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almost periodic point

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The structure of pointwise recurrent expansive homeomorphisms
Part of
- Topological dynamics
ENHUI SHI, HUI XU, ZIQI YU
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.