The average-shadowing property and strong ergodicity
type: Item
instance of: scholarly article
title: The average-shadowing property and strong ergodicity
zbMATH Open document ID: 1210.37016
author: Yingxuan Niu
published in: Journal of Mathematical Analysis and Applications
publication date: 2011-02-09T00:00:00Z
review text: Let \(f\) and \(g\) be discrete dynamical systems on compact metric spaces with the average shadowing property (ASP). The paper proves the following facts: \noindent 1. Density of minimal points of \(f\) implies its total strong ergodicity (i.e. strong ergodicity of \(f^k\) for every \(k\in\mathbb{N}_+\)). \noindent 2. The product \(f\times g\) is topologically transitive and has the ASP. \noindent 3. If \(f\) is nontrivial and distal then it can't have the ASP. \noindent 4. The full shift map over finite alphabet has the ASP.
reviewed by: Marcin Kulczycki
Mathematics Subject Classification ID: 37C50
zbMATH DE Number: 5848899
zbMATH Keywords: average shadowing
zbMATH Keywords: topological ergodicity
zbMATH Keywords: pseudo-orbit
zbMATH Keywords: minimality
MaRDI profile type: Publication
full work available at URL: j.jmaa.2010.11.024
OpenAlex ID: W2060021534
cites work: Equilibrium states and the ergodic theory of Anosov diffeomorphisms
cites work: Q4188476
cites work: Q4333092
cites work: Q3154121
cites work: Q4297122
cites work: Small perturbations of chaotic dynamical systems
cites work: The average-shadowing property and topological ergodicity
cites work: Q4895967
cites work: Q4379347
cites work: Q3469889
cites work: Various shadowing properties for positively expansive maps
DOI: 10.1016/J.JMAA.2010.11.024
description: scientific article; zbMATH DE number 5848899