Continuum-wise expansive diffeomorphisms

Resum

In this paper, we show that the $C^1$ interior of the set of all continuum-wise expansive diffeomorphisms of a closed manifold coincides with the $C^1$ interior of the set of all expansive diffeomorphisms. And the $C^1$ interior of the set of all continuum-wise fully expansive diffeomorphisms on a surface is investigated. Furthermore, we have necessary and sufficient conditions for a diffeomorphism belonging to these open sets to be Anosov.