Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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POSITIVELY EXPANSIVE MAPS AND THE LIMIT SHADOWING PROPERTIES

  • Received : 2020.01.14
  • Accepted : 2020.03.19
  • Published : 2021.01.01
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Abstract

In this paper, the notion of two-sided limit shadowing property is considered for a positively expansive open map. More precisely, let f be a positively expansive open map of a compact metric space X. It is proved that if f is topologically mixing, then it has the two-sided limit shadowing property. As a corollary, we have that if X is connected, then the notions of the two-sided limit shadowing property and the average-shadowing property are equivalent.

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Acknowledgement

This work is supported by JSPS KAKENHI Grant Numbers 16K05167 and 19K03578.

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