On totally periodic ω-limit sets for monotone maps on regular curves

Abstract

An ω-limit set of a continuous self-mapping of a compact metric space X is said to be totally periodic if all of its points are periodic. In [3] Askri and Naghmouchi proved that if f is a one-to-one continuous self mapping of a regular curve, then every totally periodic ω-limit set of f is finite. This also holds whenever f is a monotone map of a local dendrite by Abdelli in [1]. In this paper we generalize these results to monotone maps on regular curves. On the other hand, we give some remarks related to expansivity and totally periodic ω-limit sets for every continuous map on compact metric space.