Parameterized IFS with the asymptotic average shadowing property

Abstract

In this paper we generalize the notion of asymptotic average shadowing property to parameterized IFS and prove some related theorems on this notion. Specially, this is proved that every uniformly contracting IFS has the asymptotic average shadowing property. As an important result, we show that if a continuous surjective IFS F on a compact metric space X has the asymptotic average shadowing property then F is chain transitive. Moreover, we introduce some examples and investigate the relationship between the original asymptotic average shadowing property and asymptotic average shadowing property for IFS. For example, there is an IFS F such that has the asymptotic average shadowing property but does not satisfy the shadowing property.