Periodic shadowing in iterated function systems

Abstract

In this paper, we introduce the notion of periodic shadowing property on iterated function systems, IFSs for short, and then some results will be obtained and compare with similar ones in the references. Among those results, we prove that every strongly expansive IFS with the shadowing property has the periodic shadowing property. In addition, like the shadowing property, we show that every uniformly expanding IFS has the periodic shadowing property. However, the periodic shadowing property is fulfilled for the uniformly contracting IFS provided that it is expansive.