Periodic Points of Regular Curve Homeomorphisms

Abstract

We prove that, if $$f:X\rightarrow X$$ is a regular curve homeomorphism then the set of periodic points is either empty or dense in the set of non-wandering points. Moreover, we prove that each infinite minimal set is approximated by periodic orbits and is conjugate to an adding machine when the set of periodic points is not empty. Furthermore, we give a characterization of equicontinuous regular curve homeomorphisms