On the density of intermediate β-shifts of finite type

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 $\Delta =\{(\beta ,\alpha )\in {\mathbb{R}}^2:\beta \in (1,2)\text{and}0\le \alpha \le 2-\beta \}$. This generalises the classical result of Parry from 1960 for greedy and (normalised) lazy $\beta$-shifts.

arXiv comment6 pages