On sufficient conditions for the transitivity of homeomorphisms

Abstract

We derive sufficient conditions for a homeomorphism of a compact metric space without isolated points to be topologically transitive. In particular, we prove that a homeomorphism with the shadowing property has a dense orbit if either it has the su-intersecting property in the whole space; or it has the barycentre property in the non-wandering set; or else it is accessible in the recurrent set. To elucidate their dynamical nature, we compare these three conditions, discuss examples with a variety of dynamics and present some applications of interest.