Denseness of intermediate 𝛽-shifts of finite-type

Li, Bing; Sahlsten, Tuomas; Samuel, Tony; Steiner, Wolfgang

doi:10.1090/proc/14279

Denseness of intermediate $\beta$-shifts of finite-type
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by Bing Li, Tuomas Sahlsten, Tony Samuel and Wolfgang Steiner PDF

Proc. Amer. Math. Soc. 147 (2019), 2045-2055 Request permission

Abstract:

We determine the structure of the set of intermediate $\beta$-shifts of finite-type. Specifically, we show that this set is dense in the parameter space \begin{align*} \Delta \coloneq \{ (\beta , \alpha ) \in \mathbb {R}^{2} \colon \beta \in (1, 2) \; \text {and} \; 0 \leq \alpha \leq 2 - \beta \}. \end{align*} This generalises the classical result of Parry from 1960 for greedy $\beta$-shifts.

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