The growth rate and dimension theory of beta-expansions

Abstract

In a recent paper of Feng and Sidorov they show that for $β\in(1,\frac{1+\sqrt{5}}{2})$ the set of $β$-expansions grows exponentially for every $x\in(0,\frac{1}{β-1})$. In this paper we study this growth rate further. We also consider the set of $β$-expansions from a dimension theory perspective.