‎Shadowing Relations with Structural and Topological Stability in Iterated Functions Systems

Fatemeh Rezaei, Mehdi Fatehi Nia

Abstract


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


Keywords


Shadowing property‎, ‎structural stability‎, ‎topological stability‎, ‎expansiveness property‎, ‎iterated functions system‎

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