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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 Arnold diffusion ： ウィキペディア英語版 Arnold diffusion In applied mathematics, Arnold diffusion is the phenomenon of instability of integrable Hamiltonian systems. The phenomenon is named after Vladimir Arnold who was the first to publish a result in the field in 1964. More precisely, Arnold diffusion refers to results asserting the existence of solutions to nearly integrable Hamiltonian systems that exhibit a significant change in the action variables. ==Background and statement== For integrable systems, one has the conservation of the action variables. According to the KAM theorem if we perturb an integrable system slightly, then many, though certainly not all, of the solutions of the perturbed system stay close, for all time, to the unperturbed system. In particular, since the action variables were originally conserved, the theorem tells us that there is only a small change in action for many solutions of the perturbed system. However, as first noted in Arnold's paper,〔 there are nearly integrable systems for which there exist solutions that exhibit arbitrarily large growth in the action variables. More precisely, Arnold considered the example of nearly integrable Hamiltonian system with Hamiltonian : $H(I,\; p,\; q,\; \backslash phi,\; t)\; =\; I^2\; +\; p^2\; +\; \backslash epsilon\; \backslash cos\; +\; \backslash mu\backslash cos(\backslash sin$ He showed that for this system, with any choice of $\backslash epsilon,\; \backslash delta,\; K\; >\; 0,$ where $K\; \backslash gg\; \backslash delta$, there exists a $\backslash mu\_0\; >\; 0$ such that for all there is a solution to the system for which : for some time $T\; \backslash gg\; 0.$ 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「Arnold diffusion」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.