On the \(C^ 1\) stability conjecture for flows
type: Item
instance of: scholarly article
title: On the \(C^ 1\) stability conjecture for flows
zbMATH Open document ID: 0866.58050
author: Lan Wen
published in: Journal of Differential Equations
publication date: 1997-07-24T00:00:00Z
review text: The paper is devoted to the proof of the \(C^1\) stability conjecture of Palais and Smale for flows: Theorem A: \(C^1\) structurally stable flows of compact manifolds without boundary satisfy Axiom A. This proof allows to extend the classical results of Peixoto for dimension 2 and those of Hu and Liao for dimension 3. The \(C^1\) connecting lemma of Hayashi is the right key to this work. As a corollary of Theorem A, the equivalence of two apparently different definitions of structural stability (Peixoto's and Andronov-Pontryagin's) is established.
Mathematics Subject Classification ID: 37D99
zbMATH DE Number: 933279
zbMATH Keywords: \(C^ 1\) structural stability
zbMATH Keywords: axiom \(A\)
zbMATH Keywords: connecting lemma
zbMATH Keywords: ergodic closing lemma
reviewed by: G.V.Khmelevskaja-Plotnikova
MaRDI profile type: Publication
full work available at URL: jdeq.1996.0121
OpenAlex ID: W2072440226
Wikidata QID: Q122941025
DOI: 10.1006/JDEQ.1996.0121
description: scientific article; zbMATH DE number 933279