Finite-rank Bratteli–Vershik homeomorphisms are expansive
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- by Takashi Shimomura
- Proc. Amer. Math. Soc. 145 (2017), 4353-4362
- 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.References
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Bibliographic Information
- Takashi Shimomura
- Affiliation: Nagoya University of Economics, Uchikubo 61-1, Inuyama 484-8504, Japan
- MR Author ID: 221337
- Email: tkshimo@nagoya-ku.ac.jp
- 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
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 4353-4362
- MSC (2010): Primary 37B05, 37B10
- DOI: https://doi.org/10.1090/proc/13575
- MathSciNet review: 3690619