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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 Exponential dichotomy ： ウィキペディア英語版 Exponential dichotomy In the mathematical theory of dynamical systems, an exponential dichotomy is a property of an equilibrium point that extends the idea of hyperbolicity to non-autonomous systems. ==Definition== If :$\backslash dot$ is a linear non-autonomous dynamical system in R''n'' with fundamental solution matrix Φ(''t''), Φ(0) = ''I'', then the equilibrium point 0 is said to have an ''exponential dichotomy'' if there exists a (constant) matrix ''P'' such that ''P''2 = ''P'' and positive constants ''K'', ''L'', α, and β such that : and :$||\; \backslash Phi(t)\; (I\; -\; P)\; \backslash Phi^(s)\; ||\; \backslash le\; Le^\backslash mboxs\; \backslash ge\; t\; >\; -\backslash infty.$ If furthermore, ''L'' = 1/''K'' and β = α, then 0 is said to have a ''uniform exponential dichotomy''. The constants α and β allow us to define the ''spectral window'' of the equilibrium point, (−α, β). 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「Exponential dichotomy」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.