Continuation to gradient flows
type: Item
instance of: scholarly article
title: Continuation to gradient flows
zbMATH Open document ID: 0753.58016
DOI: 10.1215/S0012-7094-91-06413-6
author: James F. Reineck
published in: Duke Mathematical Journal
publication date: 1992-09-27T00:00:00Z
review text: At first of this interesting paper, background definitions and results from the theory of the Conley index are recalled. Then the author proves that any isolated invariant set of a smooth flow on a manifold can be continued to an isolated invariant set of a gradient flow. Remaining part of the paper deals with the attractor-repeller pairs, Morse decompositions, index filtration and boundary map for attractor-repeller pairs.
Mathematics Subject Classification ID: 37D15
Mathematics Subject Classification ID: 37C70
Mathematics Subject Classification ID: 55P15
Mathematics Subject Classification ID: 55P99
zbMATH DE Number: 58547
zbMATH Keywords: isolated invariant sets
zbMATH Keywords: Conley index
zbMATH Keywords: homotopy theory
zbMATH Keywords: Morse-Smale flows
reviewed by: A. Klíč
MaRDI profile type: Publication
cites work: Q4180600
cites work: Witten's complex and infinite dimensional Morse theory
cites work: Morse-Smale flows and homotopy theory
cites work: The Connection Matrix Theory for Morse Decompositions
cites work: The Connection Map for Attractor-Repeller Pairs
cites work: Dynamical systems, shape theory and the Conley index
cites work: Connected Simple Systems and The Conley Index of Isolated Invariant Sets
cites work: Morse Theory, the Conley Index and Floer Homology
description: scientific article; zbMATH DE number 58547