On Non-Wandering Sets with Non-empty Interior for Endomorphisms

In this paper, we study transitivity for endomorphisms. Our results are related to a conjecture of F. Abdenur, C. Bonatti and L. Díaz, concerning the relationship between transitivity and the existence of a non-wandering set with nonempty interior. We obtain transitivity under the assumption that there exists a hyperbolic non-wandering set with non-empty interior, and in the setting of accessible partially hyperbolic endomorphisms.