Connected components of attractors and other stable sets
type: Item
instance of: scholarly article
title: Connected components of attractors and other stable sets
zbMATH Open document ID: 0877.58039
DOI: 10.1007/BF02215978
author: Morris W. Hirsch
author: Mike Hurley
published in: Aequationes Mathematicae
publication date: 1997-12-08T00:00:00Z
full work available at URL: https://eudml.org/doc/137690
review text: The action of a continuous map \(f\) on a locally connected metric space, especially the action induced by \(f\) on the space of connected components of an attractor \(A\) or a stable set \(Y\) of \(f\), is studied. The main result: if the compact invariant set \(A\) is an attractor in the sense of Conley, then \(A\) has a finite number of connected components, and these are permuted by \(f\); the permutation is cyclic if and only if the attractor \(A\) is indecomposable. This is related to some results of \textit{J. Buescu} and \textit{I. Stewart} [Ergodic Theory Dyn. Syst. 15, No. 2, 271-290 (1995; Zbl 0848.54027)] and \textit{I. Melbourne}, \textit{M. Dellnitz} and \textit{M. Golubitsky} [Arch. Ration. Mech. Anal. 123, No. 1, 75-98 (1993; Zbl 0805.58043)].
Mathematics Subject Classification ID: 37C70
zbMATH DE Number: 1019200
zbMATH Keywords: continuous map
zbMATH Keywords: connected components of attractors
zbMATH Keywords: locally connected metric space
reviewed by: Boris V. Loginov
MaRDI profile type: Publication
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OpenAlex ID: W2035523653
description: scientific article; zbMATH DE number 1019200