Structural stability of vector fields on 3-manifolds with boundary
type: Item
instance of: scholarly article
title: Structural stability of vector fields on 3-manifolds with boundary
zbMATH Open document ID: 0551.34032
DOI: 10.1016/0022-0396(84)90148-7
published in: Journal of Differential Equations
publication date: 1984-01-01T00:00:00Z
review text: From the structural stability viewpoint vector fields on M which are tangent to the boundary of M are analysed. A class of vector fields is characterized as structurally stable; this class corresponds to the class of Morse-Smale vector fields on closed manifolds, studied by Palis, Smale, Peixoto and others. In this class, new phenomena occur, as saddle connections along the boundary of M which are persistent by small perturbations. Thus, the techniques introduced by \textit{J. Palis} [Topology 8, 385-405 (1969; Zbl 0189.239)], which inspired the proof of the stability of a vector field in such a class were substantially changed. Such modifications represent a main difficulty in extending our results to higher dimensions.
Mathematics Subject Classification ID: 34D30
Mathematics Subject Classification ID: 37-XX
zbMATH DE Number: 3877583
zbMATH Keywords: structural stability
zbMATH Keywords: Morse-Smale vector fields
zbMATH Keywords: small perturbations
author: M. J. Pacifico
MaRDI profile type: Publication
full work available at URL: 0022-0396(84)90148-7
OpenAlex ID: W2061032854
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description: scientific article; zbMATH DE number 3877583