Recurrence and the asymptotic pseudo-orbit tracing property
type: Item
instance of: scholarly article
title: Recurrence and the asymptotic pseudo-orbit tracing property
zbMATH Open document ID: 1139.37005
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2007-04-13T00:00:00Z
review text: The paper introduces the asymptotic pseudo-orbit tracing property (APOTP) for continuous maps from a compact metric space into itself and gives several sufficient and necessary conditions. At the end of the paper it is proved that a homeomorphism that is chain transitive on its omega-limit set and has the APOTP is a (topologically transitive) nonwandering homeomorphism. Note that finding sufficient conditions for nonwandering homeomorphisms has been an interesting problem in dynamical systems, see e.g. \textit{M. Hurley} [J. Differ. Equations 54, 60--72 (1984; Zbl 0493.58013)].
Mathematics Subject Classification ID: 37B20
Mathematics Subject Classification ID: 54H20
zbMATH DE Number: 5142223
zbMATH Keywords: asymptotic pseudo-orbit tracing property
zbMATH Keywords: chain recurrence
zbMATH Keywords: topologically transitive
zbMATH Keywords: topologically mixing
zbMATH Keywords: nonwandering map
author: Rongbao Gu
MaRDI profile type: Publication
full work available at URL: j.na.2006.02.044
OpenAlex ID: W2053109757
cites work: Q4180600
cites work: Consequences of topological stability
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cites work: Chain transitivity, attractivity, and strong repellors for semidynamical systems
cites work: Q4164074
cites work: Pseudo-Orbit Shadowing in the Family of Tent Maps
cites work: Shadowing Property of Continuous Maps
cites work: Shadowing Property for Inverse Limit Spaces
cites work: Q4239046
DOI: 10.1016/J.NA.2006.02.044
description: scientific article; zbMATH DE number 5142223