A note on ergodicity of systems with the asymptotic average shadowing property
type: Item
instance of: scholarly article
title: A note on ergodicity of systems with the asymptotic average shadowing property
zbMATH Open document ID: 1242.37019
DOI: 10.1155/2011/360583
author: Risong Li
author: Xiaoliang Zhou
published in: Discrete Dynamics in Nature and Society
publication date: 2012-03-13T00:00:00Z
review text: This note proves that if a Lyapunov stable map of a compact metric space into itself is topologically transitive and has the asymptotic average shadowing (AASP) property, then the space must be a single point. This property follows in an elementary way from what is already known about AASP. In fact, it is true even without the assumptions of compactness and transitivity.
reviewed by: Marcin Kulczycki
Mathematics Subject Classification ID: 37C50
zbMATH DE Number: 6014502
zbMATH Keywords: asymptotic average shadowing property
zbMATH Keywords: Lyapunov stability
zbMATH Keywords: topological transitivity
Wikidata QID: Q58655464
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/360583
OpenAlex ID: W2167797239
cites work: Small perturbations of chaotic dynamical systems
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cites work: The asymptotic average shadowing property and transitivity
cites work: On ergodicity of systems with the asymptotic average shadowing property
cites work: Exploring the asymptotic average shadowing property
description: scientific article; zbMATH DE number 6014502