Spectral decomposition for topologically Anosov homeomorphisms on noncompact and non-metrizable spaces

Details Spectral decomposition for topologically Anosov homeomorphisms on noncompact and non-metrizable spaces Spectral decomposition for topologically Anosov homeomorphisms on noncompact and non-metrizable spaces

2011-09-13

arxiv.org/abs/1109.2823v1

Mathematics

Dynamical Systems

Scientific paper

We introduce 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 Smale's spectral decomposition theorem to topologically Anosov homeomorphisms on first countable locally compact paracompact Hausdorff spaces.

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