No CrossRef data available.
Article contents
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.
MSC classification
- Type
- Original Article
- Information
- Copyright
- © The Author(s), 2022. Published by Cambridge University Press
References
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20230904123214871-0233:S014338572200075X:S014338572200075X_inline337.png?pub-status=live)