## Purely periodic $\beta$-expansions with Pisot unit base

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- by Shunji Ito and Hui Rao
- Proc. Amer. Math. Soc.
**133**(2005), 953-964 - DOI: https://doi.org/10.1090/S0002-9939-04-07794-9
- Published electronically: November 19, 2004
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## 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.## References

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## Bibliographic 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, Peopleâ€™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