Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ON STRONG EXPONENTIAL LIMIT SHADOWING PROPERTY

  • Darabi, Ali (Department of Mathematics Shahid Chamran University of Ahvaz)
  • Received : 2021.11.25
  • Accepted : 2022.02.22
  • Published : 2022.10.01
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Abstract

In this study, we show that the strong exponential limit shadowing property (SELmSP, for short), which has been recently introduced, exists on a neighborhood of a hyperbolic set of a diffeomorphism. We also prove that Ω-stable diffeomorphisms and 𝓛-hyperbolic homeomorphisms have this type of shadowing property. By giving examples, it is shown that this type of shadowing is different from the other shadowings, and the chain transitivity and chain mixing are not necessary for it. Furthermore, we extend this type of shadowing property to positively expansive maps with the shadowing property.

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Acknowledgement

The author was supported by grant agreement No.SCU. MM1400.418 from SCU (Shahid Chamran University of Ahvaz) in Iran.

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