翻訳と辞書 Words near each other ・ Invariance of domain ・ Invariance principle (linguistics) ・ Invariance theorem ・ Invariances ・ Invariant ・ Invariant (computer science) ・ Invariant (mathematics) ・ Invariant (physics) ・ Invariant basis number ・ Invariant convex cone ・ Invariant differential operator ・ Invariant estimator ・ Invariant extended Kalman filter ・ Invariant factor ・ Invariant factorization of LPDOs ・ Invariant manifold ・ Invariant mass ・ Invariant measure ・ Invariant of a binary form ・ Invariant polynomial ・ Invariant set postulate ・ Invariant speed ・ Invariant subspace ・ Invariant subspace problem ・ Invariant theory ・ Invariant-based programming ・ Invariants of tensors ・ Invasion ・ Invasion (1966 film) ・ Invasion (2014 film) Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Invariant manifold ： ウィキペディア英語版 Invariant manifold In dynamical systems, a branch of mathematics, an invariant manifold is a topological manifold that is invariant under the action of the dynamical system.〔Hirsh M.W., Pugh C.C., Shub M., Invariant Manifolds, Lect. Notes. Math., 583, Springer, Berlin — Heidelberg, 1977 〕 Examples include the slow manifold, center manifold, stable manifold, unstable manifold, subcenter manifold and inertial manifold. Typically, although by no means always, invariant manifolds are constructed as a 'perturbation' of an invariant subspace about an equilibrium. In dissipative systems, an invariant manifold based upon the gravest, longest lasting modes forms an effective low-dimensional, reduced, model of the dynamics. 〔A. J. Roberts. The utility of an invariant manifold description of the evolution of a dynamical system. SIAM J. Math. Anal., 20:1447–1458, 1989. http://locus.siam.org/SIMA/volume-20/art_0520094.html〕 ==Definition== Consider the differential equation $dx/dt\; =\; f(x),\backslash \; x\; \backslash in\; \backslash mathbb\; R^n,$ with flow $x(t)=\backslash phi\_t(x\_0)$ being the solution of the differential equation with $x(0)=x\_0$. A set $S\; \backslash subset\; \backslash mathbb\; R^n$ is called an ''invariant set'' for the differential equation if, for each $x\_0\; \backslash in\; S$, the solution $t\; \backslash mapsto\; \backslash phi\_t(x\_0)$, defined on its maximal interval of existence, has its image in $S$. Alternatively, the orbit passing through each $x\_0\; \backslash in\; S$ lies in $S$. In addition, $S$ is called an ''invariant manifold'' if $S$ is a manifold. 〔C. Chicone. Ordinary Differential Equations with Applications, volume 34 of Texts in Applied Mathematics. Springer, 2006, p.34〕 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「Invariant manifold」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.