Čech cohomology of attractors of discrete dynamical systems
type: Item
instance of: scholarly article
title: Čech cohomology of attractors of discrete dynamical systems
zbMATH Open document ID: 1297.54075
published in: Journal of Differential Equations
publication date: 2014-08-20T00:00:00Z
review text: The question addressed in this paper is the following. Assume that \(K\) is an asymptotically stable attractor for a homeomorphism \(f:\mathbb R^n\to\mathbb R^n\), with basin of attraction \(A(K)\). What hypotheses are sufficient to ensure that the inclusion of \(K\) into \(A(K)\) induces an isomorphism of their Čech cohomology groups? The main results are that this holds if the coefficients of the cohomology groups are taken in \(\mathbb{Q}\) or \(\mathbb{Z}_p\), and that it holds for the integral Čech cohomology if and only if the cohomology of either \(K\) or \(A(K)\) is finitely generated. In addition, the cohomology of periodic point-free attractors of volume-contracting homeomorphisms of \(\mathbb{R}^3\) is computed.
reviewed by: Thomas B. Ward
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 55N05
Mathematics Subject Classification ID: 55P55
zbMATH DE Number: 6332804
zbMATH Keywords: Čech cohomology
zbMATH Keywords: attractor
zbMATH Keywords: basin of attraction
zbMATH Keywords: homeomorphism
author: Francisco R. Ruiz del Portal
author: J. J. Sánchez-Gabites
MaRDI profile type: Publication
full work available at URL: j.jde.2014.05.055
OpenAlex ID: W2049543162
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DOI: 10.1016/J.JDE.2014.05.055
description: scientific article; zbMATH DE number 6332804