Weak Shadowing Property for IFS

TL;DR

This paper explores the shadowing property in iterated function systems (IFS), extending key results, defining conjugacy, and analyzing how shadowing behaves under these transformations.

Contribution

It introduces the concept of topological conjugacy for IFS and proves the equivalence of shadowing property preservation under conjugacy.

Findings

Shadowing property is preserved under topological conjugacy for IFS

Examples illustrating the relationship between original and IFS shadowing properties

Extension of classical shadowing results to the context of IFS

Abstract

In this paper we consider the shadowing property for iterated function systems,(IFS). Some important result about shadowing property are extended to iterated function systems. For example, we define topological conjugacy for IFS and prove that if F and G are two topological conjugate IFS then F has the shadowing property iff so does G. More- over, we introduce some examples and investigate the relationship between the original shadowing property and shadowing property for IFS.