Purely periodic 𝛽-expansions with Pisot unit base

Ito, Shunji; Rao, Hui

doi:10.1090/S0002-9939-04-07794-9

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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