Two-Sided Limit Shadowing Property on Iterated Function Systems

Abstract

In this article, we introduce the two-sided limit shadowing property on an iterated function system (IF S) and attain some results such as totally transitivity, and shadowing property. Also, by means of the strong shadowing property, we achieve topologically mixing for this IF S. Then, we study the strong two-sided limit shadowing property and obtain the topologically mixing property, immediately. Moreover, we find a criterion to obtain the two-sided limit shadowing property. The relationship between two-sided limit shadowing property and another kinds of shadowing was studied in [3] and [6]. Let us mention some notations and necessary definitions on ordinary dynamical systems and iterated function systems. One can see these definitions in [2], [5], [8], and [10] for dynamical systems with one generator. Let (X,d) be a compact metric space and f : X → X be a homeomorphism. Assume that ε and δ are positive integer numbers. A sequence {x i } i∈Z is said to be a