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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 Melnikov distance ： ウィキペディア英語版 Melnikov distance One of the main tools to determine the existence of (or non-existence of) chaos in a perturbed hamiltonian system is the Melnikov theory. In this theory, the distance between the stable and unstable manifolds of the perturbed system is calculated up to the first order term. Consider a smooth dynamical system $\backslash ddot\; x\; =\; f(x)\; +\; \backslash epsilon\; g(t)$, with $\backslash epsilon\; \backslash ge\; 0$ and $g(t)$ periodic with period $T$. Suppose for $\backslash epsilon\; =\; 0$ the system has a hyperbolic fixed point x0 and a homoclinic orbit $\backslash phi(t)$ corresponding to this fixed point. Then for sufficiently small $\backslash epsilon\; \backslash ne\; 0$ there exists a ''T''-periodic hyperbolic solution. The stable and unstable manifolds of this periodic solution intersect transversally. The distance between these manifolds measured along a direction that is perpendicular to the unperturbed homoclinc orbit $\backslash phi(t)$ is called the Melnikov distance. If $d(t)$ denotes this distance, then $d(t)\; =\; \backslash epsilon\; (M(t)\; +\; O(\backslash epsilon))$. The function $M(t)$ is called the Melnikov function. == References == *. 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「Melnikov distance」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.