Weak Shadowing as a Generic Property for IFS's

Abstract

In this paper we consider shadowing and weak shadowing properties for iterated function systems IFS and give some results on these concepts. At first, a sufficient condition for shadowing property is given and by this result we present two IFS which have the shadowing property. It is proved that every uniformly expanding as well as every uniformly contracting  IFS has the weak shadowing property.  By an example we show that in  IFS's   shadowing property does not implies  weak shadowing property. Finally  we have the main result of the paper and prove  that the weak shadowing  is a generic property in the set of all IFS's.