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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 Nekhoroshev estimates ： ウィキペディア英語版 Nekhoroshev estimates The Nekhoroshev estimates are an important result in the theory of Hamiltonian systems concerning the long-time stability of solutions of integrable systems under a small perturbation of the Hamiltonian. The first paper on the subject was written by Nikolay Nekhoroshev in 1971. The theorem complements both the KAM theorem and the phenomenon of instability for nearly integrable Hamiltonian systems, sometimes called Arnold Diffusion, in the following way: The KAM Theorem tells us that ''many'' solutions to nearly integrable Hamiltonian systems persist under a perturbation for ''all'' time, while, as Vladimir Arnold first demonstrated in 1964, some solutions do not stay close to their integrable counterparts for all time. The Nekhoroshev estimates tell us that, nonetheless, ''all'' solutions stay close to their integrable counterparts for an ''exponentially long time''. Thus, they restrict how quickly solutions can become unstable. ==Statement== Let $H(I)\; +\; \backslash epsilon\; h(I,\; \backslash theta)$ be a nearly integrable $n$ degree-of-freedom Hamiltonian, where $(I,\; \backslash theta)$ are the action-angle variables. Ignoring the technical assumptions and details in the statement, Nekhoroshev estimates assert that: : for : where $c$ is a complicated constant. For a precise, refined statement of the theorem see. 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「Nekhoroshev estimates」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.