Stability of parametrized families of gradient vector fields
type: Item
instance of: scholarly article
title: Stability of parametrized families of gradient vector fields
zbMATH Open document ID: 0533.58018
DOI: 10.2307/2006976
published in: Annals of Mathematics. Second Series
publication date: 1983-01-01T00:00:00Z
review text: This paper studies the structural stability of a \(C^{\infty}\) one parameter family of gradient vector fields defined on a closed \(C^{\infty}\) manifold. Let \(X^ g\!_ 1(M)\) be the set of such vector fields endowed with the \(C^{\infty}\) Whitney topology. The main result of the paper is the following. Theorem. There exists an open and dense G C \(X^ g\!_ 1(M)\) such that if \(\{X_{\mu}\}\) is in G then \(\{\chi_{\mu}\}\) is structurally stable.
Mathematics Subject Classification ID: 37C75
Mathematics Subject Classification ID: 34D30
Mathematics Subject Classification ID: 57R25
zbMATH DE Number: 3846512
zbMATH Keywords: Morse-Smale gradient fields
zbMATH Keywords: genericity
zbMATH Keywords: structural stability
author: Jacob Palis
author: Floris Takens
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2307/2006976
OpenAlex ID: W2328469656
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description: scientific article; zbMATH DE number 3846512