Chain recurrence in multidimensional time discrete dynamical systems
type: Item
instance of: scholarly article
title: Chain recurrence in multidimensional time discrete dynamical systems
zbMATH Open document ID: 1163.37005
author: Piotr Oprocha
published in: Discrete and Continuous Dynamical Systems
publication date: 2008-09-29T00:00:00Z
review text: Expansive homeomorphisms with certain shadowing properties are said to be topologically Anosov (TA). \textit{R. Bowen}, in generalizing the smooth case of Smale's Spectral Decomposition Theorem [Dyn. Syst., Proc. Symp. Univ. Warwick 1973/74, Lect. Notes Math. 468, 35--36 (1975; Zbl 0327.58010)], showed that the set of non-wandering points of a TA map \(f\) can be decomposed into a disjoint union of closed invariant sets \(R_1,\dots, R_l\) such that \(|R_i\) is topologically transitive, \(i= 1,\dots, l\). In this paper the author considers \(d\)-dimensional systems and the main result is a multidimensional version of Bowen's Spectral Decomposition Theorem for such systems. Problems of expansivity and pseudo-orbit tracing (shadowing) are emphasized.
reviewed by: Geoffrey R. Goodson
Mathematics Subject Classification ID: 37B05
Mathematics Subject Classification ID: 37C50
Mathematics Subject Classification ID: 37B25
Mathematics Subject Classification ID: 37B20
zbMATH DE Number: 5347959
zbMATH Keywords: chain recurrence
zbMATH Keywords: shadowing hyperbolicity
zbMATH Keywords: expansivity spectral decomposition
MaRDI profile type: Publication
full work available at URL: dcds.2008.20.1039
OpenAlex ID: W1993552444
DOI: 10.3934/DCDS.2008.20.1039
description: scientific article; zbMATH DE number 5347959