id	sid	tid	token	lemma	pos
7m01bk1495q	1	1	the	the	DET
7m01bk1495q	1	2	entropy	entropy	NOUN
7m01bk1495q	1	3	of	of	ADP
7m01bk1495q	1	4	a	a	DET
7m01bk1495q	1	5	discrete	discrete	ADJ
7m01bk1495q	1	6	dynamical	dynamical	ADJ
7m01bk1495q	1	7	system	system	NOUN
7m01bk1495q	1	8	is	be	AUX
7m01bk1495q	1	9	a	a	DET
7m01bk1495q	1	10	rough	rough	ADJ
7m01bk1495q	1	11	gauge	gauge	NOUN
7m01bk1495q	1	12	of	of	ADP
7m01bk1495q	1	13	its	its	PRON
7m01bk1495q	1	14	complexity	complexity	NOUN
7m01bk1495q	1	15	.	.	PUNCT
7m01bk1495q	2	1	we	we	PRON
7m01bk1495q	2	2	wish	wish	VERB
7m01bk1495q	2	3	to	to	PART
7m01bk1495q	2	4	find	find	VERB
7m01bk1495q	2	5	a	a	DET
7m01bk1495q	2	6	bound	bind	VERB
7m01bk1495q	2	7	for	for	ADP
7m01bk1495q	2	8	the	the	DET
7m01bk1495q	2	9	entropy	entropy	NOUN
7m01bk1495q	2	10	of	of	ADP
7m01bk1495q	2	11	a	a	DET
7m01bk1495q	2	12	system	system	NOUN
7m01bk1495q	2	13	.	.	PUNCT
7m01bk1495q	3	1	we	we	PRON
7m01bk1495q	3	2	particularly	particularly	ADV
7m01bk1495q	3	3	concern	concern	VERB
7m01bk1495q	3	4	ourselves	ourselves	PRON
7m01bk1495q	3	5	with	with	ADP
7m01bk1495q	3	6	the	the	DET
7m01bk1495q	3	7	specific	specific	ADJ
7m01bk1495q	3	8	family	family	NOUN
7m01bk1495q	3	9	of	of	ADP
7m01bk1495q	3	10	maps	map	NOUN
7m01bk1495q	3	11	$	$	SYM
7m01bk1495q	3	12	f:\overline{\r	f:\overline{\r	ADV
7m01bk1495q	3	13	}	}	PUNCT
7m01bk1495q	3	14	\	\	X
7m01bk1495q	3	15	imes	ime	NOUN
7m01bk1495q	3	16	\overline{\r	\overline{\r	SPACE
7m01bk1495q	3	17	}	}	PUNCT
7m01bk1495q	3	18	\	\	PROPN
7m01bk1495q	3	19	ightarrow	ightarrow	VERB
7m01bk1495q	3	20	\overline{\r	\overline{\r	SPACE
7m01bk1495q	3	21	}	}	PUNCT
7m01bk1495q	3	22	\	\	PROPN
7m01bk1495q	3	23	imes	imes	PROPN
7m01bk1495q	3	24	\overline{\r}$	\overline{\r}$	ADV
7m01bk1495q	3	25	defined	define	VERB
7m01bk1495q	3	26	by	by	ADP
7m01bk1495q	3	27	$	$	SYM
7m01bk1495q	3	28	f(x	f(x	NUM
7m01bk1495q	3	29	,	,	PUNCT
7m01bk1495q	3	30	y	y	PROPN
7m01bk1495q	3	31	)	)	PUNCT
7m01bk1495q	3	32	=	=	PROPN
7m01bk1495q	3	33	\left(y\	\left(y\	NOUN
7m01bk1495q	3	34	rac{x+a}{x-1},x+a-1\	rac{x+a}{x-1},x+a-1\	ADP
7m01bk1495q	3	35	ight)$	ight)$	PROPN
7m01bk1495q	3	36	,	,	PUNCT
7m01bk1495q	3	37	where	where	SCONJ
7m01bk1495q	3	38	$	$	SYM
7m01bk1495q	3	39	a	a	DET
7m01bk1495q	3	40	\in	\in	PROPN
7m01bk1495q	3	41	\r$	\r$	NOUN
7m01bk1495q	3	42	is	be	AUX
7m01bk1495q	3	43	a	a	DET
7m01bk1495q	3	44	parameter	parameter	NOUN
7m01bk1495q	3	45	subject	subject	ADJ
7m01bk1495q	3	46	to	to	ADP
7m01bk1495q	3	47	conditions	condition	NOUN
7m01bk1495q	3	48	specified	specify	VERB
7m01bk1495q	3	49	later	later	ADV
7m01bk1495q	3	50	.	.	PUNCT
7m01bk1495q	4	1	this	this	DET
7m01bk1495q	4	2	family	family	NOUN
7m01bk1495q	4	3	first	first	ADV
7m01bk1495q	4	4	appeared	appear	VERB
7m01bk1495q	4	5	in	in	ADP
7m01bk1495q	4	6	various	various	ADJ
7m01bk1495q	4	7	statistical	statistical	ADJ
7m01bk1495q	4	8	physics	physics	NOUN
7m01bk1495q	4	9	papers	paper	NOUN
7m01bk1495q	4	10	and	and	CCONJ
7m01bk1495q	4	11	was	be	AUX
7m01bk1495q	4	12	considered	consider	VERB
7m01bk1495q	4	13	mathematically	mathematically	ADV
7m01bk1495q	4	14	by	by	ADP
7m01bk1495q	4	15	bedford	bedford	PROPN
7m01bk1495q	4	16	and	and	CCONJ
7m01bk1495q	4	17	diller	diller	NOUN
7m01bk1495q	4	18	.	.	PUNCT
7m01bk1495q	5	1	our	our	PRON
7m01bk1495q	5	2	method	method	NOUN
7m01bk1495q	5	3	is	be	AUX
7m01bk1495q	5	4	combinatorial	combinatorial	ADJ
7m01bk1495q	5	5	,	,	PUNCT
7m01bk1495q	5	6	using	use	VERB
7m01bk1495q	5	7	invariant	invariant	ADJ
7m01bk1495q	5	8	and	and	CCONJ
7m01bk1495q	5	9	critical	critical	ADJ
7m01bk1495q	5	10	curves	curve	NOUN
7m01bk1495q	5	11	for	for	ADP
7m01bk1495q	5	12	$	$	SYM
7m01bk1495q	5	13	f$	f$	NOUN
7m01bk1495q	5	14	to	to	PART
7m01bk1495q	5	15	define	define	VERB
7m01bk1495q	5	16	a	a	DET
7m01bk1495q	5	17	partition	partition	NOUN
7m01bk1495q	5	18	of	of	ADP
7m01bk1495q	5	19	$	$	SYM
7m01bk1495q	5	20	\overline{\r	\overline{\r	NOUN
7m01bk1495q	5	21	}	}	PUNCT
7m01bk1495q	5	22	\	\	PROPN
7m01bk1495q	5	23	imes	imes	PROPN
7m01bk1495q	5	24	\overline{\r}$	\overline{\r}$	PROPN
7m01bk1495q	5	25	that	that	PRON
7m01bk1495q	5	26	is	be	AUX
7m01bk1495q	5	27	convenient	convenient	ADJ
7m01bk1495q	5	28	for	for	ADP
7m01bk1495q	5	29	coding	code	VERB
7m01bk1495q	5	30	orbits	orbit	NOUN
7m01bk1495q	5	31	under	under	ADP
7m01bk1495q	5	32	$	$	SYM
7m01bk1495q	5	33	f$.	f$.	ADJ
7m01bk1495q	5	34	we	we	PRON
7m01bk1495q	5	35	may	may	AUX
7m01bk1495q	5	36	expand	expand	VERB
7m01bk1495q	5	37	these	these	DET
7m01bk1495q	5	38	codings	coding	NOUN
7m01bk1495q	5	39	to	to	PART
7m01bk1495q	5	40	hold	hold	VERB
7m01bk1495q	5	41	for	for	ADP
7m01bk1495q	5	42	points	point	NOUN
7m01bk1495q	5	43	without	without	ADP
7m01bk1495q	5	44	well	well	ADV
7m01bk1495q	5	45	-	-	PUNCT
7m01bk1495q	5	46	defined	define	VERB
7m01bk1495q	5	47	orbits	orbit	NOUN
7m01bk1495q	5	48	.	.	PUNCT
7m01bk1495q	6	1	these	these	DET
7m01bk1495q	6	2	more	more	ADJ
7m01bk1495q	6	3	general	general	ADJ
7m01bk1495q	6	4	codings	coding	NOUN
7m01bk1495q	6	5	allow	allow	VERB
7m01bk1495q	6	6	us	we	PRON
7m01bk1495q	6	7	to	to	PART
7m01bk1495q	6	8	construct	construct	VERB
7m01bk1495q	6	9	a	a	DET
7m01bk1495q	6	10	set	set	NOUN
7m01bk1495q	6	11	with	with	ADP
7m01bk1495q	6	12	easier	easy	ADJ
7m01bk1495q	6	13	-	-	PUNCT
7m01bk1495q	6	14	to	to	PART
7m01bk1495q	6	15	-	-	PUNCT
7m01bk1495q	6	16	calculate	calculate	NOUN
7m01bk1495q	6	17	entropy	entropy	NOUN
7m01bk1495q	6	18	.	.	PUNCT
7m01bk1495q	7	1	this	this	DET
7m01bk1495q	7	2	new	new	ADJ
7m01bk1495q	7	3	set	set	NOUN
7m01bk1495q	7	4	's	's	PART
7m01bk1495q	7	5	entropy	entropy	NOUN
7m01bk1495q	7	6	is	be	AUX
7m01bk1495q	7	7	a	a	DET
7m01bk1495q	7	8	lower	lower	ADV
7m01bk1495q	7	9	bound	bound	ADJ
7m01bk1495q	7	10	for	for	ADP
7m01bk1495q	7	11	the	the	DET
7m01bk1495q	7	12	entropy	entropy	NOUN
7m01bk1495q	7	13	of	of	ADP
7m01bk1495q	7	14	$	$	SYM
7m01bk1495q	7	15	f$.	f$.	X