^{}Department of Mathematics, Faculty of Mathematical and Computer Sciences, Shahid Chamran University of Ahvaz, P.O. Box 61357-43135, Ahvaz, Iran.

Abstract

In this paper, some properties of the periodic shadowing are presented. It is shown that a homeomorphism has the periodic shadowing property if and only if so does every lift of it to the universal covering space. Also, it is proved that continuous mappings on a compact metric space with the periodic shadowing and the average shadowing property also have the shadowing property and then are chaotic in the sense of Li-Yorke. Moreover, any distal homeomorphisms on a compact metric space with the periodic shadowing property do not have the asymptotic average shadowing property.

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