Spectral decomposition and stability of mild expansive systems
Keywords
Mild expansiveness, mild topological stability, $\Omega$-stability, shadowing property, spectral decompositionAbstract
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 \cite{Sm} and Bowen \cite{Bo}. 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.References
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