# American Institute of Mathematical Sciences

May  2018, 38(5): 2487-2503. doi: 10.3934/dcds.2018103

## Topological stability and spectral decomposition for homeomorphisms on noncompact spaces

 Department of Mathematics, Chungnam National University, Daejeon 305-764, Korea

* Corresponding author (yangyinong1201@gmail.com)

Received  August 2017 Published  March 2018

In this paper, we introduce the notions of expansiveness, shadowing property and topological stability for homeomorphisms on noncompact metric spaces which are dynamical properties and equivalent to the classical definitions in case of compact metric spaces. Then we extend the Walters's stability theorem and Smale's spectral decomposition theorem to homeomorphisms on locally compact metric spaces.

Citation: Keonhee Lee, Ngoc-Thach Nguyen, Yinong Yang. Topological stability and spectral decomposition for homeomorphisms on noncompact spaces. Discrete & Continuous Dynamical Systems, 2018, 38 (5) : 2487-2503. doi: 10.3934/dcds.2018103
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