JEDNOSTKA NAUKOWA KATEGORII A+

# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## The growth rate and dimension theory of beta-expansions

### Tom 219 / 2012

Fundamenta Mathematicae 219 (2012), 271-285 MSC: 37A45, 37C45. DOI: 10.4064/fm219-3-6

#### Streszczenie

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.

#### Autorzy

• Simon BakerSchool of Mathematics
The University of Manchester