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A family of non-sofic beta expansions

Published online by Cambridge University Press:  04 August 2014

SHIGEKI AKIYAMA
SHIGEKI AKIYAMA*
Affiliation:
Institute of Mathematics, University of Tsukuba, Tennodai 1-1-1, Tsukuba, Ibaraki, 305-8571, Japan email akiyama@math.tsukuba.ac.jp
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Abstract

Let ${\it\beta}_{n}>1$ be a root of $x^{n}-x-1$ for $n=4,5,\ldots$ ; we will prove that ${\it\beta}_{n}$ is not a Parry number, i.e., the associated beta transformation does not correspond to a sofic symbolic system. A generalization is shown in the last section.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 36 , Issue 2 , April 2016 , pp. 343 - 354
Copyright
© Cambridge University Press, 2014 

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