Finite-rank Bratteli–Vershik homeomorphisms are expansive

Shimomura, Takashi

doi:10.1090/proc/13575

Finite-rank Bratteli–Vershik homeomorphisms are expansive
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by Takashi Shimomura PDF

Proc. Amer. Math. Soc. 145 (2017), 4353-4362 Request permission

Abstract:

Downarowicz and Maass (2008) have shown that every Cantor minimal homeomorphism with finite topological rank $K > 1$ is expansive. Bezuglyi, Kwiatkowski, and Medynets (2009) extended the result to non-minimal aperiodic cases. In this paper, we show that all finite-rank zero-dimensional systems are expansive or have infinite odometer systems; this is an extension of the two aforementioned results. Nevertheless, the methods follow similar approaches.

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