Shadowing Relations with Structural and Topological Stability in Iterated Functions Systems
Keywords:
Shadowing property, structural stability, topological stability, expansiveness property, iterated functions systemAbstract
This paper aims at formulating definitions of topological stability, structural stability, and expansiveness property for an iterated functions system( abbrev, IFS). It is going to show that the shadowing property is necessary condition for topological stability in IFSs. Then, it proves the previous weak converse demonstration with the addition of expansiveness property for IFSs. Then, by giving an example, we show that in an IFS, the shadowing property doesn't imply structural stability
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