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The structure of pointwise recurrent expansive homeomorphisms
Published online by Cambridge University Press: 03 November 2022
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 semisimplicity.
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- © The Author(s), 2022. Published by Cambridge University Press