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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 Poincaré–Bendixson theorem ： ウィキペディア英語版 Poincaré–Bendixson theorem In mathematics, the Poincaré–Bendixson theorem is a statement about the long-term behaviour of orbits of continuous dynamical systems on the plane, cylinder, or two-sphere. ==Theorem== Given a differentiable real dynamical system defined on an open subset of the plane, then every non-empty compact ω-limit set of an orbit, which contains only finitely many fixed points, is either * a fixed point, * a periodic orbit, or * a connected set composed of a finite number of fixed points together with homoclinic and heteroclinic orbits connecting these. Moreover, there is at most one orbit connecting different fixed points in the same direction. However, there could be countably many homoclinic orbits connecting one fixed point. A weaker version of the theorem was originally conceived by Henri Poincaré, although he lacked a complete proof which was later given by . 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「Poincaré–Bendixson theorem」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.