翻訳と辞書 Words near each other ・ Hypercompe peruvensis ・ Hypercompe praeclara ・ Hyperbolic law of cosines ・ Hyperbolic link ・ Hyperbolic manifold ・ Hyperbolic motion ・ Hyperbolic motion (relativity) ・ Hyperbolic navigation ・ Hyperbolic orthogonality ・ Hyperbolic partial differential equation ・ Hyperbolic plane (disambiguation) ・ Hyperbolic point ・ Hyperbolic quaternion ・ Hyperbolic secant distribution ・ Hyperbolic sector ・ Hyperbolic set ・ Hyperbolic space ・ Hyperbolic spiral ・ Hyperbolic structure ・ Hyperbolic tetrahedral-octahedral honeycomb ・ Hyperbolic trajectory ・ Hyperbolic tree ・ Hyperbolic triangle ・ Hyperbolic trigonometry ・ Hyperbolic volume ・ Hyperbolization theorem ・ Hyperboloid ・ Hyperboloid model ・ Hyperboloid structure ・ Hyperbolus 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 Hyperbolic set ： ウィキペディア英語版 Hyperbolic set In dynamical systems theory, a subset Λ of a smooth manifold ''M'' is said to have a hyperbolic structure with respect to a smooth map ''f'' if its tangent bundle may be split into two invariant subbundles, one of which is contracting and the other is expanding under ''f'', with respect to some Riemannian metric on ''M''. An analogous definition applies to the case of flows. In the special case when the entire manifold ''M'' is hyperbolic, the map ''f'' is called an Anosov diffeomorphism. The dynamics of ''f'' on a hyperbolic set, or hyperbolic dynamics, exhibits features of local structural stability and has been much studied, cf. Axiom A. == Definition == Let ''M'' be a compact smooth manifold, ''f'': ''M'' → ''M'' a diffeomorphism, and ''Df'': ''TM'' → ''TM'' the differential of ''f''. An ''f''-invariant subset Λ of ''M'' is said to be hyperbolic, or to have a hyperbolic structure, if the restriction to Λ of the tangent bundle of ''M'' admits a splitting into a Whitney sum of two ''Df''-invariant subbundles, called the stable bundle and the unstable bundle and denoted ''E''''s'' and ''E''''u''. With respect to some Riemannian metric on ''M'', the restriction of ''Df'' to ''E''''s'' must be a contraction and the restriction of ''Df'' to ''E''''u'' must be an expansion. Thus, there exist constants 0<''λ''<1 and ''c''>0 such that :$T\_\backslash Lambda\; M\; =\; E^s\backslash oplus\; E^u$ and :$(Df)\_x\; E^s\_x\; =\; E^s\_$ and $(Df)\_x\; E^u\_x\; =\; E^u\_$ for all $x\backslash in\; \backslash Lambda$ and :$\backslash |Df^nv\backslash |\; \backslash le\; c\backslash lambda^n\backslash |v\backslash |$ for all $v\backslash in\; E^s$ and $n>\; 0$ and :$\backslash |Df^v\backslash |\; \backslash le\; c\backslash lambda^n\; \backslash |v\backslash |$ for all $v\backslash in\; E^u$ and $n>0$. If Λ is hyperbolic then there exists a Riemannian metric for which ''c'' = 1 — such a metric is called adapted. 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「Hyperbolic set」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.