Correction to: Connecting invariant manifolds and the solution of the $C^1$ stability and $\Omega$-stability conjectures for flows
Correction to: Connecting invariant manifolds and the solution of the $C^1$ stability and $\Omega$-stability conjectures for flows
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DOI：
10.2307/121106
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发表时间：
1999-07
影响因子：
4.9
通讯作者：
S. Hayashi
中科院分区：
文献类型：
--
作者：
S. Hayashi
稳定向量场满足[1]中的公理A）。文[1]中引入的连接引理是证明连续流稳定性和连续稳定性的新颖而重要的部分。Toyoshiba [5]指出了最后一个猜想的证明中的一个错误，他后来又根据Mann ′ e和Palis的连接引理和以前的论证对它作了一个独立的证明。定理B证明的关键步骤是用C_（？）从周期轨道中分离奇点（[1，推论III]）。
Ω-stable vector fields satisfy Axiom A) in[1]. The novel and essential part in the proof of the stability and Ω-stabilityconjectures for flows is the connecting lemma introduced in [1]. A mistake inthe proof of the last conjecture was pointed out to me by Toyoshiba [5], wholater also provided an independent proof of it, again based on the connectinglemma and previous arguments by Man˜´e and Palis.The crucial step to the proof of Theorem B is the separation of singu-larities from periodic orbits ([1, Corollary III]) by the C