id	sid	tid	token	lemma	pos
rx913n23n21	1	1	in	in	ADP
rx913n23n21	1	2	this	this	DET
rx913n23n21	1	3	thesis	thesis	NOUN
rx913n23n21	1	4	we	we	PRON
rx913n23n21	1	5	study	study	VERB
rx913n23n21	1	6	the	the	DET
rx913n23n21	1	7	riemannian	riemannian	ADJ
rx913n23n21	1	8	geometry	geometry	NOUN
rx913n23n21	1	9	of	of	ADP
rx913n23n21	1	10	diffeomorphism	diffeomorphism	NOUN
rx913n23n21	1	11	groups	group	NOUN
rx913n23n21	1	12	equipped	equip	VERB
rx913n23n21	1	13	with	with	ADP
rx913n23n21	1	14	a	a	DET
rx913n23n21	1	15	variety	variety	NOUN
rx913n23n21	1	16	of	of	ADP
rx913n23n21	1	17	sobolev	sobolev	NOUN
rx913n23n21	1	18	-	-	PUNCT
rx913n23n21	1	19	type	type	NOUN
rx913n23n21	1	20	metrics	metric	NOUN
rx913n23n21	1	21	.	.	PUNCT
rx913n23n21	2	1	most	most	ADV
rx913n23n21	2	2	notably	notably	ADV
rx913n23n21	2	3	,	,	PUNCT
rx913n23n21	2	4	we	we	PRON
rx913n23n21	2	5	consider	consider	VERB
rx913n23n21	2	6	the	the	DET
rx913n23n21	2	7	group	group	NOUN
rx913n23n21	2	8	of	of	ADP
rx913n23n21	2	9	volume	volume	NOUN
rx913n23n21	2	10	-	-	PUNCT
rx913n23n21	2	11	preserving	preserve	VERB
rx913n23n21	2	12	diffeomorphisms	diffeomorphism	NOUN
rx913n23n21	2	13	equipped	equip	VERB
rx913n23n21	2	14	with	with	ADP
rx913n23n21	2	15	a	a	DET
rx913n23n21	2	16	weak	weak	ADJ
rx913n23n21	2	17	l^2	l^2	NOUN
rx913n23n21	2	18	metric	metric	ADJ
rx913n23n21	2	19	,	,	PUNCT
rx913n23n21	2	20	whose	whose	DET
rx913n23n21	2	21	geodesics	geodesic	NOUN
rx913n23n21	2	22	correspond	correspond	VERB
rx913n23n21	2	23	to	to	ADP
rx913n23n21	2	24	lagrangian	lagrangian	ADJ
rx913n23n21	2	25	solutions	solution	NOUN
rx913n23n21	2	26	to	to	ADP
rx913n23n21	2	27	the	the	DET
rx913n23n21	2	28	euler	euler	PROPN
rx913n23n21	2	29	equations	equation	NOUN
rx913n23n21	2	30	.	.	PUNCT
rx913n23n21	3	1	a	a	DET
rx913n23n21	3	2	well	well	ADV
rx913n23n21	3	3	known	know	VERB
rx913n23n21	3	4	result	result	NOUN
rx913n23n21	3	5	of	of	ADP
rx913n23n21	3	6	ebin	ebin	NOUN
rx913n23n21	3	7	and	and	CCONJ
rx913n23n21	3	8	marsden	marsden	PROPN
rx913n23n21	3	9	states	state	VERB
rx913n23n21	3	10	that	that	SCONJ
rx913n23n21	3	11	lagrangian	lagrangian	ADJ
rx913n23n21	3	12	solutions	solution	NOUN
rx913n23n21	3	13	to	to	ADP
rx913n23n21	3	14	the	the	DET
rx913n23n21	3	15	euler	euler	PROPN
rx913n23n21	3	16	equations	equation	NOUN
rx913n23n21	3	17	,	,	PUNCT
rx913n23n21	3	18	when	when	SCONJ
rx913n23n21	3	19	framed	frame	VERB
rx913n23n21	3	20	as	as	ADP
rx913n23n21	3	21	an	an	DET
rx913n23n21	3	22	initial	initial	ADJ
rx913n23n21	3	23	value	value	NOUN
rx913n23n21	3	24	problem	problem	NOUN
rx913n23n21	3	25	,	,	PUNCT
rx913n23n21	3	26	are	be	AUX
rx913n23n21	3	27	exactly	exactly	ADV
rx913n23n21	3	28	as	as	ADV
rx913n23n21	3	29	smooth	smooth	ADJ
rx913n23n21	3	30	as	as	ADP
rx913n23n21	3	31	their	their	PRON
rx913n23n21	3	32	initial	initial	ADJ
rx913n23n21	3	33	conditions	condition	NOUN
rx913n23n21	3	34	.	.	PUNCT
rx913n23n21	4	1	we	we	PRON
rx913n23n21	4	2	investigate	investigate	VERB
rx913n23n21	4	3	a	a	DET
rx913n23n21	4	4	similar	similar	ADJ
rx913n23n21	4	5	regularity	regularity	NOUN
rx913n23n21	4	6	property	property	NOUN
rx913n23n21	4	7	for	for	ADP
rx913n23n21	4	8	lagrangian	lagrangian	ADJ
rx913n23n21	4	9	solutions	solution	NOUN
rx913n23n21	4	10	to	to	ADP
rx913n23n21	4	11	the	the	DET
rx913n23n21	4	12	euler	euler	PROPN
rx913n23n21	4	13	equations	equation	NOUN
rx913n23n21	4	14	when	when	SCONJ
rx913n23n21	4	15	framed	frame	VERB
rx913n23n21	4	16	as	as	ADP
rx913n23n21	4	17	a	a	DET
rx913n23n21	4	18	two	two	NUM
rx913n23n21	4	19	-	-	PUNCT
rx913n23n21	4	20	point	point	NOUN
rx913n23n21	4	21	boundary	boundary	ADJ
rx913n23n21	4	22	value	value	NOUN
rx913n23n21	4	23	problem	problem	NOUN
rx913n23n21	4	24	.	.	PUNCT
rx913n23n21	5	1	in	in	ADP
rx913n23n21	5	2	particular	particular	ADJ
rx913n23n21	5	3	,	,	PUNCT
rx913n23n21	5	4	we	we	PRON
rx913n23n21	5	5	prove	prove	VERB
rx913n23n21	5	6	that	that	SCONJ
rx913n23n21	5	7	these	these	DET
rx913n23n21	5	8	l^2	l^2	NOUN
rx913n23n21	5	9	geodesics	geodesic	NOUN
rx913n23n21	5	10	are	be	AUX
rx913n23n21	5	11	exactly	exactly	ADV
rx913n23n21	5	12	as	as	ADV
rx913n23n21	5	13	smooth	smooth	ADJ
rx913n23n21	5	14	as	as	ADP
rx913n23n21	5	15	their	their	PRON
rx913n23n21	5	16	boundary	boundary	ADJ
rx913n23n21	5	17	conditions	condition	NOUN
rx913n23n21	5	18	.	.	PUNCT
rx913n23n21	6	1	we	we	PRON
rx913n23n21	6	2	achieve	achieve	VERB
rx913n23n21	6	3	like	like	ADP
rx913n23n21	6	4	results	result	NOUN
rx913n23n21	6	5	in	in	ADP
rx913n23n21	6	6	an	an	DET
rx913n23n21	6	7	array	array	NOUN
rx913n23n21	6	8	of	of	ADP
rx913n23n21	6	9	other	other	ADJ
rx913n23n21	6	10	settings	setting	NOUN
rx913n23n21	6	11	including	include	VERB
rx913n23n21	6	12	3d	3d	PRON
rx913n23n21	6	13	axisymmetric	axisymmetric	ADJ
rx913n23n21	6	14	ideal	ideal	ADJ
rx913n23n21	6	15	fluids	fluid	NOUN
rx913n23n21	6	16	,	,	PUNCT
rx913n23n21	6	17	symplectic	symplectic	ADJ
rx913n23n21	6	18	euler	euler	NOUN
rx913n23n21	6	19	equations	equation	NOUN
rx913n23n21	6	20	,	,	PUNCT
rx913n23n21	6	21	euler	euler	ADJ
rx913n23n21	6	22	-	-	PUNCT
rx913n23n21	6	23	alpha	alpha	NOUN
rx913n23n21	6	24	equations	equation	NOUN
rx913n23n21	6	25	,	,	PUNCT
rx913n23n21	6	26	and	and	CCONJ
rx913n23n21	6	27	one	one	NUM
rx913n23n21	6	28	dimensional	dimensional	ADJ
rx913n23n21	6	29	integrable	integrable	ADJ
rx913n23n21	6	30	systems	system	NOUN
rx913n23n21	6	31	including	include	VERB
rx913n23n21	6	32	the	the	DET
rx913n23n21	6	33	mu	mu	PROPN
rx913n23n21	6	34	-	-	PUNCT
rx913n23n21	6	35	ch	ch	NOUN
rx913n23n21	6	36	and	and	CCONJ
rx913n23n21	6	37	hunter	hunter	NOUN
rx913n23n21	6	38	-	-	PUNCT
rx913n23n21	6	39	saxton	saxton	NOUN
rx913n23n21	6	40	equations	equation	NOUN
rx913n23n21	6	41	.	.	PUNCT