Ergodic measure-expansive diffeomorphisms.

In this paper, we consider the set of diffeomorphisms which are measure-expansive for any ergodic measure, and study the set from the viewpoint of geometric theory of dynamical systems. It is proved that (1) there exists a non-emptyC1-open set of robustly non-hyperbolic and transitive diffeomorphisms such that each element of the set is measure-expansive for any ergodic measure, and that (2)C1-generically, a diffeomorphism is measure-expansive for any generic ergodic measure. [ABSTRACT FROM AUTHOR]