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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Carathéodory–Jacobi–Lie theorem ： ウィキペディア英語版 Carathéodory–Jacobi–Lie theorem The Carathéodory–Jacobi–Lie theorem is a theorem in symplectic geometry which generalizes Darboux's theorem. ==Statement== Let ''M'' be a 2''n''-dimensional symplectic manifold with symplectic form ω. For ''p'' ∈ ''M'' and ''r'' ≤ ''n'', let ''f''1, ''f''2, ..., ''f''r be smooth functions defined on an open neighborhood ''V'' of ''p'' whose differentials are linearly independent at each point, or equivalently :$df\_1(p)\; \backslash wedge\; \backslash ldots\; \backslash wedge\; df\_r(p)\; \backslash neq\; 0,$ where = 0. (In other words they are pairwise in involution.) Here is the Poisson bracket. Then there are functions ''f''r+1, ..., ''f''n, ''g''1, ''g''2, ..., ''g''n defined on an open neighborhood ''U'' ⊂ ''V'' of ''p'' such that (fi, gi) is a symplectic chart of ''M'', i.e., ω is expressed on ''U'' as :$\backslash omega\; =\; \backslash sum\_^n\; df\_i\; \backslash wedge\; dg\_i.$ 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Carathéodory–Jacobi–Lie theorem」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.