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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Purely periodic $\beta$-expansions with Pisot unit base
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by Shunji Ito and Hui Rao PDF
Proc. Amer. Math. Soc. 133 (2005), 953-964 Request permission

Abstract:

Let $\beta >1$ be a Pisot unit. A family of sets $\{X_i\}_{1\leq i\leq q}$ defined by a $\beta$-numeration system has been extensively studied as an atomic surface or Rauzy fractal. For the purpose of constructing a Markov partition, a domain $\hat X=\bigcup _{i=1}^q \hat X_i$ constructed by an atomic surface has appeared in several papers. In this paper we show that the domain $\hat X$ completely characterizes the set of purely periodic $\beta$-expansions.
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Additional Information
  • Shunji Ito
  • Affiliation: Department of Information and Systems Engineering, Kanazawa University, Kanazawa, Japan
  • Email: ito@t.kanazawa-u.ac.jp
  • Hui Rao
  • Affiliation: Department of Mathematics, Tsinghua University, Beijing, People’s Republic of China
  • Email: hrao@math.tsinghua.edu.cn
  • Received by editor(s): May 28, 2003
  • Published electronically: November 19, 2004
  • Additional Notes: The second author was supported by the Japanese Science Promotion Society (JSPS)
  • Communicated by: David E. Rohrlich
  • © Copyright 2004 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 133 (2005), 953-964
  • MSC (2000): Primary 11R06; Secondary 37B50
  • DOI: https://doi.org/10.1090/S0002-9939-04-07794-9
  • MathSciNet review: 2117194