Anosov maps on closed topological manifolds
type: Item
instance of: scholarly article
title: Anosov maps on closed topological manifolds
zbMATH Open document ID: 0647.58039
author: S. H. Smith
published in: Journal of the Mathematical Society of Japan
publication date: 1987-01-01T00:00:00Z
review text: In this paper Anosov maps on compact metric spaces are studied. As the author remarks, it is seen from a paper (in Japanese) of \textit{A. Morimoto} in Tokyo Univ. Seminar Notes 39 (1979) that every expanding map is topologically stable in the class of continuous surjective maps. It is proved in the paper under review that if f is an Anosov map on a compact topological manifold M and if f is a local homeomorphism and topologically stable in the class of continuous surjective maps, then f is expanding. A Smale-Bowen's decomposition type theorem is established for surjective Anosov maps on compact metric spaces.
Mathematics Subject Classification ID: 37D99
Mathematics Subject Classification ID: 54H20
zbMATH DE Number: 4056640
zbMATH Keywords: topological stability
zbMATH Keywords: pseudo-orbit tracing property
zbMATH Keywords: expansive map
zbMATH Keywords: Anosov maps
zbMATH Keywords: expanding map
zbMATH Keywords: Smale-Bowen's decomposition
reviewed by: Luchezar Stoyanov
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/03930505
OpenAlex ID: W2047592621
DOI: 10.2969/JMSJ/03930505
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description: scientific article; zbMATH DE number 4056640