Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Request Permissions   Purchase Content 
 

 

Finite-rank Bratteli-Vershik homeomorphisms are expansive


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

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 37B05, 37B10

Retrieve articles in all journals with MSC (2010): 37B05, 37B10


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