The structure of pointwise recurrent expansive homeomorphisms
| Autor: | ENHUI SHI, HUI XU, ZIQI YU |
|---|---|
| Rok vydání: | 2022 |
| Předmět: | |
| ISSN: | 0143-3857 |
| DOI: | 10.48550/arxiv.2201.00110 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|