejpam-5830	184	31	-	-	PUNCT
ejpam-5830	184	32	cocycle	cocycle	NOUN
ejpam-5830	184	33	over	over	ADP
ejpam-5830	184	34	t	t	PROPN
ejpam-5830	184	35	that	that	PRON
ejpam-5830	184	36	is	be	AUX
ejpam-5830	184	37	independent	independent	ADJ
ejpam-5830	184	38	of	of	ADP
ejpam-5830	184	39	the	the	DET
ejpam-5830	184	40	last	last	ADJ
ejpam-5830	184	41	variable	variable	NOUN
ejpam-5830	184	42	,	,	PUNCT
ejpam-5830	184	43	which	which	PRON
ejpam-5830	184	44	determines	determine	VERB
ejpam-5830	184	45	an	an	DET
ejpam-5830	184	46	element	element	NOUN
ejpam-5830	185	1	[	[	X
ejpam-5830	185	2	α]o	α]o	X
ejpam-5830	185	3	∈	∈	X
ejpam-5830	185	4	hn	hn	INTJ
ejpam-5830	185	5	(	(	PUNCT
ejpam-5830	185	6	zk	zk	PROPN
ejpam-5830	185	7	+	+	NOUN
ejpam-5830	185	8	;	;	PUNCT
ejpam-5830	185	9	rl	rl	X
ejpam-5830	185	10	)	)	PUNCT
ejpam-5830	185	11	in	in	ADP
ejpam-5830	185	12	the	the	DET
ejpam-5830	185	13	n	n	CCONJ
ejpam-5830	185	14	-	-	PUNCT
ejpam-5830	185	15	th	th	X
ejpam-5830	185	16	c∞	c∞	PROPN
ejpam-5830	185	17	cohomology	cohomology	NOUN
ejpam-5830	185	18	class	class	NOUN
ejpam-5830	185	19	with	with	ADP
ejpam-5830	185	20	respect	respect	NOUN
ejpam-5830	185	21	to	to	ADP
ejpam-5830	185	22	the	the	DET
ejpam-5830	185	23	coboundary	coboundary	ADJ
ejpam-5830	185	24	operator	operator	NOUN
ejpam-5830	185	25	.	.	PUNCT
ejpam-5830	186	1	each	each	DET
ejpam-5830	186	2	[	[	X
ejpam-5830	186	3	α]o	α]o	X
ejpam-5830	186	4	is	be	AUX
ejpam-5830	186	5	a	a	DET
ejpam-5830	186	6	cohomological	cohomological	ADJ
ejpam-5830	186	7	invariant	invariant	NOUN
ejpam-5830	186	8	of	of	ADP
ejpam-5830	186	9	α	α	PRON
ejpam-5830	186	10	,	,	PUNCT
ejpam-5830	186	11	meaning	mean	VERB
ejpam-5830	186	12	that	that	SCONJ
ejpam-5830	186	13	[	[	X
ejpam-5830	186	14	α]o	α]o	X
ejpam-5830	187	1	=	=	X
ejpam-5830	188	1	[	[	X
ejpam-5830	188	2	β]o	β]o	VERB
ejpam-5830	188	3	whenever	whenever	SCONJ
ejpam-5830	188	4	α	α	PROPN
ejpam-5830	188	5	(	(	PUNCT
ejpam-5830	188	6	t	t	PROPN
ejpam-5830	188	7	,	,	PUNCT
ejpam-5830	188	8	x	x	NOUN
ejpam-5830	188	9	)	)	PUNCT
ejpam-5830	188	10	=	=	SYM
ejpam-5830	188	11	β	β	X
ejpam-5830	188	12	(	(	PUNCT
ejpam-5830	188	13	t	t	PROPN
ejpam-5830	188	14	,	,	PUNCT
ejpam-5830	188	15	x	x	NOUN
ejpam-5830	188	16	)	)	PUNCT
ejpam-5830	188	17	+	+	ADV
ejpam-5830	188	18	dφ	dφ	X
ejpam-5830	188	19	(	(	PUNCT
ejpam-5830	188	20	t	t	PROPN
ejpam-5830	188	21	,	,	PUNCT
ejpam-5830	188	22	x	x	NOUN
ejpam-5830	188	23	)	)	PUNCT
ejpam-5830	188	24	,	,	PUNCT
ejpam-5830	188	25	(	(	PUNCT
ejpam-5830	188	26	5	5	NUM
ejpam-5830	188	27	)	)	PUNCT
ejpam-5830	188	28	since	since	SCONJ
ejpam-5830	188	29	[	[	X
ejpam-5830	188	30	dφ]o	dφ]o	NOUN
ejpam-5830	188	31	=	=	SYM
ejpam-5830	188	32	0	0	NUM
ejpam-5830	188	33	.	.	PUNCT
ejpam-5830	189	1	the	the	DET
ejpam-5830	189	2	action	action	NOUN
ejpam-5830	189	3	t	t	PROPN
ejpam-5830	189	4	is	be	AUX
ejpam-5830	189	5	said	say	VERB
ejpam-5830	189	6	to	to	PART
ejpam-5830	189	7	satisfy	satisfy	VERB
ejpam-5830	189	8	the	the	DET
ejpam-5830	189	9	c∞	c∞	PROPN
ejpam-5830	189	10	livschitz	livschitz	NOUN
ejpam-5830	189	11	property	property	NOUN
ejpam-5830	189	12	for	for	ADP
ejpam-5830	189	13	n	n	NOUN
ejpam-5830	189	14	-	-	PUNCT
ejpam-5830	189	15	cocycles	cocycle	NOUN
ejpam-5830	189	16	if	if	SCONJ
ejpam-5830	189	17	the	the	DET
ejpam-5830	189	18	set	set	NOUN
ejpam-5830	189	19	{	{	PUNCT
ejpam-5830	189	20	[	[	X
ejpam-5830	189	21	α]o	α]o	X
ejpam-5830	189	22	|	|	NOUN
ejpam-5830	189	23	o	o	X
ejpam-5830	189	24	∈	∈	PROPN
ejpam-5830	189	25	pt	pt	PROPN
ejpam-5830	189	26	}	}	PUNCT
ejpam-5830	189	27	constitutes	constitute	VERB
ejpam-5830	189	28	a	a	DET
ejpam-5830	189	29	complete	complete	ADJ
ejpam-5830	189	30	set	set	NOUN
ejpam-5830	189	31	of	of	ADP
ejpam-5830	189	32	cohomology	cohomology	NOUN
ejpam-5830	189	33	invariants	invariant	NOUN
ejpam-5830	189	34	for	for	ADP
ejpam-5830	189	35	n	n	NOUN
ejpam-5830	189	36	-	-	PUNCT
ejpam-5830	189	37	cocycles	cocycle	NOUN
ejpam-5830	189	38	of	of	ADP
ejpam-5830	189	39	class	class	NOUN
ejpam-5830	189	40	c∞.	c∞.	PROPN
ejpam-5830	189	41	that	that	PRON
ejpam-5830	189	42	is	be	AUX
ejpam-5830	189	43	,	,	PUNCT
ejpam-5830	189	44	if	if	SCONJ
ejpam-5830	189	45	given	give	VERB
ejpam-5830	189	46	n	n	CCONJ
ejpam-5830	189	47	-	-	PUNCT
ejpam-5830	189	48	cocycles	cocycle	NOUN
ejpam-5830	189	49	of	of	ADP
ejpam-5830	189	50	class	class	NOUN
ejpam-5830	189	51	c∞	c∞	PROPN
ejpam-5830	189	52	α	α	NOUN
ejpam-5830	189	53	and	and	CCONJ
ejpam-5830	189	54	β	β	PRON
ejpam-5830	190	1	such	such	ADJ
ejpam-5830	190	2	that	that	SCONJ
ejpam-5830	190	3	[	[	X
ejpam-5830	190	4	α]o	α]o	X
ejpam-5830	190	5	=	=	X
ejpam-5830	191	1	[	[	X
ejpam-5830	191	2	β]o	β]o	VERB
ejpam-5830	191	3	for	for	ADP
ejpam-5830	191	4	every	every	DET
ejpam-5830	191	5	periodic	periodic	ADJ
ejpam-5830	191	6	orbit	orbit	NOUN
ejpam-5830	191	7	o	o	NOUN
ejpam-5830	191	8	,	,	PUNCT
ejpam-5830	191	9	there	there	PRON
ejpam-5830	191	10	exists	exist	VERB
ejpam-5830	191	11	a	a	DET
ejpam-5830	191	12	(	(	PUNCT
ejpam-5830	191	13	n−	n−	NOUN
ejpam-5830	191	14	1)-cochain	1)-cochain	NUM
ejpam-5830	191	15	φ	φ	PROPN
ejpam-5830	191	16	that	that	PRON
ejpam-5830	191	17	is	be	AUX
ejpam-5830	191	18	a	a	DET
ejpam-5830	191	19	solution	solution	NOUN
ejpam-5830	191	20	of	of	ADP
ejpam-5830	191	21	equation	equation	NOUN
ejpam-5830	191	22	(	(	PUNCT
ejpam-5830	191	23	5	5	NUM
ejpam-5830	191	24	)	)	PUNCT
ejpam-5830	191	25	.	.	PUNCT
ejpam-5830	192	1	in	in	ADP
ejpam-5830	192	2	this	this	DET
ejpam-5830	192	3	case	case	NOUN
ejpam-5830	192	4	,	,	PUNCT
ejpam-5830	192	5	the	the	DET
ejpam-5830	192	6	n	n	NOUN
ejpam-5830	192	7	-	-	PUNCT
ejpam-5830	192	8	cocycles	cocycle	NOUN
ejpam-5830	192	9	of	of	ADP
ejpam-5830	192	10	class	class	NOUN
ejpam-5830	192	11	c∞	c∞	PROPN
ejpam-5830	192	12	α	α	NOUN
ejpam-5830	192	13	and	and	CCONJ
ejpam-5830	192	14	β	β	X
ejpam-5830	192	15	are	be	AUX
ejpam-5830	192	16	said	say	VERB
ejpam-5830	192	17	to	to	PART
ejpam-5830	192	18	be	be	AUX
ejpam-5830	192	19	c∞-cohomologous	c∞-cohomologous	ADJ
ejpam-5830	192	20	.	.	PUNCT
ejpam-5830	193	1	an	an	DET
ejpam-5830	193	2	n	n	NUM
ejpam-5830	193	3	-	-	PUNCT
ejpam-5830	193	4	cocycle	cocycle	NOUN
ejpam-5830	193	5	α	α	PROPN
ejpam-5830	193	6	(	(	PUNCT
ejpam-5830	193	7	t	t	PROPN
ejpam-5830	193	8	,	,	PUNCT
ejpam-5830	193	9	x	x	NOUN
ejpam-5830	193	10	)	)	PUNCT
ejpam-5830	193	11	of	of	ADP
ejpam-5830	193	12	class	class	NOUN
ejpam-5830	193	13	c∞	c∞	PROPN
ejpam-5830	193	14	is	be	AUX
ejpam-5830	193	15	called	call	VERB
ejpam-5830	193	16	cohomologically	cohomologically	ADV
ejpam-5830	193	17	trivial	trivial	ADJ
ejpam-5830	193	18	if	if	SCONJ
ejpam-5830	193	19	it	it	PRON
ejpam-5830	193	20	is	be	AUX
ejpam-5830	193	21	cohomologous	cohomologous	ADJ
ejpam-5830	193	22	to	to	ADP
ejpam-5830	193	23	a	a	DET
ejpam-5830	193	24	constant	constant	ADJ
ejpam-5830	193	25	n	n	CCONJ
ejpam-5830	193	26	-	-	PUNCT
ejpam-5830	193	27	cocycle	cocycle	NOUN
ejpam-5830	193	28	β(t	β(t	PROPN
ejpam-5830	193	29	)	)	PUNCT
ejpam-5830	193	30	.	.	PUNCT
ejpam-5830	194	1	the	the	DET
ejpam-5830	194	2	(	(	PUNCT
ejpam-5830	194	3	n−	n−	NOUN
ejpam-5830	194	4	1)-cochain	1)-cochain	NUM
ejpam-5830	194	5	φ	φ	PROPN
ejpam-5830	194	6	that	that	PRON
ejpam-5830	194	7	is	be	AUX
ejpam-5830	194	8	a	a	DET
ejpam-5830	194	9	solution	solution	NOUN
ejpam-5830	194	10	of	of	ADP
ejpam-5830	194	11	equation	equation	NOUN
ejpam-5830	194	12	(	(	PUNCT
ejpam-5830	194	13	5	5	NUM
ejpam-5830	194	14	)	)	PUNCT
ejpam-5830	194	15	is	be	AUX
ejpam-5830	194	16	called	call	VERB
ejpam-5830	194	17	a	a	DET
ejpam-5830	194	18	trivialization	trivialization	NOUN
ejpam-5830	194	19	of	of	ADP
ejpam-5830	194	20	α	α	NOUN
ejpam-5830	194	21	.	.	PUNCT
ejpam-5830	195	1	an	an	DET
ejpam-5830	195	2	n	n	NUM
ejpam-5830	195	3	-	-	PUNCT
ejpam-5830	195	4	cocycle	cocycle	NOUN
ejpam-5830	195	5	α	α	NOUN
ejpam-5830	195	6	of	of	ADP
ejpam-5830	195	7	class	class	NOUN
ejpam-5830	195	8	c∞	c∞	PROPN
ejpam-5830	195	9	cohomologous	cohomologous	ADJ
ejpam-5830	195	10	to	to	ADP
ejpam-5830	195	11	the	the	DET
ejpam-5830	195	12	trivial	trivial	ADJ
ejpam-5830	195	13	cocycle	cocycle	NOUN
ejpam-5830	195	14	β(t	β(t	PROPN
ejpam-5830	195	15	)	)	PUNCT
ejpam-5830	196	1	=	=	SYM
ejpam-5830	196	2	0	0	NUM
ejpam-5830	197	1	for	for	ADP
ejpam-5830	197	2	all	all	DET
ejpam-5830	197	3	t	t	NOUN
ejpam-5830	197	4	∈	∈	X
ejpam-5830	197	5	zk	zk	PROPN
ejpam-5830	197	6	+	+	X
ejpam-5830	197	7	is	be	AUX
ejpam-5830	197	8	called	call	VERB
ejpam-5830	197	9	a	a	DET
ejpam-5830	197	10	coboundary	coboundary	NOUN
ejpam-5830	197	11	,	,	PUNCT
ejpam-5830	197	12	and	and	CCONJ
ejpam-5830	197	13	equation	equation	NOUN
ejpam-5830	197	14	α	α	X
ejpam-5830	197	15	(	(	PUNCT
ejpam-5830	197	16	t	t	PROPN
ejpam-5830	197	17	,	,	PUNCT
ejpam-5830	197	18	x	x	NOUN
ejpam-5830	197	19	)	)	PUNCT
ejpam-5830	197	20	=	=	SYM
ejpam-5830	197	21	dφ	dφ	X
ejpam-5830	197	22	(	(	PUNCT
ejpam-5830	197	23	t	t	PROPN
ejpam-5830	197	24	,	,	PUNCT
ejpam-5830	197	25	x	x	X
ejpam-5830	197	26	)	)	PUNCT
ejpam-5830	197	27	is	be	AUX
ejpam-5830	197	28	called	call	VERB
ejpam-5830	197	29	the	the	DET
ejpam-5830	197	30	cohomological	cohomological	ADJ
ejpam-5830	197	31	equation	equation	NOUN
ejpam-5830	197	32	.	.	PUNCT
ejpam-5830	198	1	similarly	similarly	ADV
ejpam-5830	198	2	,	,	PUNCT
ejpam-5830	198	3	c∞	c∞	PROPN
ejpam-5830	198	4	cohomology	cohomology	NOUN
ejpam-5830	198	5	can	can	AUX
ejpam-5830	198	6	be	be	AUX
ejpam-5830	198	7	defined	define	VERB
ejpam-5830	198	8	for	for	ADP
ejpam-5830	198	9	an	an	DET
ejpam-5830	198	10	action	action	NOUN
ejpam-5830	198	11	t	t	NOUN
ejpam-5830	198	12	of	of	ADP
ejpam-5830	198	13	g	g	PROPN
ejpam-5830	198	14	=	=	PUNCT
ejpam-5830	198	15	zk	zk	PROPN
ejpam-5830	198	16	or	or	CCONJ
ejpam-5830	198	17	g	g	PROPN
ejpam-5830	198	18	=	=	NOUN
ejpam-5830	198	19	rk	rk	NOUN
ejpam-5830	198	20	.	.	NOUN
ejpam-5830	199	1	in	in	ADP
ejpam-5830	199	2	the	the	DET
ejpam-5830	199	3	case	case	NOUN
ejpam-5830	199	4	g	g	NOUN
ejpam-5830	199	5	=	=	SYM
ejpam-5830	199	6	rk	rk	PROPN
ejpam-5830	199	7	,	,	PUNCT
ejpam-5830	199	8	the	the	DET
ejpam-5830	199	9	n	n	NUM
ejpam-5830	199	10	-	-	PUNCT
ejpam-5830	199	11	cochains	cochain	NOUN
ejpam-5830	199	12	are	be	AUX
ejpam-5830	199	13	vector	vector	NOUN
ejpam-5830	199	14	fields	field	NOUN
ejpam-5830	199	15	of	of	ADP
ejpam-5830	199	16	n	n	CCONJ
ejpam-5830	199	17	-	-	PUNCT
ejpam-5830	199	18	differential	differential	NOUN
ejpam-5830	199	19	forms	form	NOUN
ejpam-5830	199	20	,	,	PUNCT
ejpam-5830	199	21	the	the	DET
ejpam-5830	199	22	cocycles	cocycle	NOUN
ejpam-5830	199	23	correspond	correspond	VERB
ejpam-5830	199	24	to	to	ADP
ejpam-5830	199	25	vector	vector	NOUN
ejpam-5830	199	26	fields	field	NOUN
ejpam-5830	199	27	of	of	ADP
ejpam-5830	199	28	closed	closed	ADJ
ejpam-5830	199	29	forms	form	NOUN
ejpam-5830	199	30	,	,	PUNCT
ejpam-5830	199	31	and	and	CCONJ
ejpam-5830	199	32	the	the	DET
ejpam-5830	199	33	coboundary	coboundary	ADJ
ejpam-5830	199	34	operators	operator	NOUN
ejpam-5830	199	35	d	d	X
ejpam-5830	199	36	are	be	AUX
ejpam-5830	199	37	given	give	VERB
ejpam-5830	199	38	by	by	ADP
ejpam-5830	199	39	restrictions	restriction	NOUN
ejpam-5830	199	40	to	to	ADP
ejpam-5830	199	41	the	the	DET
ejpam-5830	199	42	orbit	orbit	NOUN
ejpam-5830	199	43	foliation	foliation	NOUN
ejpam-5830	199	44	of	of	ADP
ejpam-5830	199	45	(	(	PUNCT
ejpam-5830	199	46	n−1)-differential	n−1)-differential	ADJ
ejpam-5830	199	47	forms	form	NOUN
ejpam-5830	199	48	of	of	ADP
ejpam-5830	199	49	class	class	NOUN
ejpam-5830	199	50	c∞	c∞	PROPN
ejpam-5830	199	51	globally	globally	ADV
ejpam-5830	199	52	defined	define	VERB
ejpam-5830	199	53	.	.	PUNCT
ejpam-5830	200	1	r.	r.	PROPN
ejpam-5830	200	2	d.	d.	PROPN
ejpam-5830	200	3	laureano	laureano	PROPN
ejpam-5830	200	4	/	/	SYM
ejpam-5830	200	5	eur	eur	PROPN
ejpam-5830	200	6	.	.	PUNCT
ejpam-5830	201	1	j.	j.	PROPN
ejpam-5830	201	2	pure	pure	PROPN
ejpam-5830	201	3	appl	appl	PROPN
ejpam-5830	201	4	.	.	PROPN
ejpam-5830	201	5	math	math	PROPN
ejpam-5830	201	6	,	,	PUNCT
ejpam-5830	201	7	18	18	NUM
ejpam-5830	201	8	(	(	PUNCT
ejpam-5830	201	9	2	2	NUM
ejpam-5830	201	10	)	)	PUNCT
ejpam-5830	201	11	(	(	PUNCT
ejpam-5830	201	12	2025	2025	NUM
ejpam-5830	201	13	)	)	PUNCT
ejpam-5830	201	14	,	,	PUNCT
ejpam-5830	201	15	5830	5830	NUM
ejpam-5830	201	16	9	9	NUM
ejpam-5830	201	17	of	of	ADP
ejpam-5830	201	18	11	11	NUM
ejpam-5830	201	19	in	in	ADP
ejpam-5830	201	20	[	[	X
ejpam-5830	201	21	29	29	NUM
ejpam-5830	201	22	]	]	PUNCT
ejpam-5830	201	23	,	,	PUNCT
ejpam-5830	201	24	katok	katok	NOUN
ejpam-5830	201	25	and	and	CCONJ
ejpam-5830	201	26	katok	katok	ADV
ejpam-5830	201	27	used	use	VERB
ejpam-5830	201	28	a	a	DET
ejpam-5830	201	29	version	version	NOUN
ejpam-5830	201	30	of	of	ADP
ejpam-5830	201	31	veech	veech	NOUN
ejpam-5830	201	32	’s	’s	PART
ejpam-5830	201	33	method	method	NOUN
ejpam-5830	201	34	in	in	ADP
ejpam-5830	201	35	[	[	X
ejpam-5830	201	36	10	10	NUM
ejpam-5830	201	37	]	]	PUNCT
ejpam-5830	201	38	to	to	PART
ejpam-5830	201	39	study	study	VERB
ejpam-5830	201	40	c∞	c∞	PROPN
ejpam-5830	201	41	cohomology	cohomology	NOUN
ejpam-5830	201	42	for	for	ADP
ejpam-5830	201	43	actions	action	NOUN
ejpam-5830	201	44	of	of	ADP
ejpam-5830	201	45	hyperbolic	hyperbolic	ADJ
ejpam-5830	201	46	automorphisms	automorphism	NOUN
ejpam-5830	201	47	of	of	ADP
ejpam-5830	201	48	the	the	DET
ejpam-5830	201	49	torus	torus	PROPN
ejpam-5830	201	50	tn	tn	PROPN
ejpam-5830	201	51	.	.	PUNCT
ejpam-5830	202	1	they	they	PRON
ejpam-5830	202	2	obtained	obtain	VERB
ejpam-5830	202	3	,	,	PUNCT
ejpam-5830	202	4	in	in	ADP
ejpam-5830	202	5	particular	particular	ADJ
ejpam-5830	202	6	,	,	PUNCT
ejpam-5830	202	7	the	the	DET
ejpam-5830	202	8	following	follow	VERB
ejpam-5830	202	9	results	result	NOUN
ejpam-5830	202	10	.	.	PUNCT
ejpam-5830	203	1	theorem	theorem	NOUN
ejpam-5830	203	2	5	5	NUM
ejpam-5830	203	3	.	.	PUNCT
ejpam-5830	204	1	let	let	VERB
ejpam-5830	204	2	t	t	PROPN
ejpam-5830	204	3	be	be	AUX
ejpam-5830	204	4	an	an	DET
ejpam-5830	204	5	action	action	NOUN
ejpam-5830	204	6	of	of	ADP
ejpam-5830	204	7	zk	zk	PROPN
ejpam-5830	204	8	by	by	ADP
ejpam-5830	204	9	hyperbolic	hyperbolic	ADJ
ejpam-5830	204	10	automorphisms	automorphism	NOUN
ejpam-5830	204	11	of	of	ADP
ejpam-5830	204	12	tn	tn	PROPN
ejpam-5830	204	13	,	,	PUNCT
ejpam-5830	204	14	and	and	CCONJ
ejpam-5830	204	15	let	let	VERB
ejpam-5830	204	16	α	α	PRON
ejpam-5830	204	17	be	be	AUX
ejpam-5830	204	18	a	a	DET
ejpam-5830	204	19	k	k	NOUN
ejpam-5830	204	20	-	-	NOUN
ejpam-5830	204	21	cocycle	cocycle	NOUN
ejpam-5830	204	22	of	of	ADP
ejpam-5830	204	23	class	class	NOUN
ejpam-5830	204	24	c∞	c∞	PROPN
ejpam-5830	204	25	over	over	ADP
ejpam-5830	204	26	t	t	PROPN
ejpam-5830	204	27	with	with	ADP
ejpam-5830	204	28	values	value	NOUN
ejpam-5830	204	29	in	in	ADP
ejpam-5830	204	30	rl	rl	PROPN
ejpam-5830	204	31	(	(	PUNCT
ejpam-5830	204	32	l	l	X
ejpam-5830	204	33	≥	≥	NUM
ejpam-5830	204	34	1	1	NUM
ejpam-5830	204	35	)	)	PUNCT
ejpam-5830	204	36	such	such	ADJ
ejpam-5830	204	37	that	that	SCONJ
ejpam-5830	204	38	[	[	X
ejpam-5830	204	39	α]o	α]o	X
ejpam-5830	204	40	=	=	SYM
ejpam-5830	204	41	0	0	NUM
ejpam-5830	204	42	for	for	ADP
ejpam-5830	204	43	every	every	DET
ejpam-5830	204	44	o	o	PROPN
ejpam-5830	204	45	∈	∈	PROPN
ejpam-5830	204	46	pt	pt	NOUN
ejpam-5830	204	47	.	.	PUNCT
ejpam-5830	205	1	then	then	ADV
ejpam-5830	205	2	,	,	PUNCT
ejpam-5830	205	3	there	there	PRON
ejpam-5830	205	4	exists	exist	VERB
ejpam-5830	205	5	a	a	DET
ejpam-5830	205	6	(	(	PUNCT
ejpam-5830	205	7	k	k	PROPN
ejpam-5830	205	8	−	−	PROPN
ejpam-5830	205	9	1)-cochain	1)-cochain	NUM
ejpam-5830	205	10	φ	φ	PROPN
ejpam-5830	205	11	of	of	ADP
ejpam-5830	205	12	class	class	NOUN
ejpam-5830	205	13	c∞	c∞	PROPN
ejpam-5830	205	14	such	such	ADJ
ejpam-5830	205	15	that	that	SCONJ
ejpam-5830	205	16	α	α	NOUN
ejpam-5830	205	17	=	=	SYM
ejpam-5830	205	18	dφ	dφ	X
ejpam-5830	205	19	.	.	PUNCT
ejpam-5830	205	20	theorem	theorem	NOUN
ejpam-5830	205	21	6	6	NUM
ejpam-5830	205	22	.	.	PUNCT
ejpam-5830	206	1	let	let	VERB
ejpam-5830	206	2	t	t	PROPN
ejpam-5830	206	3	be	be	AUX
ejpam-5830	206	4	an	an	DET
ejpam-5830	206	5	action	action	NOUN
ejpam-5830	206	6	of	of	ADP
ejpam-5830	206	7	zk	zk	PROPN
ejpam-5830	206	8	by	by	ADP
ejpam-5830	206	9	hyperbolic	hyperbolic	ADJ
ejpam-5830	206	10	automorphisms	automorphism	NOUN
ejpam-5830	206	11	of	of	ADP
ejpam-5830	206	12	tn	tn	PROPN
ejpam-5830	206	13	,	,	PUNCT
ejpam-5830	206	14	and	and	CCONJ
ejpam-5830	206	15	for	for	ADP
ejpam-5830	206	16	1	1	NUM
ejpam-5830	206	17	≤	≤	NOUN
ejpam-5830	207	1	n	n	DET
ejpam-5830	207	2	≤	≤	NOUN
ejpam-5830	207	3	k	k	PRON
ejpam-5830	208	1	−	−	PROPN
ejpam-5830	208	2	1	1	NUM
ejpam-5830	208	3	,	,	PUNCT
ejpam-5830	208	4	let	let	VERB
ejpam-5830	208	5	α	α	PRON
ejpam-5830	208	6	be	be	AUX
ejpam-5830	208	7	a	a	DET
ejpam-5830	208	8	n	n	NOUN
ejpam-5830	208	9	-	-	PUNCT
ejpam-5830	208	10	cocycle	cocycle	NOUN
ejpam-5830	208	11	of	of	ADP
ejpam-5830	208	12	class	class	NOUN
ejpam-5830	208	13	c∞	c∞	PROPN
ejpam-5830	208	14	over	over	ADP
ejpam-5830	208	15	t	t	PROPN
ejpam-5830	208	16	with	with	ADP
ejpam-5830	208	17	values	value	NOUN
ejpam-5830	208	18	in	in	ADP
ejpam-5830	208	19	rl	rl	PROPN
ejpam-5830	208	20	(	(	PUNCT
ejpam-5830	208	21	l	l	X
ejpam-5830	208	22	≥	≥	NUM
ejpam-5830	208	23	1	1	NUM
ejpam-5830	208	24	)	)	PUNCT
ejpam-5830	208	25	.	.	PUNCT
ejpam-5830	209	1	then	then	ADV
ejpam-5830	209	2	,	,	PUNCT
ejpam-5830	209	3	α	α	PROPN
ejpam-5830	209	4	is	be	AUX
ejpam-5830	209	5	c∞-cohomologous	c∞-cohomologous	ADJ
ejpam-5830	209	6	to	to	ADP
ejpam-5830	209	7	a	a	DET
ejpam-5830	209	8	constant	constant	ADJ
ejpam-5830	209	9	cocycle	cocycle	NOUN
ejpam-5830	209	10	β	β	NOUN
ejpam-5830	209	11	,	,	PUNCT
ejpam-5830	209	12	that	that	ADV
ejpam-5830	209	13	is	is	ADV
ejpam-5830	209	14	,	,	PUNCT
ejpam-5830	209	15	α	α	PROPN
ejpam-5830	209	16	(	(	PUNCT
ejpam-5830	209	17	t	t	PROPN
ejpam-5830	209	18	,	,	PUNCT
ejpam-5830	209	19	x	x	NOUN
ejpam-5830	209	20	)	)	PUNCT
ejpam-5830	209	21	=	=	SYM
ejpam-5830	209	22	β	β	X
ejpam-5830	209	23	(	(	PUNCT
ejpam-5830	209	24	t	t	PROPN
ejpam-5830	209	25	)	)	PUNCT
ejpam-5830	209	26	+	+	ADV
ejpam-5830	209	27	dφ	dφ	X
ejpam-5830	209	28	(	(	PUNCT
ejpam-5830	209	29	t	t	PROPN
ejpam-5830	209	30	,	,	PUNCT
ejpam-5830	209	31	x	x	NOUN
ejpam-5830	209	32	)	)	PUNCT
ejpam-5830	209	33	,	,	PUNCT
ejpam-5830	209	34	where	where	SCONJ
ejpam-5830	209	35	φ	φ	PROPN
ejpam-5830	209	36	is	be	AUX
ejpam-5830	209	37	a	a	DET
ejpam-5830	209	38	(	(	PUNCT
ejpam-5830	209	39	n−	n−	NOUN
ejpam-5830	209	40	1)-cochain	1)-cochain	NUM
ejpam-5830	209	41	of	of	ADP
ejpam-5830	209	42	class	class	NOUN
ejpam-5830	209	43	c∞.	c∞.	PROPN
ejpam-5830	209	44	these	these	DET
ejpam-5830	209	45	results	result	NOUN
ejpam-5830	209	46	illustrate	illustrate	VERB
ejpam-5830	209	47	the	the	DET
ejpam-5830	209	48	power	power	NOUN
ejpam-5830	209	49	of	of	ADP
ejpam-5830	209	50	the	the	DET
ejpam-5830	209	51	livschitz	livschitz	ADJ
ejpam-5830	209	52	property	property	NOUN
ejpam-5830	209	53	for	for	ADP
ejpam-5830	209	54	higher	high	ADJ
ejpam-5830	209	55	-	-	PUNCT
ejpam-5830	209	56	order	order	NOUN
ejpam-5830	209	57	cohomology	cohomology	NOUN
ejpam-5830	209	58	and	and	CCONJ
ejpam-5830	209	59	complete	complete	VERB
ejpam-5830	209	60	the	the	DET
ejpam-5830	209	61	analysis	analysis	NOUN
ejpam-5830	209	62	of	of	ADP
ejpam-5830	209	63	c∞	c∞	ADJ
ejpam-5830	209	64	cohomology	cohomology	NOUN
ejpam-5830	209	65	for	for	ADP
ejpam-5830	209	66	actions	action	NOUN
ejpam-5830	209	67	of	of	ADP
ejpam-5830	209	68	hyperbolic	hyperbolic	ADJ
ejpam-5830	209	69	automorphisms	automorphism	NOUN
ejpam-5830	209	70	.	.	PUNCT
ejpam-5830	210	1	we	we	PRON
ejpam-5830	210	2	observe	observe	VERB
ejpam-5830	210	3	that	that	SCONJ
ejpam-5830	210	4	for	for	ADP
ejpam-5830	210	5	n	n	NOUN
ejpam-5830	210	6	=	=	SYM
ejpam-5830	210	7	k	k	X
ejpam-5830	210	8	(	(	PUNCT
ejpam-5830	210	9	theorem	theorem	NOUN
ejpam-5830	210	10	5	5	NUM
ejpam-5830	210	11	)	)	PUNCT
ejpam-5830	210	12	,	,	PUNCT
ejpam-5830	210	13	c∞	c∞	PROPN
ejpam-5830	210	14	livschitz	livschitz	NOUN
ejpam-5830	210	15	property	property	NOUN
ejpam-5830	210	16	holds	hold	VERB
ejpam-5830	210	17	:	:	PUNCT
ejpam-5830	210	18	the	the	DET
ejpam-5830	210	19	k	k	PROPN
ejpam-5830	210	20	-	-	PUNCT
ejpam-5830	210	21	th	th	VERB
ejpam-5830	210	22	c∞	c∞	PROPN
ejpam-5830	210	23	cohomology	cohomology	NOUN
ejpam-5830	210	24	class	class	NOUN
ejpam-5830	210	25	of	of	ADP
ejpam-5830	210	26	the	the	DET
ejpam-5830	210	27	action	action	NOUN
ejpam-5830	210	28	t	t	PROPN
ejpam-5830	210	29	of	of	ADP
ejpam-5830	210	30	zk	zk	PROPN
ejpam-5830	210	31	is	be	AUX
ejpam-5830	210	32	determined	determine	VERB
ejpam-5830	210	33	by	by	ADP
ejpam-5830	210	34	the	the	DET
ejpam-5830	210	35	periodic	periodic	ADJ
ejpam-5830	210	36	orbits	orbit	NOUN
ejpam-5830	210	37	,	,	PUNCT
ejpam-5830	210	38	meaning	mean	VERB
ejpam-5830	210	39	that	that	SCONJ
ejpam-5830	210	40	periodic	periodic	ADJ
ejpam-5830	210	41	information	information	NOUN
ejpam-5830	210	42	is	be	AUX
ejpam-5830	210	43	necessary	necessary	ADJ
ejpam-5830	210	44	and	and	CCONJ
ejpam-5830	210	45	sufficient	sufficient	ADJ
ejpam-5830	210	46	to	to	PART
ejpam-5830	210	47	identify	identify	VERB
ejpam-5830	210	48	coboundaries	coboundarie	NOUN
ejpam-5830	210	49	in	in	ADP
ejpam-5830	210	50	the	the	DET
ejpam-5830	210	51	k	k	PROPN
ejpam-5830	210	52	-	-	PUNCT
ejpam-5830	210	53	th	th	X
ejpam-5830	210	54	c∞	c∞	PROPN
ejpam-5830	210	55	cohomology	cohomology	NOUN
ejpam-5830	210	56	.	.	PUNCT
ejpam-5830	211	1	there	there	PRON
ejpam-5830	211	2	is	be	VERB
ejpam-5830	211	3	therefore	therefore	ADV
ejpam-5830	211	4	a	a	DET
ejpam-5830	211	5	bijective	bijective	ADJ
ejpam-5830	211	6	correspondence	correspondence	NOUN
ejpam-5830	211	7	between	between	ADP
ejpam-5830	211	8	k	k	NOUN
ejpam-5830	211	9	-	-	PUNCT
ejpam-5830	211	10	cocycles	cocycle	NOUN
ejpam-5830	211	11	and	and	CCONJ
ejpam-5830	211	12	functions	function	NOUN
ejpam-5830	211	13	on	on	ADP
ejpam-5830	211	14	m	m	NOUN
ejpam-5830	211	15	with	with	ADP
ejpam-5830	211	16	values	value	NOUN
ejpam-5830	211	17	in	in	ADP
ejpam-5830	211	18	rl	rl	NOUN
ejpam-5830	211	19	.	.	PUNCT
ejpam-5830	212	1	for	for	ADP
ejpam-5830	212	2	the	the	DET
ejpam-5830	212	3	remaining	remain	VERB
ejpam-5830	212	4	possible	possible	ADJ
ejpam-5830	212	5	values	value	NOUN
ejpam-5830	212	6	of	of	ADP
ejpam-5830	212	7	n	n	PROPN
ejpam-5830	212	8	(	(	PUNCT
ejpam-5830	212	9	theorem	theorem	VERB
ejpam-5830	212	10	6	6	NUM
ejpam-5830	212	11	)	)	PUNCT
ejpam-5830	212	12	,	,	PUNCT
ejpam-5830	212	13	n	n	X
ejpam-5830	212	14	∈	∈	PROPN
ejpam-5830	212	15	{	{	PUNCT
ejpam-5830	212	16	1	1	NUM
ejpam-5830	212	17	,	,	PUNCT
ejpam-5830	212	18	.	.	PUNCT
ejpam-5830	212	19	.	.	PUNCT
ejpam-5830	212	20	.	.	PUNCT
ejpam-5830	213	1	,	,	PUNCT
ejpam-5830	214	1	k	k	PROPN
ejpam-5830	215	1	−	−	NOUN
ejpam-5830	216	1	1	1	NUM
ejpam-5830	216	2	}	}	PUNCT
ejpam-5830	216	3	,	,	PUNCT
ejpam-5830	216	4	each	each	DET
ejpam-5830	216	5	n	n	NOUN
ejpam-5830	216	6	-	-	PUNCT
ejpam-5830	216	7	cocycle	cocycle	NOUN
ejpam-5830	216	8	of	of	ADP
ejpam-5830	216	9	class	class	NOUN
ejpam-5830	216	10	c∞	c∞	PROPN
ejpam-5830	216	11	is	be	AUX
ejpam-5830	216	12	cohomologous	cohomologous	ADJ
ejpam-5830	216	13	to	to	ADP
ejpam-5830	216	14	a	a	DET
ejpam-5830	216	15	constant	constant	ADJ
ejpam-5830	216	16	n	n	CCONJ
ejpam-5830	216	17	-	-	PUNCT
ejpam-5830	216	18	cocycle	cocycle	NOUN
ejpam-5830	216	19	via	via	ADP
ejpam-5830	216	20	an	an	DET
ejpam-5830	216	21	(	(	PUNCT
ejpam-5830	216	22	n−	n−	NOUN
ejpam-5830	216	23	1)-cochain	1)-cochain	NUM
ejpam-5830	216	24	of	of	ADP
ejpam-5830	216	25	class	class	NOUN
ejpam-5830	216	26	c∞.	c∞.	PROPN
ejpam-5830	216	27	thus	thus	ADV
ejpam-5830	216	28	,	,	PUNCT
ejpam-5830	216	29	the	the	DET
ejpam-5830	216	30	article	article	NOUN
ejpam-5830	216	31	[	[	X
ejpam-5830	216	32	29	29	NUM
ejpam-5830	216	33	]	]	PUNCT
ejpam-5830	216	34	provides	provide	VERB
ejpam-5830	216	35	a	a	DET
ejpam-5830	216	36	complete	complete	ADJ
ejpam-5830	216	37	description	description	NOUN
ejpam-5830	216	38	of	of	ADP
ejpam-5830	216	39	c∞	c∞	PROPN
ejpam-5830	216	40	cohomology	cohomology	NOUN
ejpam-5830	216	41	for	for	ADP
ejpam-5830	216	42	cocycles	cocycle	NOUN
ejpam-5830	216	43	with	with	ADP
ejpam-5830	216	44	values	value	NOUN
ejpam-5830	216	45	in	in	ADP
ejpam-5830	216	46	γ	γ	X
ejpam-5830	216	47	=	=	SYM
ejpam-5830	216	48	rl	rl	NOUN
ejpam-5830	216	49	induced	induce	VERB
ejpam-5830	216	50	by	by	ADP
ejpam-5830	216	51	an	an	DET
ejpam-5830	216	52	action	action	NOUN
ejpam-5830	216	53	of	of	ADP
ejpam-5830	216	54	g	g	PROPN
ejpam-5830	216	55	=	=	SYM
ejpam-5830	216	56	zk	zk	PROPN
ejpam-5830	216	57	through	through	ADP
ejpam-5830	216	58	hyperbolic	hyperbolic	ADJ
ejpam-5830	216	59	automorphisms	automorphism	NOUN
ejpam-5830	216	60	of	of	ADP
ejpam-5830	216	61	the	the	DET
ejpam-5830	216	62	toroidal	toroidal	ADJ
ejpam-5830	216	63	manifold	manifold	PROPN
ejpam-5830	216	64	tn	tn	PROPN
ejpam-5830	216	65	.	.	PUNCT
ejpam-5830	217	1	the	the	DET
ejpam-5830	217	2	main	main	ADJ
ejpam-5830	217	3	technique	technique	NOUN
ejpam-5830	217	4	used	use	VERB
ejpam-5830	217	5	involves	involve	NOUN
ejpam-5830	217	6	moving	move	VERB
ejpam-5830	217	7	to	to	ADP
ejpam-5830	217	8	a	a	DET
ejpam-5830	217	9	dual	dual	ADJ
ejpam-5830	217	10	problem	problem	NOUN
ejpam-5830	217	11	.	.	PUNCT
ejpam-5830	218	1	the	the	DET
ejpam-5830	218	2	dual	dual	ADJ
ejpam-5830	218	3	of	of	ADP
ejpam-5830	218	4	a	a	DET
ejpam-5830	218	5	vector	vector	NOUN
ejpam-5830	218	6	function	function	NOUN
ejpam-5830	218	7	on	on	ADP
ejpam-5830	218	8	the	the	DET
ejpam-5830	218	9	torus	torus	PROPN
ejpam-5830	218	10	tn	tn	PROPN
ejpam-5830	218	11	is	be	AUX
ejpam-5830	218	12	the	the	DET
ejpam-5830	218	13	collection	collection	NOUN
ejpam-5830	218	14	of	of	ADP
ejpam-5830	218	15	its	its	PRON
ejpam-5830	218	16	fourier	fourier	ADJ
ejpam-5830	218	17	coefficients	coefficient	NOUN
ejpam-5830	218	18	,	,	PUNCT
ejpam-5830	218	19	i.e.	i.e.	X
ejpam-5830	218	20	,	,	PUNCT
ejpam-5830	218	21	a	a	DET
ejpam-5830	218	22	vector	vector	NOUN
ejpam-5830	218	23	function	function	NOUN
ejpam-5830	218	24	on	on	ADP
ejpam-5830	218	25	zn	zn	PROPN
ejpam-5830	218	26	.	.	PUNCT
ejpam-5830	219	1	the	the	DET
ejpam-5830	219	2	dual	dual	ADJ
ejpam-5830	219	3	cohomological	cohomological	ADJ
ejpam-5830	219	4	equation	equation	NOUN
ejpam-5830	219	5	is	be	AUX
ejpam-5830	219	6	reduced	reduce	VERB
ejpam-5830	219	7	to	to	ADP
ejpam-5830	219	8	equations	equation	NOUN
ejpam-5830	219	9	for	for	ADP
ejpam-5830	219	10	the	the	DET
ejpam-5830	219	11	action	action	NOUN
ejpam-5830	219	12	on	on	ADP
ejpam-5830	219	13	each	each	DET
ejpam-5830	219	14	orbit	orbit	NOUN
ejpam-5830	219	15	o	o	NOUN
ejpam-5830	219	16	of	of	ADP
ejpam-5830	219	17	the	the	DET
ejpam-5830	219	18	dual	dual	ADJ
ejpam-5830	219	19	action	action	NOUN
ejpam-5830	219	20	.	.	PUNCT
ejpam-5830	220	1	in	in	ADP
ejpam-5830	220	2	particular	particular	ADJ
ejpam-5830	220	3	,	,	PUNCT
ejpam-5830	220	4	the	the	DET
ejpam-5830	220	5	differentiability	differentiability	NOUN
ejpam-5830	220	6	of	of	ADP
ejpam-5830	220	7	the	the	DET
ejpam-5830	220	8	original	original	ADJ
ejpam-5830	220	9	cocycle	cocycle	NOUN
ejpam-5830	220	10	corresponds	correspond	VERB
ejpam-5830	220	11	to	to	ADP
ejpam-5830	220	12	a	a	DET
ejpam-5830	220	13	super	super	ADJ
ejpam-5830	220	14	-	-	ADJ
ejpam-5830	220	15	polynomial	polynomial	ADJ
ejpam-5830	220	16	decay	decay	NOUN
ejpam-5830	220	17	of	of	ADP
ejpam-5830	220	18	its	its	PRON
ejpam-5830	220	19	fourier	fourier	ADJ
ejpam-5830	220	20	coefficients	coefficient	NOUN
ejpam-5830	220	21	.	.	PUNCT
ejpam-5830	221	1	for	for	ADP
ejpam-5830	221	2	n	n	NOUN
ejpam-5830	221	3	=	=	SYM
ejpam-5830	221	4	1	1	NUM
ejpam-5830	221	5	,	,	PUNCT
ejpam-5830	221	6	theorem	theorem	VERB
ejpam-5830	221	7	6	6	NUM
ejpam-5830	221	8	was	be	AUX
ejpam-5830	221	9	established	establish	VERB
ejpam-5830	221	10	by	by	ADP
ejpam-5830	221	11	katok	katok	NOUN
ejpam-5830	221	12	and	and	CCONJ
ejpam-5830	221	13	spatzier	spatzier	ADJ
ejpam-5830	221	14	in	in	ADP
ejpam-5830	221	15	[	[	X
ejpam-5830	221	16	30	30	NUM
ejpam-5830	221	17	]	]	PUNCT
ejpam-5830	221	18	for	for	ADP
ejpam-5830	221	19	the	the	DET
ejpam-5830	221	20	anosov	anosov	NOUN
ejpam-5830	221	21	case	case	NOUN
ejpam-5830	221	22	and	and	CCONJ
ejpam-5830	221	23	in	in	ADP
ejpam-5830	221	24	[	[	X
ejpam-5830	221	25	31	31	NUM
ejpam-5830	221	26	]	]	PUNCT
ejpam-5830	221	27	for	for	ADP
ejpam-5830	221	28	the	the	DET
ejpam-5830	221	29	partially	partially	ADV
ejpam-5830	221	30	hyperbolic	hyperbolic	ADJ
ejpam-5830	221	31	case	case	NOUN
ejpam-5830	221	32	.	.	PUNCT
ejpam-5830	222	1	as	as	SCONJ
ejpam-5830	222	2	noted	note	VERB
ejpam-5830	222	3	by	by	ADP
ejpam-5830	222	4	katok	katok	NOUN
ejpam-5830	222	5	and	and	CCONJ
ejpam-5830	222	6	katok	katok	NOUN
ejpam-5830	222	7	,	,	PUNCT
ejpam-5830	222	8	livschitz	livschitz	PROPN
ejpam-5830	222	9	’s	’s	PART
ejpam-5830	222	10	method	method	NOUN
ejpam-5830	222	11	is	be	AUX
ejpam-5830	222	12	not	not	PART
ejpam-5830	222	13	valid	valid	ADJ
ejpam-5830	222	14	for	for	ADP
ejpam-5830	222	15	higher	high	ADJ
ejpam-5830	222	16	-	-	PUNCT
ejpam-5830	222	17	order	order	NOUN
ejpam-5830	222	18	cohomology	cohomology	NOUN
ejpam-5830	222	19	.	.	PUNCT
ejpam-5830	223	1	katok	katok	NOUN
ejpam-5830	223	2	and	and	CCONJ
ejpam-5830	223	3	spatzier	spatzier	ADJ
ejpam-5830	223	4	present	present	NOUN
ejpam-5830	223	5	in	in	ADP
ejpam-5830	223	6	[	[	X
ejpam-5830	223	7	30	30	NUM
ejpam-5830	223	8	]	]	X
ejpam-5830	223	9	an	an	DET
ejpam-5830	223	10	adaptation	adaptation	NOUN
ejpam-5830	223	11	of	of	ADP
ejpam-5830	223	12	livschitz	livschitz	PROPN
ejpam-5830	223	13	’s	’s	PART
ejpam-5830	223	14	method	method	NOUN
ejpam-5830	223	15	to	to	PART
ejpam-5830	223	16	establish	establish	VERB
ejpam-5830	223	17	the	the	DET
ejpam-5830	223	18	c∞	c∞	PROPN
ejpam-5830	223	19	,	,	PUNCT
ejpam-5830	223	20	c1	c1	PROPN
ejpam-5830	223	21	and	and	CCONJ
ejpam-5830	223	22	hölder	hölder	NOUN
ejpam-5830	223	23	livschitz	livschitz	NOUN
ejpam-5830	223	24	properties	property	NOUN
ejpam-5830	223	25	but	but	CCONJ
ejpam-5830	223	26	only	only	ADV
ejpam-5830	223	27	for	for	ADP
ejpam-5830	223	28	1	1	NUM
ejpam-5830	223	29	-	-	PUNCT
ejpam-5830	223	30	cocycles	cocycle	NOUN
ejpam-5830	223	31	of	of	ADP
ejpam-5830	223	32	anosov	anosov	NOUN
ejpam-5830	223	33	actions	action	NOUN
ejpam-5830	223	34	of	of	ADP
ejpam-5830	223	35	g	g	NOUN
ejpam-5830	223	36	=	=	PUNCT
ejpam-5830	223	37	rk	rk	NOUN
ejpam-5830	223	38	.	.	NOUN
ejpam-5830	223	39	5	5	NUM
ejpam-5830	223	40	.	.	X
ejpam-5830	223	41	conclusion	conclusion	VERB
ejpam-5830	223	42	the	the	DET
ejpam-5830	223	43	research	research	NOUN
ejpam-5830	223	44	on	on	ADP
ejpam-5830	223	45	cohomology	cohomology	NOUN
ejpam-5830	223	46	for	for	ADP
ejpam-5830	223	47	dynamical	dynamical	ADJ
ejpam-5830	223	48	systems	system	NOUN
ejpam-5830	223	49	,	,	PUNCT
ejpam-5830	223	50	particularly	particularly	ADV
ejpam-5830	223	51	cocycles	cocycle	NOUN
ejpam-5830	223	52	and	and	CCONJ
ejpam-5830	223	53	higher	high	ADJ
ejpam-5830	223	54	-	-	PUNCT
ejpam-5830	223	55	dimensional	dimensional	ADJ
ejpam-5830	223	56	actions	action	NOUN
ejpam-5830	223	57	,	,	PUNCT
ejpam-5830	223	58	has	have	AUX
ejpam-5830	223	59	made	make	VERB
ejpam-5830	223	60	significant	significant	ADJ
ejpam-5830	223	61	advances	advance	NOUN
ejpam-5830	223	62	over	over	ADP
ejpam-5830	223	63	the	the	DET
ejpam-5830	223	64	past	past	ADJ
ejpam-5830	223	65	decades	decade	NOUN
ejpam-5830	223	66	.	.	PUNCT
ejpam-5830	224	1	from	from	ADP
ejpam-5830	224	2	livschitz	livschitz	PROPN
ejpam-5830	224	3	’s	’s	PART
ejpam-5830	224	4	foundational	foundational	ADJ
ejpam-5830	224	5	results	result	NOUN
ejpam-5830	224	6	to	to	ADP
ejpam-5830	224	7	generalizations	generalization	NOUN
ejpam-5830	224	8	for	for	ADP
ejpam-5830	224	9	c∞	c∞	PROPN
ejpam-5830	224	10	cocycles	cocycle	NOUN
ejpam-5830	224	11	and	and	CCONJ
ejpam-5830	224	12	actions	action	NOUN
ejpam-5830	224	13	on	on	ADP
ejpam-5830	224	14	manifolds	manifold	NOUN
ejpam-5830	224	15	,	,	PUNCT
ejpam-5830	224	16	this	this	DET
ejpam-5830	224	17	area	area	NOUN
ejpam-5830	224	18	continues	continue	VERB
ejpam-5830	224	19	to	to	PART
ejpam-5830	224	20	reveal	reveal	VERB
ejpam-5830	224	21	profound	profound	ADJ
ejpam-5830	224	22	connections	connection	NOUN
ejpam-5830	224	23	between	between	ADP
ejpam-5830	224	24	dynamical	dynamical	ADJ
ejpam-5830	224	25	properties	property	NOUN
ejpam-5830	224	26	and	and	CCONJ
ejpam-5830	224	27	cohomological	cohomological	ADJ
ejpam-5830	224	28	invariants	invariant	NOUN
ejpam-5830	224	29	.	.	PUNCT
ejpam-5830	225	1	applications	application	NOUN
ejpam-5830	225	2	extend	extend	VERB
ejpam-5830	225	3	to	to	ADP
ejpam-5830	225	4	hyperbolic	hyperbolic	ADJ
ejpam-5830	225	5	dynamics	dynamic	NOUN
ejpam-5830	225	6	,	,	PUNCT
ejpam-5830	225	7	lie	lie	NOUN
ejpam-5830	225	8	groups	group	NOUN
ejpam-5830	225	9	,	,	PUNCT
ejpam-5830	225	10	r.	r.	PROPN
ejpam-5830	225	11	d.	d.	PROPN
ejpam-5830	225	12	laureano	laureano	PROPN
ejpam-5830	225	13	/	/	SYM
ejpam-5830	225	14	eur	eur	PROPN
ejpam-5830	225	15	.	.	PUNCT
ejpam-5830	226	1	j.	j.	PROPN
ejpam-5830	226	2	pure	pure	PROPN
ejpam-5830	226	3	appl	appl	PROPN
ejpam-5830	226	4	.	.	PROPN
ejpam-5830	226	5	math	math	PROPN
ejpam-5830	226	6	,	,	PUNCT
ejpam-5830	226	7	18	18	NUM
ejpam-5830	226	8	(	(	PUNCT
ejpam-5830	226	9	2	2	NUM
ejpam-5830	226	10	)	)	PUNCT
ejpam-5830	226	11	(	(	PUNCT
ejpam-5830	226	12	2025	2025	NUM
ejpam-5830	226	13	)	)	PUNCT
ejpam-5830	226	14	,	,	PUNCT
ejpam-5830	226	15	5830	5830	NUM
ejpam-5830	226	16	10	10	NUM
ejpam-5830	226	17	of	of	ADP
ejpam-5830	226	18	11	11	NUM
ejpam-5830	226	19	and	and	CCONJ
ejpam-5830	226	20	beyond	beyond	ADP
ejpam-5830	226	21	,	,	PUNCT
ejpam-5830	226	22	providing	provide	VERB
ejpam-5830	226	23	a	a	DET
ejpam-5830	226	24	fertile	fertile	ADJ
ejpam-5830	226	25	ground	ground	NOUN
ejpam-5830	226	26	for	for	ADP
ejpam-5830	226	27	further	further	ADJ
ejpam-5830	226	28	exploration	exploration	NOUN
ejpam-5830	226	29	.	.	PUNCT
ejpam-5830	227	1	future	future	ADJ
ejpam-5830	227	2	research	research	NOUN
ejpam-5830	227	3	will	will	AUX
ejpam-5830	227	4	likely	likely	ADV
ejpam-5830	227	5	uncover	uncover	VERB
ejpam-5830	227	6	new	new	ADJ
ejpam-5830	227	7	techniques	technique	NOUN
ejpam-5830	227	8	and	and	CCONJ
ejpam-5830	227	9	frameworks	framework	NOUN
ejpam-5830	227	10	to	to	PART
ejpam-5830	227	11	tackle	tackle	VERB
ejpam-5830	227	12	even	even	ADV
ejpam-5830	227	13	more	more	ADV
ejpam-5830	227	14	complex	complex	ADJ
ejpam-5830	227	15	dynamical	dynamical	ADJ
ejpam-5830	227	16	and	and	CCONJ
ejpam-5830	227	17	cohomological	cohomological	ADJ
ejpam-5830	227	18	questions	question	NOUN
ejpam-5830	227	19	.	.	PUNCT
ejpam-5830	228	1	references	reference	NOUN
ejpam-5830	228	2	[	[	X
ejpam-5830	228	3	1	1	X
ejpam-5830	228	4	]	]	PUNCT
ejpam-5830	228	5	a	a	DET
ejpam-5830	228	6	livšic	livšic	NOUN
ejpam-5830	228	7	.	.	PUNCT
ejpam-5830	229	1	some	some	DET
ejpam-5830	229	2	homology	homology	NOUN
ejpam-5830	229	3	properties	property	NOUN
ejpam-5830	229	4	of	of	ADP
ejpam-5830	229	5	y	y	PROPN
ejpam-5830	229	6	-	-	PUNCT
ejpam-5830	229	7	systems	system	NOUN
ejpam-5830	229	8	.	.	PUNCT
ejpam-5830	230	1	math	math	NOUN
ejpam-5830	230	2	.	.	PUNCT
ejpam-5830	231	1	notes	note	NOUN
ejpam-5830	231	2	of	of	ADP
ejpam-5830	231	3	u.s.s.r	u.s.s.r	PROPN
ejpam-5830	231	4	.	.	PROPN
ejpam-5830	231	5	academy	academy	PROPN
ejpam-5830	231	6	of	of	ADP
ejpam-5830	231	7	sciences	sciences	PROPN
ejpam-5830	231	8	,	,	PUNCT
ejpam-5830	231	9	10:758–763	10:758–763	NUM
ejpam-5830	231	10	,	,	PUNCT
ejpam-5830	231	11	1971	1971	NUM
ejpam-5830	231	12	.	.	PUNCT
ejpam-5830	232	1	[	[	X
ejpam-5830	232	2	2	2	X
ejpam-5830	232	3	]	]	PUNCT
ejpam-5830	232	4	a	a	DET
ejpam-5830	232	5	livšic	livšic	PROPN
ejpam-5830	232	6	.	.	PUNCT
ejpam-5830	233	1	cohomology	cohomology	NOUN
ejpam-5830	233	2	of	of	ADP
ejpam-5830	233	3	dynamical	dynamical	ADJ
ejpam-5830	233	4	systems	system	NOUN
ejpam-5830	233	5	.	.	PUNCT
ejpam-5830	234	1	math	math	NOUN
ejpam-5830	234	2	.	.	PUNCT
ejpam-5830	235	1	u.s.s.r.-izv	u.s.s.r.-izv	PROPN
ejpam-5830	235	2	.	.	PROPN
ejpam-5830	235	3	,	,	PUNCT
ejpam-5830	235	4	6:1278–1301	6:1278–1301	NUM
ejpam-5830	235	5	,	,	PUNCT
ejpam-5830	235	6	1972	1972	NUM
ejpam-5830	235	7	.	.	PUNCT
ejpam-5830	236	1	[	[	X
ejpam-5830	236	2	3	3	NUM
ejpam-5830	236	3	]	]	X
ejpam-5830	236	4	r	r	NOUN
ejpam-5830	236	5	d	d	X
ejpam-5830	236	6	laureano	laureano	NOUN
ejpam-5830	236	7	.	.	PUNCT
ejpam-5830	237	1	livschitz	livschitz	PROPN
ejpam-5830	237	2	theorem	theorem	VERB
ejpam-5830	237	3	in	in	ADP
ejpam-5830	237	4	suspension	suspension	NOUN
ejpam-5830	237	5	flows	flow	NOUN
ejpam-5830	237	6	and	and	CCONJ
ejpam-5830	237	7	markov	markov	NOUN
ejpam-5830	237	8	systems	system	NOUN
ejpam-5830	237	9	:	:	PUNCT
ejpam-5830	237	10	approach	approach	NOUN
ejpam-5830	237	11	in	in	ADP
ejpam-5830	237	12	cohomology	cohomology	NOUN
ejpam-5830	237	13	of	of	ADP
ejpam-5830	237	14	systems	system	NOUN
ejpam-5830	237	15	.	.	PUNCT
ejpam-5830	238	1	symmetry	symmetry	PROPN
ejpam-5830	238	2	,	,	PUNCT
ejpam-5830	238	3	12:338–351	12:338–351	PROPN
ejpam-5830	238	4	,	,	PUNCT
ejpam-5830	238	5	2020	2020	NUM
ejpam-5830	238	6	.	.	PUNCT
ejpam-5830	239	1	[	[	X
ejpam-5830	239	2	4	4	NUM
ejpam-5830	239	3	]	]	X
ejpam-5830	239	4	r	r	NOUN
ejpam-5830	239	5	d	d	NOUN
ejpam-5830	239	6	laureano	laureano	NOUN
ejpam-5830	239	7	.	.	PUNCT
ejpam-5830	240	1	from	from	ADP
ejpam-5830	240	2	anosov	anosov	NOUN
ejpam-5830	240	3	closing	close	VERB
ejpam-5830	240	4	lemma	lemma	PROPN
ejpam-5830	240	5	to	to	ADP
ejpam-5830	240	6	global	global	ADJ
ejpam-5830	240	7	data	datum	NOUN
ejpam-5830	240	8	of	of	ADP
ejpam-5830	240	9	cohomological	cohomological	ADJ
ejpam-5830	240	10	nature	nature	NOUN
ejpam-5830	240	11	.	.	PUNCT
ejpam-5830	241	1	eur	eur	PROPN
ejpam-5830	241	2	.	.	PUNCT
ejpam-5830	242	1	j.	j.	PROPN
ejpam-5830	242	2	pure	pure	PROPN
ejpam-5830	242	3	.	.	PUNCT
ejpam-5830	243	1	appl	appl	PROPN
ejpam-5830	243	2	.	.	PROPN
ejpam-5830	243	3	math	math	PROPN
ejpam-5830	243	4	.	.	PUNCT
ejpam-5830	243	5	,	,	PUNCT
ejpam-5830	244	1	17(3):1403–1416	17(3):1403–1416	NUM
ejpam-5830	244	2	,	,	PUNCT
ejpam-5830	244	3	2024	2024	NUM
ejpam-5830	244	4	.	.	PUNCT
ejpam-5830	245	1	[	[	X
ejpam-5830	245	2	5	5	NUM
ejpam-5830	245	3	]	]	PUNCT
ejpam-5830	245	4	a	a	DET
ejpam-5830	245	5	katok	katok	NOUN
ejpam-5830	245	6	and	and	CCONJ
ejpam-5830	245	7	b	b	NOUN
ejpam-5830	245	8	hasselblatt	hasselblatt	NOUN
ejpam-5830	245	9	.	.	PUNCT
ejpam-5830	246	1	introduction	introduction	NOUN
ejpam-5830	246	2	to	to	ADP
ejpam-5830	246	3	the	the	DET
ejpam-5830	246	4	modern	modern	ADJ
ejpam-5830	246	5	theory	theory	NOUN
ejpam-5830	246	6	of	of	ADP
ejpam-5830	246	7	dynamical	dynamical	ADJ
ejpam-5830	246	8	systems	system	NOUN
ejpam-5830	246	9	.	.	PUNCT
ejpam-5830	247	1	cambridge	cambridge	PROPN
ejpam-5830	247	2	university	university	PROPN
ejpam-5830	247	3	press	press	NOUN
ejpam-5830	247	4	,	,	PUNCT
ejpam-5830	247	5	1995	1995	NUM
ejpam-5830	247	6	.	.	PUNCT
ejpam-5830	248	1	[	[	X
ejpam-5830	248	2	6	6	NUM
ejpam-5830	248	3	]	]	X
ejpam-5830	248	4	r	r	NOUN
ejpam-5830	248	5	bowen	bowen	NOUN
ejpam-5830	248	6	.	.	PUNCT
ejpam-5830	249	1	symbolic	symbolic	ADJ
ejpam-5830	249	2	dynamics	dynamic	NOUN
ejpam-5830	249	3	for	for	ADP
ejpam-5830	249	4	hyperbolic	hyperbolic	ADJ
ejpam-5830	249	5	flows	flow	NOUN
ejpam-5830	249	6	.	.	PUNCT
ejpam-5830	250	1	amer	amer	PROPN
ejpam-5830	250	2	.	.	PUNCT
ejpam-5830	251	1	j.	j.	PROPN
ejpam-5830	251	2	math	math	PROPN
ejpam-5830	251	3	.	.	PUNCT
ejpam-5830	251	4	,	,	PUNCT
ejpam-5830	252	1	95:429–460	95:429–460	NUM
ejpam-5830	252	2	,	,	PUNCT
ejpam-5830	252	3	1973	1973	NUM
ejpam-5830	252	4	.	.	PUNCT
ejpam-5830	253	1	[	[	X
ejpam-5830	253	2	7	7	NUM
ejpam-5830	253	3	]	]	X
ejpam-5830	253	4	m	m	PROPN
ejpam-5830	253	5	ratner	ratner	PROPN
ejpam-5830	253	6	.	.	PUNCT
ejpam-5830	253	7	markov	markov	PROPN
ejpam-5830	253	8	partitions	partition	NOUN
ejpam-5830	253	9	for	for	ADP
ejpam-5830	253	10	anosov	anosov	NOUN
ejpam-5830	253	11	flows	flow	NOUN
ejpam-5830	253	12	on	on	ADP
ejpam-5830	253	13	n	n	CCONJ
ejpam-5830	253	14	-	-	PUNCT
ejpam-5830	253	15	dimensional	dimensional	ADJ
ejpam-5830	253	16	manifolds	manifold	NOUN
ejpam-5830	253	17	.	.	PUNCT
ejpam-5830	254	1	israel	israel	PROPN
ejpam-5830	254	2	j.	j.	PROPN
ejpam-5830	254	3	math	math	PROPN
ejpam-5830	254	4	.	.	PUNCT
ejpam-5830	254	5	,	,	PUNCT
ejpam-5830	254	6	15:92–114	15:92–114	NUM
ejpam-5830	254	7	,	,	PUNCT
ejpam-5830	254	8	1973	1973	NUM
ejpam-5830	254	9	.	.	PUNCT
ejpam-5830	255	1	[	[	X
ejpam-5830	255	2	8	8	X
ejpam-5830	255	3	]	]	X
ejpam-5830	255	4	p	p	PROPN
ejpam-5830	255	5	agarwal	agarwal	PROPN
ejpam-5830	255	6	h	h	PROPN
ejpam-5830	255	7	irmak	irmak	PROPN
ejpam-5830	255	8	and	and	CCONJ
ejpam-5830	255	9	r	r	NOUN
ejpam-5830	255	10	agarwal	agarwal	PROPN
ejpam-5830	255	11	.	.	PUNCT
ejpam-5830	256	1	the	the	DET
ejpam-5830	256	2	complex	complex	ADJ
ejpam-5830	256	3	error	error	NOUN
ejpam-5830	256	4	functions	function	NOUN
ejpam-5830	256	5	and	and	CCONJ
ejpam-5830	256	6	various	various	ADJ
ejpam-5830	256	7	extensive	extensive	ADJ
ejpam-5830	256	8	results	result	NOUN
ejpam-5830	256	9	together	together	ADV
ejpam-5830	256	10	with	with	ADP
ejpam-5830	256	11	implications	implication	NOUN
ejpam-5830	256	12	pertaining	pertain	VERB
ejpam-5830	256	13	to	to	ADP
ejpam-5830	256	14	certain	certain	ADJ
ejpam-5830	256	15	special	special	ADJ
ejpam-5830	256	16	functions	function	NOUN
ejpam-5830	256	17	.	.	PUNCT
ejpam-5830	257	1	turkish	turkish	ADJ
ejpam-5830	257	2	j.	j.	PROPN
ejpam-5830	257	3	math	math	PROPN
ejpam-5830	257	4	.	.	PUNCT
ejpam-5830	257	5	,	,	PUNCT
ejpam-5830	257	6	46:662–674	46:662–674	NOUN
ejpam-5830	257	7	,	,	PUNCT
ejpam-5830	257	8	2022	2022	NUM
ejpam-5830	257	9	.	.	PUNCT
ejpam-5830	258	1	[	[	X
ejpam-5830	258	2	9	9	NUM
ejpam-5830	258	3	]	]	X
ejpam-5830	258	4	p	p	PROPN
ejpam-5830	258	5	agarwal	agarwal	PROPN
ejpam-5830	258	6	m	m	VERB
ejpam-5830	258	7	ruzhansky	ruzhansky	ADJ
ejpam-5830	258	8	,	,	PUNCT
ejpam-5830	258	9	y	y	PROPN
ejpam-5830	258	10	je	je	PROPN
ejpam-5830	258	11	cho	cho	PROPN
ejpam-5830	258	12	and	and	CCONJ
ejpam-5830	258	13	i	i	PRON
ejpam-5830	258	14	area	area	NOUN
ejpam-5830	258	15	(	(	PUNCT
ejpam-5830	258	16	editors	editor	NOUN
ejpam-5830	258	17	)	)	PUNCT
ejpam-5830	258	18	.	.	PUNCT
ejpam-5830	259	1	advances	advance	NOUN
ejpam-5830	259	2	in	in	ADP
ejpam-5830	259	3	real	real	ADJ
ejpam-5830	259	4	and	and	CCONJ
ejpam-5830	259	5	complex	complex	ADJ
ejpam-5830	259	6	analysis	analysis	NOUN
ejpam-5830	259	7	with	with	ADP
ejpam-5830	259	8	applications	application	NOUN
ejpam-5830	259	9	.	.	PUNCT
ejpam-5830	260	1	birkhäuser	birkhäuser	X
ejpam-5830	260	2	singapore	singapore	PROPN
ejpam-5830	260	3	,	,	PUNCT
ejpam-5830	260	4	2017	2017	NUM
ejpam-5830	260	5	.	.	PUNCT
ejpam-5830	261	1	[	[	X
ejpam-5830	261	2	10	10	NUM
ejpam-5830	261	3	]	]	X
ejpam-5830	261	4	w	w	X
ejpam-5830	261	5	veech	veech	NOUN
ejpam-5830	261	6	.	.	PUNCT
ejpam-5830	262	1	periodic	periodic	ADJ
ejpam-5830	262	2	points	point	NOUN
ejpam-5830	262	3	and	and	CCONJ
ejpam-5830	262	4	invariant	invariant	ADJ
ejpam-5830	262	5	pseudomeasures	pseudomeasure	NOUN
ejpam-5830	262	6	for	for	ADP
ejpam-5830	262	7	toral	toral	ADJ
ejpam-5830	262	8	endomorphisms	endomorphism	NOUN
ejpam-5830	262	9	.	.	PUNCT
ejpam-5830	263	1	ergodic	ergodic	ADJ
ejpam-5830	263	2	theory	theory	NOUN
ejpam-5830	263	3	dynam	dynam	PROPN
ejpam-5830	263	4	.	.	PUNCT
ejpam-5830	264	1	systems	system	NOUN
ejpam-5830	264	2	,	,	PUNCT
ejpam-5830	264	3	6:449–473	6:449–473	NOUN
ejpam-5830	264	4	,	,	PUNCT
ejpam-5830	264	5	1986	1986	NUM
ejpam-5830	264	6	.	.	PUNCT
ejpam-5830	265	1	[	[	X
ejpam-5830	265	2	11	11	NUM
ejpam-5830	265	3	]	]	X
ejpam-5830	265	4	w	w	PROPN
ejpam-5830	265	5	parry	parry	PROPN
ejpam-5830	265	6	.	.	PUNCT
ejpam-5830	266	1	the	the	DET
ejpam-5830	266	2	livsic	livsic	ADJ
ejpam-5830	266	3	periodic	periodic	ADJ
ejpam-5830	266	4	point	point	NOUN
ejpam-5830	266	5	theorem	theorem	NOUN
ejpam-5830	266	6	for	for	ADP
ejpam-5830	266	7	two	two	NUM
ejpam-5830	266	8	non	non	ADJ
ejpam-5830	266	9	-	-	ADJ
ejpam-5830	266	10	abelian	abelian	ADJ
ejpam-5830	266	11	cocycles	cocycle	NOUN
ejpam-5830	266	12	.	.	PUNCT
ejpam-5830	267	1	ergodic	ergodic	ADJ
ejpam-5830	267	2	theory	theory	NOUN
ejpam-5830	267	3	dynam	dynam	PROPN
ejpam-5830	267	4	.	.	PUNCT
ejpam-5830	268	1	systems	system	NOUN
ejpam-5830	268	2	,	,	PUNCT
ejpam-5830	268	3	19:687–701	19:687–701	PROPN
ejpam-5830	268	4	,	,	PUNCT
ejpam-5830	268	5	1999	1999	NUM
ejpam-5830	268	6	.	.	PUNCT
ejpam-5830	269	1	[	[	X
ejpam-5830	269	2	12	12	NUM
ejpam-5830	269	3	]	]	X
ejpam-5830	269	4	k	k	PROPN
ejpam-5830	269	5	schmidt	schmidt	PROPN
ejpam-5830	269	6	.	.	PUNCT
ejpam-5830	270	1	remarks	remark	NOUN
ejpam-5830	270	2	on	on	ADP
ejpam-5830	270	3	livšic	livšic	PROPN
ejpam-5830	270	4	’s	’s	PART
ejpam-5830	270	5	theory	theory	NOUN
ejpam-5830	270	6	for	for	ADP
ejpam-5830	270	7	nonabelian	nonabelian	ADJ
ejpam-5830	270	8	cocycles	cocycle	NOUN
ejpam-5830	270	9	.	.	PUNCT
ejpam-5830	271	1	ergodic	ergodic	ADJ
ejpam-5830	271	2	theory	theory	NOUN
ejpam-5830	271	3	dynam	dynam	PROPN
ejpam-5830	271	4	.	.	PUNCT
ejpam-5830	272	1	systems	system	NOUN
ejpam-5830	272	2	,	,	PUNCT
ejpam-5830	272	3	19:703–721	19:703–721	PROPN
ejpam-5830	272	4	,	,	PUNCT
ejpam-5830	272	5	1999	1999	NUM
ejpam-5830	272	6	.	.	PUNCT
ejpam-5830	273	1	[	[	X
ejpam-5830	273	2	13	13	NUM
ejpam-5830	273	3	]	]	SYM
ejpam-5830	273	4	m	m	VERB
ejpam-5830	273	5	pollicott	pollicott	ADJ
ejpam-5830	273	6	and	and	CCONJ
ejpam-5830	273	7	c	c	PROPN
ejpam-5830	273	8	walkden	walkden	PROPN
ejpam-5830	273	9	.	.	PUNCT
ejpam-5830	274	1	livšic	livšic	VERB
ejpam-5830	274	2	theorems	theorem	NOUN
ejpam-5830	274	3	for	for	ADP
ejpam-5830	274	4	connected	connected	ADJ
ejpam-5830	274	5	lie	lie	NOUN
ejpam-5830	274	6	groups	group	NOUN
ejpam-5830	274	7	.	.	PUNCT
ejpam-5830	275	1	trans	trans	PROPN
ejpam-5830	275	2	.	.	PUNCT
ejpam-5830	276	1	amer	amer	PROPN
ejpam-5830	276	2	.	.	PUNCT
ejpam-5830	276	3	math	math	PROPN
ejpam-5830	276	4	.	.	PUNCT
ejpam-5830	277	1	soc	soc	PROPN
ejpam-5830	277	2	.	.	PROPN
ejpam-5830	277	3	,	,	PUNCT
ejpam-5830	277	4	353:2879–2895	353:2879–2895	NUM
ejpam-5830	277	5	,	,	PUNCT
ejpam-5830	277	6	2001	2001	NUM
ejpam-5830	277	7	.	.	PUNCT
ejpam-5830	278	1	[	[	X
ejpam-5830	278	2	14	14	NUM
ejpam-5830	278	3	]	]	X
ejpam-5830	278	4	w	w	PROPN
ejpam-5830	278	5	parry	parry	PROPN
ejpam-5830	278	6	and	and	CCONJ
ejpam-5830	278	7	m	m	VERB
ejpam-5830	278	8	pollicott	pollicott	ADJ
ejpam-5830	278	9	.	.	PUNCT
ejpam-5830	279	1	the	the	DET
ejpam-5830	279	2	livšic	livšic	PROPN
ejpam-5830	279	3	cocycle	cocycle	NOUN
ejpam-5830	279	4	equation	equation	NOUN
ejpam-5830	279	5	for	for	ADP
ejpam-5830	279	6	compact	compact	ADJ
ejpam-5830	279	7	lie	lie	NOUN
ejpam-5830	279	8	group	group	NOUN
ejpam-5830	279	9	extensions	extension	NOUN
ejpam-5830	279	10	of	of	ADP
ejpam-5830	279	11	hyperbolic	hyperbolic	ADJ
ejpam-5830	279	12	systems	system	NOUN
ejpam-5830	279	13	.	.	PUNCT
ejpam-5830	280	1	j.	j.	PROPN
ejpam-5830	280	2	london	london	PROPN
ejpam-5830	280	3	math	math	PROPN
ejpam-5830	280	4	.	.	PUNCT
ejpam-5830	281	1	soc	soc	PROPN
ejpam-5830	281	2	.	.	PROPN
ejpam-5830	281	3	,	,	PUNCT
ejpam-5830	281	4	56:405–416	56:405–416	NUM
ejpam-5830	281	5	,	,	PUNCT
ejpam-5830	281	6	1997	1997	NUM
ejpam-5830	281	7	.	.	PUNCT
ejpam-5830	282	1	[	[	X
ejpam-5830	282	2	15	15	NUM
ejpam-5830	282	3	]	]	X
ejpam-5830	282	4	w	w	PROPN
ejpam-5830	282	5	parry	parry	PROPN
ejpam-5830	282	6	and	and	CCONJ
ejpam-5830	282	7	m	m	PRON
ejpam-5830	282	8	pollicott	pollicott	ADJ
ejpam-5830	282	9	.	.	PUNCT
ejpam-5830	283	1	zeta	zeta	NOUN
ejpam-5830	283	2	functions	function	NOUN
ejpam-5830	283	3	and	and	CCONJ
ejpam-5830	283	4	the	the	DET
ejpam-5830	283	5	periodic	periodic	ADJ
ejpam-5830	283	6	orbit	orbit	NOUN
ejpam-5830	283	7	structure	structure	NOUN
ejpam-5830	283	8	of	of	ADP
ejpam-5830	283	9	hyperbolic	hyperbolic	ADJ
ejpam-5830	283	10	dynamics	dynamic	NOUN
ejpam-5830	283	11	.	.	PUNCT
ejpam-5830	284	1	astérique	astérique	ADJ
ejpam-5830	284	2	,	,	PUNCT
ejpam-5830	284	3	tomo	tomo	NOUN
ejpam-5830	284	4	187	187	NUM
ejpam-5830	284	5	-	-	SYM
ejpam-5830	284	6	188	188	NUM
ejpam-5830	284	7	,	,	PUNCT
ejpam-5830	284	8	1990	1990	NUM
ejpam-5830	284	9	.	.	PUNCT
ejpam-5830	285	1	[	[	X
ejpam-5830	285	2	16	16	NUM
ejpam-5830	285	3	]	]	SYM
ejpam-5830	285	4	v	v	ADP
ejpam-5830	285	5	niţică	niţică	NOUN
ejpam-5830	285	6	and	and	CCONJ
ejpam-5830	285	7	a	a	DET
ejpam-5830	285	8	török	török	NUM
ejpam-5830	285	9	.	.	PUNCT
ejpam-5830	286	1	regularity	regularity	NOUN
ejpam-5830	286	2	of	of	ADP
ejpam-5830	286	3	the	the	DET
ejpam-5830	286	4	transfer	transfer	NOUN
ejpam-5830	286	5	map	map	NOUN
ejpam-5830	286	6	for	for	ADP
ejpam-5830	286	7	cohomologous	cohomologous	ADJ
ejpam-5830	286	8	cocycles	cocycle	NOUN
ejpam-5830	286	9	.	.	PUNCT
ejpam-5830	287	1	ergodic	ergodic	ADJ
ejpam-5830	287	2	theory	theory	NOUN
ejpam-5830	287	3	dynam	dynam	PROPN
ejpam-5830	287	4	.	.	PUNCT
ejpam-5830	288	1	systems	system	NOUN
ejpam-5830	288	2	,	,	PUNCT
ejpam-5830	288	3	18:1187–1209	18:1187–1209	NUM
ejpam-5830	288	4	,	,	PUNCT
ejpam-5830	288	5	1998	1998	NUM
ejpam-5830	288	6	.	.	PUNCT
ejpam-5830	289	1	[	[	X
ejpam-5830	289	2	17	17	NUM
ejpam-5830	289	3	]	]	X
ejpam-5830	289	4	c	c	X
ejpam-5830	289	5	walkden	walkden	PROPN
ejpam-5830	289	6	.	.	PUNCT
ejpam-5830	290	1	livsic	livsic	ADJ
ejpam-5830	290	2	regularity	regularity	NOUN
ejpam-5830	290	3	theorems	theorem	NOUN
ejpam-5830	290	4	for	for	ADP
ejpam-5830	290	5	twisted	twisted	ADJ
ejpam-5830	290	6	cocycle	cocycle	NOUN
ejpam-5830	290	7	equations	equation	NOUN
ejpam-5830	290	8	over	over	ADP
ejpam-5830	290	9	hyperbolic	hyperbolic	ADJ
ejpam-5830	290	10	systems	system	NOUN
ejpam-5830	290	11	.	.	PUNCT
ejpam-5830	291	1	j.	j.	PROPN
ejpam-5830	291	2	london	london	PROPN
ejpam-5830	291	3	math	math	PROPN
ejpam-5830	291	4	.	.	PUNCT
ejpam-5830	292	1	soc	soc	PROPN
ejpam-5830	292	2	.	.	PUNCT
ejpam-5830	292	3	,	,	PUNCT
ejpam-5830	292	4	61:286–300	61:286–300	NUM
ejpam-5830	292	5	,	,	PUNCT
ejpam-5830	292	6	2000	2000	NUM
ejpam-5830	292	7	.	.	PUNCT
ejpam-5830	293	1	[	[	X
ejpam-5830	293	2	18	18	NUM
ejpam-5830	293	3	]	]	X
ejpam-5830	293	4	c	c	X
ejpam-5830	293	5	walkden	walkden	X
ejpam-5830	293	6	.	.	PUNCT
ejpam-5830	294	1	livšic	livšic	VERB
ejpam-5830	294	2	theorems	theorem	NOUN
ejpam-5830	294	3	for	for	ADP
ejpam-5830	294	4	hyperbolic	hyperbolic	ADJ
ejpam-5830	294	5	flows	flow	NOUN
ejpam-5830	294	6	.	.	PUNCT
ejpam-5830	295	1	trans	trans	PROPN
ejpam-5830	295	2	.	.	PUNCT
ejpam-5830	296	1	amer	amer	PROPN
ejpam-5830	296	2	.	.	PUNCT
ejpam-5830	296	3	math	math	PROPN
ejpam-5830	296	4	.	.	PUNCT
ejpam-5830	297	1	soc	soc	PROPN
ejpam-5830	297	2	.	.	PROPN
ejpam-5830	297	3	,	,	PUNCT
ejpam-5830	297	4	352:1299	352:1299	NUM
ejpam-5830	297	5	–	–	PUNCT
ejpam-5830	297	6	1313	1313	NUM
ejpam-5830	297	7	,	,	PUNCT
ejpam-5830	297	8	2000	2000	NUM
ejpam-5830	297	9	.	.	PUNCT
ejpam-5830	298	1	[	[	X
ejpam-5830	298	2	19	19	NUM
ejpam-5830	298	3	]	]	SYM
ejpam-5830	298	4	v	v	ADP
ejpam-5830	298	5	niţică	niţică	NOUN
ejpam-5830	298	6	and	and	CCONJ
ejpam-5830	298	7	a	a	DET
ejpam-5830	298	8	török	török	NUM
ejpam-5830	298	9	.	.	PUNCT
ejpam-5830	299	1	cohomology	cohomology	NOUN
ejpam-5830	299	2	of	of	ADP
ejpam-5830	299	3	dynamical	dynamical	ADJ
ejpam-5830	299	4	systems	system	NOUN
ejpam-5830	299	5	and	and	CCONJ
ejpam-5830	299	6	rigidity	rigidity	NOUN
ejpam-5830	299	7	of	of	ADP
ejpam-5830	299	8	partially	partially	ADV
ejpam-5830	299	9	hyperbolic	hyperbolic	ADJ
ejpam-5830	299	10	actions	action	NOUN
ejpam-5830	299	11	of	of	ADP
ejpam-5830	299	12	higher	high	ADJ
ejpam-5830	299	13	-	-	PUNCT
ejpam-5830	299	14	rank	rank	NOUN
ejpam-5830	299	15	lattices	lattice	NOUN
ejpam-5830	299	16	.	.	PUNCT
ejpam-5830	300	1	duke	duke	PROPN
ejpam-5830	300	2	math	math	PROPN
ejpam-5830	300	3	.	.	PUNCT
ejpam-5830	301	1	j.	j.	PROPN
ejpam-5830	301	2	,	,	PUNCT
ejpam-5830	301	3	79:751–810	79:751–810	PROPN
ejpam-5830	301	4	,	,	PUNCT
ejpam-5830	301	5	1995	1995	NUM
ejpam-5830	301	6	.	.	PUNCT
ejpam-5830	302	1	r.	r.	PROPN
ejpam-5830	302	2	d.	d.	PROPN
ejpam-5830	302	3	laureano	laureano	PROPN
ejpam-5830	302	4	/	/	SYM
ejpam-5830	302	5	eur	eur	PROPN
ejpam-5830	302	6	.	.	PUNCT
ejpam-5830	303	1	j.	j.	PROPN
ejpam-5830	303	2	pure	pure	PROPN
ejpam-5830	303	3	appl	appl	PROPN
ejpam-5830	303	4	.	.	PROPN
ejpam-5830	303	5	math	math	PROPN
ejpam-5830	303	6	,	,	PUNCT
ejpam-5830	303	7	18	18	NUM
ejpam-5830	303	8	(	(	PUNCT
ejpam-5830	303	9	2	2	NUM
ejpam-5830	303	10	)	)	PUNCT
ejpam-5830	303	11	(	(	PUNCT
ejpam-5830	303	12	2025	2025	NUM
ejpam-5830	303	13	)	)	PUNCT
ejpam-5830	303	14	,	,	PUNCT
ejpam-5830	303	15	5830	5830	NUM
ejpam-5830	303	16	11	11	NUM
ejpam-5830	303	17	of	of	ADP
ejpam-5830	303	18	11	11	NUM
ejpam-5830	304	1	[	[	SYM
ejpam-5830	304	2	20	20	NUM
ejpam-5830	304	3	]	]	SYM
ejpam-5830	304	4	v	v	ADP
ejpam-5830	304	5	niţică	niţică	NOUN
ejpam-5830	304	6	and	and	CCONJ
ejpam-5830	304	7	a	a	DET
ejpam-5830	304	8	török	török	NUM
ejpam-5830	304	9	.	.	PUNCT
ejpam-5830	305	1	regularity	regularity	NOUN
ejpam-5830	305	2	results	result	NOUN
ejpam-5830	305	3	for	for	ADP
ejpam-5830	305	4	the	the	DET
ejpam-5830	305	5	solutions	solution	NOUN
ejpam-5830	305	6	of	of	ADP
ejpam-5830	305	7	the	the	DET
ejpam-5830	305	8	livšic	livšic	PROPN
ejpam-5830	305	9	cohomology	cohomology	NOUN
ejpam-5830	305	10	equation	equation	NOUN
ejpam-5830	305	11	with	with	ADP
ejpam-5830	305	12	values	value	NOUN
ejpam-5830	305	13	in	in	ADP
ejpam-5830	305	14	diffeomorfism	diffeomorfism	NOUN
ejpam-5830	305	15	groups	group	NOUN
ejpam-5830	305	16	.	.	PUNCT
ejpam-5830	306	1	ergodic	ergodic	ADJ
ejpam-5830	306	2	theory	theory	NOUN
ejpam-5830	306	3	dynam	dynam	PROPN
ejpam-5830	306	4	.	.	PUNCT
ejpam-5830	307	1	systems	system	NOUN
ejpam-5830	307	2	,	,	PUNCT
ejpam-5830	307	3	16:325–333	16:325–333	NUM
ejpam-5830	307	4	,	,	PUNCT
ejpam-5830	307	5	1996	1996	NUM
ejpam-5830	307	6	.	.	PUNCT
ejpam-5830	308	1	[	[	X
ejpam-5830	308	2	21	21	NUM
ejpam-5830	308	3	]	]	SYM
ejpam-5830	308	4	v	v	NOUN
ejpam-5830	308	5	guillemin	guillemin	NOUN
ejpam-5830	308	6	and	and	CCONJ
ejpam-5830	308	7	d	d	PROPN
ejpam-5830	308	8	kazhdan	kazhdan	PROPN
ejpam-5830	308	9	.	.	PUNCT
ejpam-5830	309	1	on	on	ADP
ejpam-5830	309	2	the	the	DET
ejpam-5830	309	3	cohomology	cohomology	NOUN
ejpam-5830	309	4	of	of	ADP
ejpam-5830	309	5	certain	certain	ADJ
ejpam-5830	309	6	dynamical	dynamical	ADJ
ejpam-5830	309	7	systems	system	NOUN
ejpam-5830	309	8	.	.	PUNCT
ejpam-5830	310	1	topology	topology	NOUN
ejpam-5830	310	2	,	,	PUNCT
ejpam-5830	310	3	19:291–299	19:291–299	NUM
ejpam-5830	310	4	,	,	PUNCT
ejpam-5830	310	5	1980	1980	NUM
ejpam-5830	310	6	.	.	PUNCT
ejpam-5830	311	1	[	[	X
ejpam-5830	311	2	22	22	NUM
ejpam-5830	311	3	]	]	SYM
ejpam-5830	311	4	v	v	NOUN
ejpam-5830	311	5	guillemin	guillemin	NOUN
ejpam-5830	311	6	and	and	CCONJ
ejpam-5830	311	7	d	d	PROPN
ejpam-5830	311	8	kazhdan	kazhdan	PROPN
ejpam-5830	311	9	.	.	PUNCT
ejpam-5830	312	1	some	some	DET
ejpam-5830	312	2	inverse	inverse	ADJ
ejpam-5830	312	3	spectral	spectral	ADJ
ejpam-5830	312	4	results	result	NOUN
ejpam-5830	312	5	for	for	ADP
ejpam-5830	312	6	negatively	negatively	ADV
ejpam-5830	312	7	curved	curve	VERB
ejpam-5830	312	8	2	2	NUM
ejpam-5830	312	9	-	-	PUNCT
ejpam-5830	312	10	manifolds	manifold	NOUN
ejpam-5830	312	11	.	.	PUNCT
ejpam-5830	313	1	topology	topology	NOUN
ejpam-5830	313	2	,	,	PUNCT
ejpam-5830	313	3	19:301–313	19:301–313	PROPN
ejpam-5830	313	4	,	,	PUNCT
ejpam-5830	313	5	1980	1980	NUM
ejpam-5830	313	6	.	.	PUNCT
ejpam-5830	314	1	[	[	X
ejpam-5830	314	2	23	23	NUM
ejpam-5830	314	3	]	]	X
ejpam-5830	314	4	h	h	PROPN
ejpam-5830	314	5	epstein	epstein	PROPN
ejpam-5830	314	6	p	p	PROPN
ejpam-5830	314	7	collet	collet	PROPN
ejpam-5830	314	8	and	and	CCONJ
ejpam-5830	314	9	g	g	NOUN
ejpam-5830	314	10	gallavotti	gallavotti	PROPN
ejpam-5830	314	11	.	.	PUNCT
ejpam-5830	315	1	perturbations	perturbation	NOUN
ejpam-5830	315	2	of	of	ADP
ejpam-5830	315	3	geodesic	geodesic	NOUN
ejpam-5830	315	4	flows	flow	NOUN
ejpam-5830	315	5	on	on	ADP
ejpam-5830	315	6	surfaces	surface	NOUN
ejpam-5830	315	7	of	of	ADP
ejpam-5830	315	8	constant	constant	ADJ
ejpam-5830	315	9	negative	negative	ADJ
ejpam-5830	315	10	curvature	curvature	NOUN
ejpam-5830	315	11	and	and	CCONJ
ejpam-5830	315	12	their	their	PRON
ejpam-5830	315	13	mixing	mix	VERB
ejpam-5830	315	14	properties	property	NOUN
ejpam-5830	315	15	.	.	PUNCT
ejpam-5830	316	1	comm	comm	NOUN
ejpam-5830	316	2	.	.	PUNCT
ejpam-5830	316	3	math	math	NOUN
ejpam-5830	316	4	.	.	PUNCT
ejpam-5830	317	1	phys	phy	NOUN
ejpam-5830	317	2	.	.	PUNCT
ejpam-5830	317	3	,	,	PUNCT
ejpam-5830	317	4	95:61–112	95:61–112	NUM
ejpam-5830	317	5	,	,	PUNCT
ejpam-5830	317	6	1984	1984	NUM
ejpam-5830	317	7	.	.	PUNCT
ejpam-5830	318	1	[	[	X
ejpam-5830	318	2	24	24	NUM
ejpam-5830	318	3	]	]	X
ejpam-5830	318	4	j	j	PROPN
ejpam-5830	318	5	marco	marco	PROPN
ejpam-5830	318	6	r	r	PROPN
ejpam-5830	318	7	de	de	X
ejpam-5830	318	8	la	la	X
ejpam-5830	318	9	llave	llave	NOUN
ejpam-5830	318	10	and	and	CCONJ
ejpam-5830	318	11	r	r	NOUN
ejpam-5830	318	12	moriyón	moriyón	PROPN
ejpam-5830	318	13	.	.	PUNCT
ejpam-5830	319	1	canonical	canonical	ADJ
ejpam-5830	319	2	perturbation	perturbation	NOUN
ejpam-5830	319	3	theory	theory	NOUN
ejpam-5830	319	4	of	of	ADP
ejpam-5830	319	5	anosov	anosov	NOUN
ejpam-5830	319	6	systems	system	NOUN
ejpam-5830	319	7	and	and	CCONJ
ejpam-5830	319	8	regularity	regularity	NOUN
ejpam-5830	319	9	results	result	NOUN
ejpam-5830	319	10	for	for	ADP
ejpam-5830	319	11	the	the	DET
ejpam-5830	319	12	livsic	livsic	ADJ
ejpam-5830	319	13	cohomology	cohomology	NOUN
ejpam-5830	319	14	equation	equation	NOUN
ejpam-5830	319	15	.	.	PUNCT
ejpam-5830	320	1	ann	ann	PROPN
ejpam-5830	320	2	.	.	PROPN
ejpam-5830	320	3	of	of	ADP
ejpam-5830	320	4	math	math	NOUN
ejpam-5830	320	5	.	.	PUNCT
ejpam-5830	320	6	,	,	PUNCT
ejpam-5830	320	7	123(2):537–612	123(2):537–612	NUM
ejpam-5830	320	8	,	,	PUNCT
ejpam-5830	320	9	1986	1986	NUM
ejpam-5830	320	10	.	.	PUNCT
ejpam-5830	321	1	[	[	X
ejpam-5830	321	2	25	25	NUM
ejpam-5830	321	3	]	]	X
ejpam-5830	321	4	j	j	PROPN
ejpam-5830	321	5	-	-	PROPN
ejpam-5830	321	6	l	l	PROPN
ejpam-5830	321	7	journé.	journé.	PROPN
ejpam-5830	321	8	a	a	DET
ejpam-5830	321	9	regularity	regularity	NOUN
ejpam-5830	321	10	lemma	lemma	PROPN
ejpam-5830	321	11	for	for	ADP
ejpam-5830	321	12	functions	function	NOUN
ejpam-5830	321	13	of	of	ADP
ejpam-5830	321	14	several	several	ADJ
ejpam-5830	321	15	variables	variable	NOUN
ejpam-5830	321	16	.	.	PUNCT
ejpam-5830	322	1	rev	rev	PROPN
ejpam-5830	322	2	.	.	PROPN
ejpam-5830	322	3	mat	mat	PROPN
ejpam-5830	322	4	.	.	PROPN
ejpam-5830	322	5	iberoamericana	iberoamericana	PROPN
ejpam-5830	322	6	,	,	PUNCT
ejpam-5830	322	7	4:187–193	4:187–193	NUM
ejpam-5830	322	8	,	,	PUNCT
ejpam-5830	322	9	1988	1988	NUM
ejpam-5830	322	10	.	.	PUNCT
ejpam-5830	323	1	[	[	X
ejpam-5830	323	2	26	26	NUM
ejpam-5830	323	3	]	]	PUNCT
ejpam-5830	323	4	s	s	VERB
ejpam-5830	323	5	hurder	hurder	NOUN
ejpam-5830	323	6	and	and	CCONJ
ejpam-5830	323	7	a	a	DET
ejpam-5830	323	8	katok	katok	NOUN
ejpam-5830	323	9	.	.	PUNCT
ejpam-5830	324	1	differentiability	differentiability	NOUN
ejpam-5830	324	2	,	,	PUNCT
ejpam-5830	324	3	rigidity	rigidity	NOUN
ejpam-5830	324	4	and	and	CCONJ
ejpam-5830	324	5	godbillon	godbillon	PROPN
ejpam-5830	324	6	–	–	PUNCT
ejpam-5830	324	7	vey	vey	ADJ
ejpam-5830	324	8	classes	class	NOUN
ejpam-5830	324	9	for	for	ADP
ejpam-5830	324	10	anosov	anosov	NOUN
ejpam-5830	324	11	flows	flow	NOUN
ejpam-5830	324	12	.	.	PUNCT
ejpam-5830	325	1	inst	inst	PROPN
ejpam-5830	325	2	.	.	PUNCT
ejpam-5830	325	3	hautes	haute	VERB
ejpam-5830	325	4	études	études	PROPN
ejpam-5830	325	5	sci	sci	PROPN
ejpam-5830	325	6	.	.	PROPN
ejpam-5830	325	7	publ	publ	PROPN
ejpam-5830	325	8	.	.	PUNCT
ejpam-5830	326	1	math	math	NOUN
ejpam-5830	326	2	.	.	PUNCT
ejpam-5830	326	3	,	,	PUNCT
ejpam-5830	326	4	72:5–61	72:5–61	NUM
ejpam-5830	326	5	,	,	PUNCT
ejpam-5830	326	6	1990	1990	NUM
ejpam-5830	326	7	.	.	PUNCT
ejpam-5830	327	1	[	[	X
ejpam-5830	327	2	27	27	NUM
ejpam-5830	327	3	]	]	X
ejpam-5830	327	4	r	r	X
ejpam-5830	327	5	de	de	X
ejpam-5830	327	6	la	la	X
ejpam-5830	327	7	llave	llave	PROPN
ejpam-5830	327	8	.	.	PUNCT
ejpam-5830	328	1	analytic	analytic	ADJ
ejpam-5830	328	2	regularity	regularity	NOUN
ejpam-5830	328	3	of	of	ADP
ejpam-5830	328	4	solutions	solution	NOUN
ejpam-5830	328	5	of	of	ADP
ejpam-5830	328	6	livsic	livsic	ADJ
ejpam-5830	328	7	cohomology	cohomology	NOUN
ejpam-5830	328	8	equations	equation	NOUN
ejpam-5830	328	9	and	and	CCONJ
ejpam-5830	328	10	some	some	DET
ejpam-5830	328	11	applications	application	NOUN
ejpam-5830	328	12	to	to	ADP
ejpam-5830	328	13	analytic	analytic	ADJ
ejpam-5830	328	14	conjugacy	conjugacy	NOUN
ejpam-5830	328	15	of	of	ADP
ejpam-5830	328	16	hyperbolic	hyperbolic	ADJ
ejpam-5830	328	17	dynamical	dynamical	ADJ
ejpam-5830	328	18	systems	system	NOUN
ejpam-5830	328	19	.	.	PUNCT
ejpam-5830	329	1	ergodic	ergodic	ADJ
ejpam-5830	329	2	theory	theory	NOUN
ejpam-5830	329	3	dynam	dynam	PROPN
ejpam-5830	329	4	.	.	PUNCT
ejpam-5830	330	1	systems	system	NOUN
ejpam-5830	330	2	,	,	PUNCT
ejpam-5830	330	3	17:649–662	17:649–662	NUM
ejpam-5830	330	4	,	,	PUNCT
ejpam-5830	330	5	1997	1997	NUM
ejpam-5830	330	6	.	.	PUNCT
ejpam-5830	331	1	[	[	X
ejpam-5830	331	2	28	28	NUM
ejpam-5830	331	3	]	]	SYM
ejpam-5830	331	4	v	v	ADP
ejpam-5830	331	5	niţiçă	niţiçă	PROPN
ejpam-5830	331	6	a	a	DET
ejpam-5830	331	7	katok	katok	NOUN
ejpam-5830	331	8	and	and	CCONJ
ejpam-5830	331	9	a	a	DET
ejpam-5830	331	10	török	török	NUM
ejpam-5830	331	11	.	.	PUNCT
ejpam-5830	332	1	nonabelian	nonabelian	ADJ
ejpam-5830	332	2	cohomology	cohomology	NOUN
ejpam-5830	332	3	of	of	ADP
ejpam-5830	332	4	abelian	abelian	PROPN
ejpam-5830	332	5	anosov	anosov	PROPN
ejpam-5830	332	6	actions	action	NOUN
ejpam-5830	332	7	.	.	PUNCT
ejpam-5830	333	1	ergodic	ergodic	ADJ
ejpam-5830	333	2	theory	theory	NOUN
ejpam-5830	333	3	dynam	dynam	PROPN
ejpam-5830	333	4	.	.	PUNCT
ejpam-5830	334	1	systems	system	NOUN
ejpam-5830	334	2	,	,	PUNCT
ejpam-5830	334	3	20:259–288	20:259–288	NUM
ejpam-5830	334	4	,	,	PUNCT
ejpam-5830	334	5	2000	2000	NUM
ejpam-5830	334	6	.	.	PUNCT
ejpam-5830	335	1	[	[	X
ejpam-5830	335	2	29	29	NUM
ejpam-5830	335	3	]	]	X
ejpam-5830	335	4	a	a	DET
ejpam-5830	335	5	katok	katok	NOUN
ejpam-5830	335	6	and	and	CCONJ
ejpam-5830	335	7	s	s	VERB
ejpam-5830	335	8	katok	katok	NOUN
ejpam-5830	335	9	.	.	PUNCT
ejpam-5830	336	1	higher	high	ADJ
ejpam-5830	336	2	cohomology	cohomology	NOUN
ejpam-5830	336	3	for	for	ADP
ejpam-5830	336	4	abelian	abelian	ADJ
ejpam-5830	336	5	groups	group	NOUN
ejpam-5830	336	6	of	of	ADP
ejpam-5830	336	7	toral	toral	ADJ
ejpam-5830	336	8	automorphisms	automorphism	NOUN
ejpam-5830	336	9	.	.	PUNCT
ejpam-5830	337	1	ergodic	ergodic	ADJ
ejpam-5830	337	2	theory	theory	NOUN
ejpam-5830	337	3	dynam	dynam	PROPN
ejpam-5830	337	4	.	.	PUNCT
ejpam-5830	338	1	systems	system	NOUN
ejpam-5830	338	2	,	,	PUNCT
ejpam-5830	338	3	15:569–592	15:569–592	NUM
ejpam-5830	338	4	,	,	PUNCT
ejpam-5830	338	5	1995	1995	NUM
ejpam-5830	338	6	.	.	PUNCT
ejpam-5830	339	1	[	[	X
ejpam-5830	339	2	30	30	NUM
ejpam-5830	339	3	]	]	X
ejpam-5830	339	4	a	a	DET
ejpam-5830	339	5	katok	katok	NOUN
ejpam-5830	339	6	and	and	CCONJ
ejpam-5830	339	7	r	r	NOUN
ejpam-5830	339	8	spatzier	spatzier	ADJ
ejpam-5830	339	9	.	.	PUNCT
ejpam-5830	340	1	first	first	ADJ
ejpam-5830	340	2	cohomology	cohomology	NOUN
ejpam-5830	340	3	of	of	ADP
ejpam-5830	340	4	anosov	anosov	NOUN
ejpam-5830	340	5	actions	action	NOUN
ejpam-5830	340	6	of	of	ADP
ejpam-5830	340	7	higher	high	ADJ
ejpam-5830	340	8	rank	rank	NOUN
ejpam-5830	340	9	abelian	abelian	NOUN
ejpam-5830	340	10	groups	group	NOUN
ejpam-5830	340	11	and	and	CCONJ
ejpam-5830	340	12	applications	application	NOUN
ejpam-5830	340	13	to	to	AUX
ejpam-5830	340	14	rigidity	rigidity	NOUN
ejpam-5830	340	15	.	.	PUNCT
ejpam-5830	341	1	inst	inst	PROPN
ejpam-5830	341	2	.	.	PUNCT
ejpam-5830	341	3	hautes	haute	VERB
ejpam-5830	341	4	études	études	PROPN
ejpam-5830	341	5	sci	sci	PROPN
ejpam-5830	341	6	.	.	PROPN
ejpam-5830	341	7	publ	publ	PROPN
ejpam-5830	341	8	.	.	PUNCT
ejpam-5830	342	1	math	math	NOUN
ejpam-5830	342	2	.	.	PUNCT
ejpam-5830	342	3	,	,	PUNCT
ejpam-5830	343	1	79:131–156	79:131–156	PROPN
ejpam-5830	343	2	,	,	PUNCT
ejpam-5830	343	3	1994	1994	NUM
ejpam-5830	343	4	.	.	PUNCT
ejpam-5830	344	1	[	[	X
ejpam-5830	344	2	31	31	NUM
ejpam-5830	344	3	]	]	PUNCT
ejpam-5830	344	4	a	a	DET
ejpam-5830	344	5	katok	katok	NOUN
ejpam-5830	344	6	and	and	CCONJ
ejpam-5830	344	7	r	r	NOUN
ejpam-5830	344	8	spatzier	spatzier	ADJ
ejpam-5830	344	9	.	.	PUNCT
ejpam-5830	345	1	subelliptic	subelliptic	ADJ
ejpam-5830	345	2	estimates	estimate	NOUN
ejpam-5830	345	3	of	of	ADP
ejpam-5830	345	4	polynomial	polynomial	ADJ
ejpam-5830	345	5	differential	differential	NOUN
ejpam-5830	345	6	operators	operator	NOUN
ejpam-5830	345	7	and	and	CCONJ
ejpam-5830	345	8	applications	application	NOUN
ejpam-5830	345	9	to	to	ADP
ejpam-5830	345	10	rigidity	rigidity	NOUN
ejpam-5830	345	11	of	of	ADP
ejpam-5830	345	12	abelian	abelian	ADJ
ejpam-5830	345	13	actions	action	NOUN
ejpam-5830	345	14	.	.	PUNCT
ejpam-5830	346	1	math	math	NOUN
ejpam-5830	346	2	.	.	PUNCT
ejpam-5830	347	1	res	re	NOUN
ejpam-5830	347	2	.	.	PUNCT
ejpam-5830	348	1	lett	lett	PROPN
ejpam-5830	348	2	.	.	PROPN
ejpam-5830	349	1	,	,	PUNCT
ejpam-5830	350	1	1:193–202	1:193–202	PROPN
ejpam-5830	350	2	,	,	PUNCT
ejpam-5830	350	3	1994	1994	NUM
ejpam-5830	350	4	.	.	PUNCT