2 results
The structure of pointwise recurrent expansive homeomorphisms
- Part of
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- Journal:
- Ergodic Theory and Dynamical Systems / Volume 43 / Issue 10 / October 2023
- Published online by Cambridge University Press:
- 03 November 2022, pp. 3448-3459
- Print publication:
- October 2023
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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.
Periodic points for amenable group actions on uniquely arcwise connected continua
- Part of
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- Journal:
- Ergodic Theory and Dynamical Systems / Volume 41 / Issue 9 / September 2021
- Published online by Cambridge University Press:
- 30 September 2020, pp. 2833-2844
- Print publication:
- September 2021
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We show that any action of a countable amenable group on a uniquely arcwise connected continuum has a periodic point of order
$\leq 2$
.
