翻訳と辞書 Words near each other ・ Homochitto River ・ Homochitto, Issaquena County, Mississippi ・ Homochitto, Mississippi ・ Homochlodes ・ Homochlorcyclizine ・ Homochronous ・ Homocioaia River ・ Homocitrate synthase ・ Homocitric acid ・ Homocitrulline ・ Homoclinal ridge ・ Homocline ・ Homocline (disambiguation) ・ Homoclinic bifurcation ・ Homoclinic connection ・ Homoclinic orbit ・ Homocodon ・ Homoconjugation ・ Homocore (zine) ・ Homocysteic acid ・ Homocysteine ・ Homocysteine desulfhydrase ・ Homocysteine methylase ・ Homocysteine S-methyltransferase ・ Homocystinuria ・ Homoderus mellyi ・ Homodes ・ Homodiaetus ・ Homodictya ・ Homodigma 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 Homoclinic orbit ： ウィキペディア英語版 Homoclinic orbit In mathematics, a homoclinic orbit is a trajectory of a flow of a dynamical system which joins a saddle equilibrium point to itself. More precisely, a homoclinic orbit lies in the intersection of the stable manifold and the unstable manifold of an equilibrium. Consider the continuous dynamical system described by the ODE :$\backslash dot\; x=f(x)$ Suppose there is an equilibrium at $x=x\_0$, then a solution $\backslash Phi(t)$ is a homoclinic orbit if :$\backslash Phi(t)\backslash rightarrow\; x\_0\backslash quad\; \backslash mathrm\backslash quad$ t\rightarrow\pm\infty If the phase space has three or more dimensions, then it is important to consider the topology of the unstable manifold of the saddle point. The figures show two cases. First, when the unstable manifold is topologically a cylinder, and secondly, when the unstable manifold is topologically a Möbius strip; in this case the homoclinic orbit is called ''twisted''. == Discrete dynamical system == Homoclinic orbits and homoclinic points are defined in the same way for iterated functions, as the intersection of the stable set and unstable set of some fixed point or periodic point of the system. We also have the notion of homoclinic orbit when considering discrete dynamical systems. In such a case, if $f:M\backslash rightarrow\; M$ is a diffeomorphism of a manifold $M$, we say that $x$ is a homoclinic point if it has the same past and future - more specifically, if it exists a fixed (or periodic) point $p$ such that :$\backslash lim\_f^n(x)=p.$ 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「Homoclinic orbit」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.