翻訳と辞書 Words near each other ・ Mean Business on North Ganson Street ・ Mean center of the United States population ・ Mean Cheay ・ Mean Chey District ・ Mean corpuscular hemoglobin ・ Mean corpuscular hemoglobin concentration ・ Mean corpuscular volume ・ Mean Creek ・ Mean Creek (band) ・ Mean curvature ・ Mean curvature flow ・ Mean dependence ・ Mean deviation ・ Mean Deviation (book) ・ Mean difference ・ Mean dimension ・ Mean Directional Accuracy (MDA) ・ Mean Dog Blues ・ Mean down time ・ Mean effective pressure ・ Mean Everything to Nothing ・ Mean field annealing ・ Mean field game theory ・ Mean field particle methods ・ Mean field theory ・ Mean flow ・ Mean Frank and Crazy Tony ・ Mean free path ・ Mean free time ・ Mean Girl Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Mean dimension ： ウィキペディア英語版 Mean dimension In mathematics, the mean (topological) dimension of a topological dynamical system is a non-negative extended real number that is a measure of the complexity of the system. Mean dimension was first introduced in 1999 by Gromov. Shortly after it was developed and studied systematically by Lindenstrauss and Weiss. In particular they proved the following key fact: a system with finite topological entropy has zero mean dimension. For various topological dynamical systems with infinite topological entropy, the mean dimension can be calculated or at least bounded from below and above. This allows mean dimension to be used to distinguish between systems with infinite topological entropy. ==General definition== A topological dynamical system consists of a compact Hausdorff topological space $\backslash textstyle\; X$ and a continuous self-map $\backslash textstyle\; T:X\backslash rightarrow\; X$. Let $\backslash textstyle\; \backslash mathcal$ denote the collection of open finite covers of $\backslash textstyle\; X$. For $\backslash textstyle\; \backslash alpha\backslash in\backslash mathcal$ define its order by :$\backslash operatorname(\backslash alpha)=\backslash max\_\backslash sum\_1\_U(x)-1$ An open finite cover $\backslash textstyle\; \backslash beta$ refines $\backslash textstyle\; \backslash alpha$, denoted $\backslash textstyle\; \backslash beta\backslash succ\backslash alpha$, if for every $\backslash textstyle\; V\backslash in\backslash beta$, there is $\backslash textstyle\; U\backslash in\backslash alpha$ so that $\backslash textstyle\; V\backslash subset\; U$. Let :$D(\backslash alpha)=\backslash min\_\; \backslash operatorname(\backslash beta)$ Note that in terms of this definition the Lebesgue covering dimension is defined by $\backslash dim\_\backslash mathrm(X)=\backslash sup\_^n\backslash alpha\_i$ of any finite collection of open covers of $\backslash textstyle\; X$. The mean dimension is the non-negative extended real number: :$\backslash operatorname(X,T)=\backslash sup\_\backslash lim\_\backslash frac$ where $\backslash textstyle\; \backslash alpha^n=\backslash bigvee\_^T^\backslash alpha.$ 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「Mean dimension」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.