The Average Shadowing Property in Continuous Iterated Function Systems

Abstract

In this paper, we introduce a new type of iterated function systems, named; CIFS. Actually in a CIFS we have some flows instead of some functions in iterated function systems. Then, we generalize the notions of average shadowing property, chain transitivity, and attractor sets on a CIFS. It is shown that every uniformly contracting CIFS has the average shadowing property. We also prove that if a CIFS, F on a compact metric space X has the average shadowing property, then F is chain transitive, but the converse is not always true. As a result, this proves that if F is an uniformly contracting CIFS on compact metric space X, then X is the only nonempty attractor of F.