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arXiv · 2012.08894

Sensitivity, local stable/unstable sets and shadowing

Mayara Antunes·Bernardo Carvalho·Margoth Tacuri
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Abstract

In this paper we study local stable/unstable sets of sensitive homeomorphisms with the shadowing property defined on compact metric spaces. We prove that local stable/unstable sets always contain a compact and perfect subset of the space. As a corollary we generalize results in [6] and [11] proving that positively countably expansive homeomorphisms defined on compact metric spaces satisfying either transitivity and the shadowing property, or the L-shadowing property, can only be defined in countably spaces.

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Mayara Antunes, Bernardo Carvalho, Margoth Tacuri. 2020-12-16. Sensitivity, local stable/unstable sets and shadowing. https://doi.org/10.1080/14689367.2023.2206545

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