Spectral decomposition for topologically Anosov homeomorphisms on noncompact and non-metrizable spaces
Dynamical Systems
2011-09-14 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1109.2823,
title = {Spectral decomposition for topologically Anosov homeomorphisms on noncompact and non-metrizable spaces},
author = {Tarun Das and Keonhee Lee and David Richeson and Jim Wiseman},
journal= {arXiv preprint arXiv:1109.2823},
year = {2011}
}