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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 Pseudo-Anosov map ： ウィキペディア英語版 Pseudo-Anosov map In mathematics, specifically in topology, a pseudo-Anosov map is a type of a diffeomorphism or homeomorphism of a surface. It is a generalization of a linear Anosov diffeomorphism of the torus. Its definition relies on the notion of a measured foliation introduced by William Thurston, who also coined the term "pseudo-Anosov diffeomorphism" when he proved his classification of diffeomorphisms of a surface. == Definition of a measured foliation == A measured foliation ''F'' on a closed surface ''S'' is a geometric structure on ''S'' which consists of a singular foliation and a measure in the transverse direction. In some neighborhood of a regular point of ''F'', there is a "flow box" ''φ'': ''U'' → R2 which sends the leaves of ''F'' to the horizontal lines in R2. If two such neighborhoods ''U''''i'' and ''U''''j'' overlap then there is a transition function ''φ''''ij'' defined on ''φ''''j''(''U''''j''), with the standard property : $\backslash phi\_\backslash circ\backslash phi\_j=\backslash phi\_i,$ which must have the form : $\backslash phi(x,y)=(f(x,y),c\backslash pm\; y)$ for some constant ''c''. This assures that along a simple curve, the variation in ''y''-coordinate, measured locally in every chart, is a geometric quantity (i.e. independent of the chart) and permits the definition of a total variation along a simple closed curve on ''S''. A finite number of singularities of ''F'' of the type of "''p''-pronged saddle", ''p''≥3, are allowed. At such a singular point, the differentiable structure of the surface is modified to make the point into a conical point with the total angle ''πp''. The notion of a diffeomorphism of ''S'' is redefined with respect to this modified differentiable structure. With some technical modifications, these definitions extend to the case of a surface with boundary. 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「Pseudo-Anosov map」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.