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On the shadowing and limit shadowing properties

Volume 249 / 2020

Noriaki Kawaguchi Fundamenta Mathematicae 249 (2020), 21-35 MSC: 37C50, 54H20, 37B20. DOI: 10.4064/fm552-4-2019 Published online: 23 August 2019


We study the relation between the shadowing property and the limit shadowing property. We prove that if a continuous self-map $f$ of a compact metric space has the limit shadowing property, then the restriction of $f$ to the non-wandering set satisfies the shadowing property. As an application, we prove the equivalence of the two shadowing properties for equicontinuous maps.


  • Noriaki KawaguchiGraduate School of Mathematical Sciences
    The University of Tokyo
    3-8-1 Komaba Meguro
    Tokyo 153-8914, Japan

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