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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 Denjoy's theorem on rotation number ： ウィキペディア英語版 Denjoy's theorem on rotation number In mathematics, the Denjoy theorem gives a sufficient condition for a diffeomorphism of the circle to be topologically conjugate to a diffeomorphism of a special kind, namely an irrational rotation. proved the theorem in the course of his topological classification of homeomorphisms of the circle. He also gave an example of a ''C''1 diffeomorphism with an irrational rotation number that is not conjugate to a rotation. == Statement of the theorem == Let ''ƒ'': ''S''1 → ''S''1 be an orientation-preserving diffeomorphism of the circle whose rotation number ''θ'' = ''ρ''(''ƒ'') is irrational. Assume that it has positive derivative ''ƒ'' ′(''x'') > 0 that is a continuous function with bounded variation on the interval [0,1). Then ''ƒ'' is topologically conjugate to the irrational rotation by ''θ''. Moreover, every orbit is dense and every nontrivial interval ''I'' of the circle intersects its forward image ''ƒ''°''q''(''I''), for some ''q'' > 0 (this means that the non-wandering set of ''ƒ'' is the whole circle). 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「Denjoy's theorem on rotation number」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.