Various shadowing properties for positively expansive maps
type: Item
instance of: scholarly article
title: Various shadowing properties for positively expansive maps
zbMATH Open document ID: 1024.37016
DOI: 10.1016/S0166-8641(02)00260-2
author: Kazuhiro Sakai
published in: Topology and its Applications
publication date: 2003-07-29T00:00:00Z
review text: This paper is devoted to various shadowing properties for a positively expansive map on a compact metrizable space. The author shows that the Lipschitz shadowing property, the \(s\)-limit shadowing property and the strong shadowing property are all equivalent to the (usual) shadowing property for a positively expansive map. Moreover, for a positively expansive open map, the average shadowing property is shown.
Mathematics Subject Classification ID: 37C50
Mathematics Subject Classification ID: 37D20
Mathematics Subject Classification ID: 37B10
Mathematics Subject Classification ID: 54H20
zbMATH DE Number: 1955982
zbMATH Keywords: average shadowing
zbMATH Keywords: compact metrizable space
zbMATH Keywords: expanding
zbMATH Keywords: limit shadowing
zbMATH Keywords: \(s\)-limit shadowing
zbMATH Keywords: Lipschitz shadowing
zbMATH Keywords: pseudo-orbit
zbMATH Keywords: strong shadowing
zbMATH Keywords: positively expansive map
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1955982