Anosov maps on closed topological manifolds (Q1104618)

In this paper Anosov maps on compact metric spaces are studied. As the author remarks, it is seen from a paper (in Japanese) of \textit{A. Morimoto} in Tokyo Univ. Seminar Notes 39 (1979) that every expanding map is topologically stable in the class of continuous surjective maps. It is proved in the paper under review that if f is an Anosov map on a compact topological manifold M and if f is a local homeomorphism and topologically stable in the class of continuous surjective maps, then f is expanding. A Smale-Bowen's decomposition type theorem is established for surjective Anosov maps on compact metric spaces.