The star systems \({\mathcal H}^*\) and a proof of the \(C^1 \Omega\)-stability conjecture for flows
type: Item
instance of: scholarly article
title: The star systems \({\mathcal H}^*\) and a proof of the \(C^1 \Omega\)-stability conjecture for flows
zbMATH Open document ID: 0973.37018
author: Shaobo Gan
published in: Journal of Differential Equations
publication date: 2001-10-24T00:00:00Z
review text: This paper is devoted to a new proof the \(C^1\Omega\) stability for flows, which is formulated in the following way: Let \(M\) be a compact \(n\)-dimensional \(C^\infty\)-Riemannian manifold without boundary \((n>1)\). Denote by \(X=X^1(M)\) the set of all \(C^1\) vector fields on \(M\), endowed with \(C^1\) topology. Let \(S\) be a \(C^1\) vector field on \(M\). If \(S\) is \(C^1\Omega\)-stable then \(S\) satisfies Axiom A and the no-cycle condition. Here the author solves this crucial point, which is considerably different from the approach of Hayashi or Wen and based on Liao`s obstruction set theory.
Mathematics Subject Classification ID: 37C75
Mathematics Subject Classification ID: 34D30
Mathematics Subject Classification ID: 37C10
zbMATH DE Number: 1454723
zbMATH Keywords: stability
zbMATH Keywords: flow
zbMATH Keywords: axiom A
zbMATH Keywords: obstruction sets theory
zbMATH Keywords: vector fields
Wikidata QID: Q123242321
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: jdeq.1999.3731
OpenAlex ID: W2074700719
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DOI: 10.1006/JDEQ.1999.3731
description: scientific article; zbMATH DE number 1454723