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arXiv · 1710.00313

On the shadowing and limit shadowing properties

Noriaki Kawaguchi
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Abstract

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.

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Noriaki Kawaguchi. 2017-10-01. On the shadowing and limit shadowing properties. https://arxiv.org/abs/1710.00313

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