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arXiv · 2512.08677

L-shadowing for the induced hyperspace homeomorphism

Mayara Antunes·Bernardo Carvalho·Welington Cordeiro
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Abstract

We prove that a homeomorphism f of a compact metric space X satisfies the L-shadowing property if and only if its induced hyperspace homeomorphism also satisfies the L-shadowing property. In the proof, assuming only the L-shadowing property, we obtain the existence of points in the asymptotic local-product-structure with iterates approaching in a uniform rate of convergence to zero. This contrasts with the lack of uniformity of contraction on local stable/unstable sets on many homeomorphisms with the L-shadowing property.

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Mayara Antunes, Bernardo Carvalho, Welington Cordeiro. 2025-12-09. L-shadowing for the induced hyperspace homeomorphism. https://arxiv.org/abs/2512.08677

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