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
ows 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. As a result, this prove that if F is an uniformly con-
tracting CIFS on compact metric space X, then X is the only nonempty
attractor of F.