The growth rate and dimension theory of beta-expansions
Volume 219 / 2012
Fundamenta Mathematicae 219 (2012), 271-285
MSC: 37A45, 37C45.
DOI: 10.4064/fm219-3-6
Abstract
In a recent paper of Feng and Sidorov they show that for $\beta\in(1,(1+\sqrt{5})/2)$ the set of $\beta$-expansions grows exponentially for every $x\in(0,1/(\beta-1))$. In this paper we study this growth rate further. We also consider the set of $\beta$-expansions from a dimension theory perspective.
