Symplectic leaves - 편집 역사

2020년 11월 13일 (금) 14:47에 imported>Pythagoras0님의 편집

2020-11-13T14:47:02Z

2014년 8월 30일 (토) 11:58에 imported>Pythagoras0님의 편집

2014-08-30T11:58:56Z

2013년 11월 1일 (금) 21:50에 imported>Pythagoras0님의 편집

2013-11-01T21:50:10Z

2013년 4월 21일 (일) 12:43에 imported>Pythagoras0님의 편집

2013-04-21T12:43:42Z

2012년 10월 29일 (월) 17:55에 imported>Pythagoras0님의 편집

2012-10-29T17:55:58Z

2012년 10월 29일 (월) 17:50에 imported>Pythagoras0님의 편집

2012-10-29T17:50:59Z

2012년 10월 29일 (월) 00:03에 imported>Pythagoras0님의 편집

2012-10-29T00:03:48Z

2012년 8월 27일 (월) 01:54에 http://bomber0.myid.net/님의 편집

2012-08-27T01:54:15Z

http://bomber0.myid.net/: 피타고라스님이 이 페이지의 이름을 symplectic leaves로 바꾸었습니다.

2012-06-09T23:59:50Z

피타고라스님이 이 페이지의 이름을 symplectic leaves로 바꾸었습니다.

2012년 6월 9일 (토) 23:58에 http://bomber0.myid.net/님의 편집

2012-06-09T23:58:34Z

차이 보기

← 이전 판		2020년 11월 13일 (금) 14:47 판
23번째 줄:		23번째 줄:
	[[분류:math and physics]]		[[분류:math and physics]]
	[[분류:classical mechanics]]		[[분류:classical mechanics]]
		+	[[분류:migrate]]

← 이전 판		2014년 8월 30일 (토) 11:58 판
16번째 줄:		16번째 줄:
	* the foliation is the map <math>\bigcup_{\R} \R \rightarrow \R^2</math>		* the foliation is the map <math>\bigcup_{\R} \R \rightarrow \R^2</math>

		+	==related items==
		+	* [[Foliation dynamics]]

	[[분류:개인노트]]		[[분류:개인노트]]

@@ 1번째 줄: / 1번째 줄: @@
-[[symplectic geometry|symplectic geometry]]
+==introduction==
 [[분류:개인노트]]
 [[분류:physics]]
 [[분류:math and physics]]
 [[분류:classical mechanics]]

← 이전 판		2013년 4월 21일 (일) 12:43 판
6번째 줄:		6번째 줄:
	[[분류:physics]]		[[분류:physics]]
	[[분류:math and physics]]		[[분류:math and physics]]
		+	[[분류:classical mechanics]]

← 이전 판		2012년 10월 29일 (월) 17:55 판
5번째 줄:		5번째 줄:
	[[분류:개인노트]]		[[분류:개인노트]]
	[[분류:physics]]		[[분류:physics]]
		+	[[분류:math and physics]]

← 이전 판		2012년 10월 29일 (월) 17:50 판
4번째 줄:		4번째 줄:
	27/02/201123:12:31‹william›<math>x \sim y</math>27/02/201123:14:18‹william›Let <math>D</math> be a degenerate distribution27/02/201123:14:49‹william›this means that for every point <math>x \in M</math>, <math>D_x</math> is a subset of <math>T_x M</math>27/02/201123:14:58‹william›subset = subspace27/02/201123:15:18‹william›distribution normally means that <math>D_x</math> is constant rank27/02/201123:15:25‹william›and <math>D_x</math> is spanned by vector fields27/02/201123:15:58‹william›which means that for every <math>x</math> there is vector fields <math>X_1,\ldots,X_r</math> locally defined around <math>x</math> such that <math>X_1(x),\ldots,X_r(x)</math> span <math>D_x</math>27/02/201123:16:19‹william›and <math>X_1(y),\ldots,X_r(y)</math> lie in <math>D_y</math> for all <math>y</math> where they are defined27/02/201123:18:02‹william›a foliation of <math>D</math> is an immersed manifold <math>A</math> of <math>M</math> with <math>TA = D</math>27/02/201123:19:10‹william›Let <math>M^{dis}</math> be the manifold with underlying set <math>M</math> and the discrete topology27/02/201123:20:09‹william›<math>M^{dis}</math> is an immersed manifold for <math>D = M \times 0</math>27/02/201123:20:36‹william›<math>M = \R^2</math>27/02/201123:20:46‹william›<math>D = \R^2 \times \R</math>27/02/201123:24:17‹william›the foliation is the map <math>\bigcup_{\R} \R \arr \R^2</math>27/02/201123:24:25‹william›the foliation is the map <math>\bigcup_{\R} \R \rightarrow \R^2</math>		27/02/201123:12:31‹william›<math>x \sim y</math>27/02/201123:14:18‹william›Let <math>D</math> be a degenerate distribution27/02/201123:14:49‹william›this means that for every point <math>x \in M</math>, <math>D_x</math> is a subset of <math>T_x M</math>27/02/201123:14:58‹william›subset = subspace27/02/201123:15:18‹william›distribution normally means that <math>D_x</math> is constant rank27/02/201123:15:25‹william›and <math>D_x</math> is spanned by vector fields27/02/201123:15:58‹william›which means that for every <math>x</math> there is vector fields <math>X_1,\ldots,X_r</math> locally defined around <math>x</math> such that <math>X_1(x),\ldots,X_r(x)</math> span <math>D_x</math>27/02/201123:16:19‹william›and <math>X_1(y),\ldots,X_r(y)</math> lie in <math>D_y</math> for all <math>y</math> where they are defined27/02/201123:18:02‹william›a foliation of <math>D</math> is an immersed manifold <math>A</math> of <math>M</math> with <math>TA = D</math>27/02/201123:19:10‹william›Let <math>M^{dis}</math> be the manifold with underlying set <math>M</math> and the discrete topology27/02/201123:20:09‹william›<math>M^{dis}</math> is an immersed manifold for <math>D = M \times 0</math>27/02/201123:20:36‹william›<math>M = \R^2</math>27/02/201123:20:46‹william›<math>D = \R^2 \times \R</math>27/02/201123:24:17‹william›the foliation is the map <math>\bigcup_{\R} \R \arr \R^2</math>27/02/201123:24:25‹william›the foliation is the map <math>\bigcup_{\R} \R \rightarrow \R^2</math>
	[[분류:개인노트]]		[[분류:개인노트]]
		+	[[분류:physics]]

@@ 1번째 줄: / 1번째 줄: @@
-[[symplectic geometry|]]
+[[symplectic geometry|symplectic geometry]]
 ‹william›The symplectic leaves are equivalence relations <math>x \tilde y</math> if and only if <math>x</math> can be connected to <math>y</math> be a piece-wise Hamiltonian path
 /02/201123:12:31‹william›<math>x \sim y</math>27/02/201123:14:18‹william›Let <math>D</math> be a degenerate distribution27/02/201123:14:49‹william›this means that for every point <math>x \in M</math>, <math>D_x</math> is a subset of <math>T_x M</math>27/02/201123:14:58‹william›subset = subspace27/02/201123:15:18‹william›distribution normally means that <math>D_x</math> is constant rank27/02/201123:15:25‹william›and <math>D_x</math> is spanned by vector fields27/02/201123:15:58‹william›which means that for every <math>x</math> there is vector fields <math>X_1,\ldots,X_r</math> locally defined around <math>x</math> such that <math>X_1(x),\ldots,X_r(x)</math> span <math>D_x</math>27/02/201123:16:19‹william›and <math>X_1(y),\ldots,X_r(y)</math> lie in <math>D_y</math> for all <math>y</math> where they are defined27/02/201123:18:02‹william›a foliation of <math>D</math> is an immersed manifold <math>A</math> of <math>M</math> with <math>TA = D</math>27/02/201123:19:10‹william›Let <math>M^{dis}</math> be the manifold with underlying set <math>M</math> and the discrete topology27/02/201123:20:09‹william›<math>M^{dis}</math> is an immersed manifold for <math>D = M \times 0</math>27/02/201123:20:36‹william›<math>M = \R^2</math>27/02/201123:20:46‹william›<math>D = \R^2 \times \R</math>27/02/201123:24:17‹william›the foliation is the map <math>\bigcup_{\R} \R \arr \R^2</math>27/02/201123:24:25‹william›the foliation is the map <math>\bigcup_{\R} \R \rightarrow \R^2</math>

← 이전 판		2012년 8월 27일 (월) 01:54 판
3번째 줄:		3번째 줄:
	‹william›The symplectic leaves are equivalence relations <math>x \tilde y</math> if and only if <math>x</math> can be connected to <math>y</math> be a piece-wise Hamiltonian path		‹william›The symplectic leaves are equivalence relations <math>x \tilde y</math> if and only if <math>x</math> can be connected to <math>y</math> be a piece-wise Hamiltonian path
	27/02/201123:12:31‹william›<math>x \sim y</math>27/02/201123:14:18‹william›Let <math>D</math> be a degenerate distribution27/02/201123:14:49‹william›this means that for every point <math>x \in M</math>, <math>D_x</math> is a subset of <math>T_x M</math>27/02/201123:14:58‹william›subset = subspace27/02/201123:15:18‹william›distribution normally means that <math>D_x</math> is constant rank27/02/201123:15:25‹william›and <math>D_x</math> is spanned by vector fields27/02/201123:15:58‹william›which means that for every <math>x</math> there is vector fields <math>X_1,\ldots,X_r</math> locally defined around <math>x</math> such that <math>X_1(x),\ldots,X_r(x)</math> span <math>D_x</math>27/02/201123:16:19‹william›and <math>X_1(y),\ldots,X_r(y)</math> lie in <math>D_y</math> for all <math>y</math> where they are defined27/02/201123:18:02‹william›a foliation of <math>D</math> is an immersed manifold <math>A</math> of <math>M</math> with <math>TA = D</math>27/02/201123:19:10‹william›Let <math>M^{dis}</math> be the manifold with underlying set <math>M</math> and the discrete topology27/02/201123:20:09‹william›<math>M^{dis}</math> is an immersed manifold for <math>D = M \times 0</math>27/02/201123:20:36‹william›<math>M = \R^2</math>27/02/201123:20:46‹william›<math>D = \R^2 \times \R</math>27/02/201123:24:17‹william›the foliation is the map <math>\bigcup_{\R} \R \arr \R^2</math>27/02/201123:24:25‹william›the foliation is the map <math>\bigcup_{\R} \R \rightarrow \R^2</math>		27/02/201123:12:31‹william›<math>x \sim y</math>27/02/201123:14:18‹william›Let <math>D</math> be a degenerate distribution27/02/201123:14:49‹william›this means that for every point <math>x \in M</math>, <math>D_x</math> is a subset of <math>T_x M</math>27/02/201123:14:58‹william›subset = subspace27/02/201123:15:18‹william›distribution normally means that <math>D_x</math> is constant rank27/02/201123:15:25‹william›and <math>D_x</math> is spanned by vector fields27/02/201123:15:58‹william›which means that for every <math>x</math> there is vector fields <math>X_1,\ldots,X_r</math> locally defined around <math>x</math> such that <math>X_1(x),\ldots,X_r(x)</math> span <math>D_x</math>27/02/201123:16:19‹william›and <math>X_1(y),\ldots,X_r(y)</math> lie in <math>D_y</math> for all <math>y</math> where they are defined27/02/201123:18:02‹william›a foliation of <math>D</math> is an immersed manifold <math>A</math> of <math>M</math> with <math>TA = D</math>27/02/201123:19:10‹william›Let <math>M^{dis}</math> be the manifold with underlying set <math>M</math> and the discrete topology27/02/201123:20:09‹william›<math>M^{dis}</math> is an immersed manifold for <math>D = M \times 0</math>27/02/201123:20:36‹william›<math>M = \R^2</math>27/02/201123:20:46‹william›<math>D = \R^2 \times \R</math>27/02/201123:24:17‹william›the foliation is the map <math>\bigcup_{\R} \R \arr \R^2</math>27/02/201123:24:25‹william›the foliation is the map <math>\bigcup_{\R} \R \rightarrow \R^2</math>
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−	~~<h5>3/6/2011</h5>~~

← 이전 판	2012년 6월 9일 (토) 23:59 판
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