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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 K-equivalence ： ウィキペディア英語版 K-equivalence In mathematics, $\backslash mathcal$-equivalence, or contact equivalence, is an equivalence relation between map germs. It was introduced by John Mather in his seminal work in Singularity theory in the 1970s as a technical tool for studying stable maps. Since then it has proved important in its own right. Roughly speaking, two map germs ''ƒ'', ''g'' are $\backslash scriptstyle\backslash mathcal$-equivalent if ''ƒ''−1(0) and ''g''−1(0) are diffeomorphic. ==Definition== Two map germs $f,g:X\; \backslash to\; (Y,0)$ are $\backslash scriptstyle\backslash mathcal$-equivalent if there is a diffeomorphism :$\backslash Psi:\; X\; \backslash times\; Y\; \backslash to\; X\backslash times\; Y$ of the form Ψ(x,y) = (φ(x),ψ(x,y)), satisfying, :$\backslash Psi(x,0)\; =\; (\backslash varphi(x),\; 0)$, and :$\backslash Psi(x,f(x))\; =\; (\backslash varphi(x),\; g(\backslash varphi(x)))$. In other words, Ψ maps the graph of ''f'' to the graph of ''g'', as well as the graph of the zero map to itself. In particular, the diffeomorphism φ maps ''f''−1(0) to ''g''−1(0). The name ''contact'' is explained by the fact that this equivalence is measuring the contact between the graph of ''f'' and the graph of the zero map. Contact equivalence is the appropriate equivalence relation for studying the sets of solution of equations, and finds many applications in dynamical systems and bifurcation theory, for example. It is easy to see that this equivalence relation is ''weaker'' than A-equivalence, in that any pair of $\backslash scriptstyle\backslash mathcal$-equivalent map germs are necessarily $\backslash scriptstyle\backslash mathcal$-equivalent. 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「K-equivalence」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.