Title

Spectral Decomposition for Topologically Anosov Homeomorphisms on Noncompact and Non-Metrizable Spaces

Document Type

Article

Publication Date

1-2013

Department

Mathematics

Language

English

Publication Title

Topology and its Applications

Abstract

We discuss topological definitions of expansivity, shadowing, and chain recurrence for homeomorphisms. They generalize the usual definitions for metric spaces. We prove various theorems about topologically Anosov homeomorphisms (maps that are expansive and have the shadowing property) on noncompact and non-metrizable spaces that generalize theorems for such homeomorphisms on compact metric spaces. The main result is a generalization of Smaleʼs spectral decomposition theorem to topologically Anosov homeomorphisms on first countable, locally compact, paracompact, Hausdorff spaces.

Comments

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DOI

10.1016/j.topol.2012.10.010

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