Spectral decomposition and stability of mild expansive systems

Abstract

In this paper we introduce another type of expansiveness, called mild expansiveness, for homeomorphisms on compact metric spaces, and present a topological version of the spectral decomposition theorem by Smale [17] and Bowen [5]. Moreover we study the topological stability of mild expansive homeomorphisms, and characterize the mild expansive diffeomorphisms on compact smooth manifolds using the notion of $\Omega$-stability.