The structure of pointwise recurrent expansive homeomorphisms

Enhui Shi; Hui Xu; Ziqi Yu

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arXiv · 2201.00110

The structure of pointwise recurrent expansive homeomorphisms

Enhui Shi·Hui Xu·Ziqi Yu

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Abstract

Let $X$ be a compact metric space and let $f:X\rightarrow X$ be a homeomorphism on $X$. We show that if $f$ is both pointwise recurrent and expansive, then the dynamical system $(X, f)$ is topologically conjugate to a subshift of some symbolic system. Moreover, if $f$ is pointwise positively recurrent, then the subshift is semisimple; a counterexample is given to show the necessity of positive recurrence to ensure the semisimilicity.

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Enhui Shi, Hui Xu, Ziqi Yu. 2022-01-01. The structure of pointwise recurrent expansive homeomorphisms. https://arxiv.org/abs/2201.00110

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