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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 Topological conjugacy ： ウィキペディア英語版 Topological conjugacy In mathematics, two functions are said to be topologically conjugate to one another if there exists a homeomorphism that will conjugate the one into the other. Topological conjugacy is important in the study of iterated functions and more generally dynamical systems, since, if the dynamics of one iterated function can be solved, then those for any topologically conjugate function follow trivially. To illustrate this directly: suppose that and are iterated functions, and there exists an such that :$g=h^\backslash circ\; f\backslash circ\; h,$ so that and are topologically conjugate. Then of course one must have :$g^n=h^\backslash circ\; f^n\backslash circ\; h,$ and so the iterated systems are conjugate as well. Here, ○ denotes function composition. ==Definition== Let and be topological spaces, and let $f\backslash colon\; X\backslash to\; X$ and $g\backslash colon\; Y\backslash to\; Y$ be continuous functions. We say that is topologically semiconjugate to if there exists a continuous surjection $h\backslash colon\; Y\backslash to\; X$ such that $f\backslash circ\; h=h\backslash circ\; g$. If is a homeomorphism, we say that and are topologically conjugate and we call a topological conjugation between and . Similarly, a flow on is topologically semiconjugate to a flow on if there is a continuous surjection $h\backslash colon\; Y\backslash to\; X$ such that $\backslash varphi(h(y),t)\; =\; h\backslash psi(y,t)$ for each $y\backslash in\; Y$, $t\backslash in\; \backslash mathbb$. If is a homeomorphism, then and are topologically conjugate. 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「Topological conjugacy」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.