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The construction of a completely scrambled system by graph covers


Author: Takashi Shimomura
Journal: Proc. Amer. Math. Soc. 144 (2016), 2109-2120
MSC (2010): Primary 37B05, 54H20
DOI: https://doi.org/10.1090/proc/12963
Published electronically: November 20, 2015
MathSciNet review: 3460171
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Abstract: In this paper, we define a new construction of completely scrambled 0-dimensional systems using the inverse limit of sequences of directed graph covers. These examples are transitive and are not locally equicontinuous. Moreover, any point that is not the unique fixed point is not a point of local equicontinuity.


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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/12963
Keywords: Completely scrambled, graph covers, 0-dimensional
Received by editor(s): May 10, 2014
Received by editor(s) in revised form: June 8, 2015
Published electronically: November 20, 2015
Communicated by: Nimish A. Shah
Article copyright: © Copyright 2015 American Mathematical Society