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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 Markus–Yamabe conjecture ： ウィキペディア英語版 Markus–Yamabe conjecture In mathematics, the Markus–Yamabe conjecture is a conjecture on global asymptotic stability. The conjecture states that if a continuously differentiable map on an $n$-dimensional real vector space has a single fixed point, and its Jacobian matrix is everywhere Hurwitz, then the fixed point is globally stable. The conjecture is true for the two-dimensional case. However, counterexamples have been constructed in higher dimensions. Hence, in the two-dimensional case ''only'', it can also be referred to as the Markus–Yamabe theorem. Related mathematical results concerning global asymptotic stability, which ''are'' applicable in dimensions higher than two, include various autonomous convergence theorems. A modified version of the Markus–Yamabe conjecture has been proposed, but at present this new conjecture remains unproven.〔See, for example, ().〕 Analog of the conjecture for nonlinear control system with scalar nonlinearity is known as Kalman's conjecture. == Mathematical statement of conjecture == :Let $f:\backslash mathbb^n\backslash rightarrow\backslash mathbb^n$ be a $C^1$ map with $f(0)\; =\; 0$ and Jacobian $Df(x)$ which is Hurwitz stable for every $x\; \backslash in\; \backslash mathbb^n$. :Then $0$ is a global attractor of the dynamical system $\backslash dot=\; f(x)$. The conjecture is true for $n=2$ and false in general for $n>2$. 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「Markus–Yamabe conjecture」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.