Expansive Behaviours for Homeomorphisms of tvs-Cone Metric Spaces

Abstract:

      Let $f$ be a homeomorphism of a compact tvs-cone metric space. In this paper, we show that $f$ is tvs-cone expansive if and only if $f$ has a generator. Further, it is proved that if $f$ is tvs-cone expansive, then the set of points having converging semiorbits under $f$ is a countable set. Results of this paper improve some expansive homeomorphisms theorems in topological dynamics, which will help to research dynamical properties for homeomorphisms of tvs-cone metric spaces.