翻訳と辞書 Words near each other ・ Expansion spring ・ Expansion tank ・ Expansion team ・ Expansion Team (album) ・ Expansion timeline of the Moscow Metro ・ Expansion tube ・ Expansion tunnel ・ Expansion valve ・ Expansion valve (steam engine) ・ Expansion, Power, Release ・ Expansionary fiscal contraction ・ Expansionism ・ Expansionist nationalism ・ Expansions (album) ・ Expansions of Eve Online ・ Expansive ・ Expansive clay ・ Expansive Heart ・ Expansive Poetry ・ Expansión (Spain) ・ ExPASy ・ Expat ・ Expat (library) ・ Expat Party ・ Expatica ・ Expatriape ・ Expatriate ・ Expatriate (album) ・ Expatriate (band) ・ Expatriate (disambiguation) 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 Expansive ： ウィキペディア英語版 Expansive In mathematics, the notion of expansivity formalizes the notion of points moving away from one another under the action of an iterated function. The idea of expansivity is fairly rigid, as the definition of positive expansivity, below, as well as the Schwarz-Ahlfors-Pick theorem demonstrate. ==Definition== If $(X,d)$ is a metric space, a homeomorphism $f\backslash colon\; X\backslash to\; X$ is said to be expansive if there is a constant :$\backslash varepsilon\_0>0,$ called the expansivity constant, such that for any pair of points $x\backslash neq\; y$ in $X$ there is an integer $n$ such that :$d(f^n(x),f^n(y))\backslash geq\backslash varepsilon\_0$. Note that in this definition, $n$ can be positive or negative, and so $f$ may be expansive in the forward or backward directions. The space $X$ is often assumed to be compact, since under that assumption expansivity is a topological property; i.e. if $d\text{'}$ is any other metric generating the same topology as $d$, and if $f$ is expansive in $(X,d)$, then $f$ is expansive in $(X,d)$ (possibly with a different expansivity constant). If :$f\backslash colon\; X\backslash to\; X$ is a continuous map, we say that $X$ is positively expansive (or forward expansive) if there is a :$\backslash varepsilon\_0$ such that, for any $x\backslash neq\; y$ in $X$, there is an $n\backslash in\backslash mathbb$ such that $d(f^n(x),f^n(y))\backslash geq\; \backslash varepsilon\_0$. 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「Expansive」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.