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Finite-rank Bratteli-Vershik homeomorphisms are expansive


Author: Takashi Shimomura
Journal: Proc. Amer. Math. Soc. 145 (2017), 4353-4362
MSC (2010): Primary 37B05, 37B10
DOI: https://doi.org/10.1090/proc/13575
Published electronically: April 7, 2017
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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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Additional Information

Takashi Shimomura
Affiliation: Nagoya University of Economics, Uchikubo 61-1, Inuyama 484-8504, Japan
Email: tkshimo@nagoya-ku.ac.jp

DOI: https://doi.org/10.1090/proc/13575
Keywords: Rank, Bratteli diagram, periodic, expansive
Received by editor(s): June 29, 2016
Received by editor(s) in revised form: October 25, 2016
Published electronically: April 7, 2017
Communicated by: Nimish Shah
Article copyright: © Copyright 2017 American Mathematical Society

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