The growth rate and dimension theory of beta-expansions

Simon Baker

The growth rate and dimension theory of beta-expansions

Dynamical Systems 2013-05-27 v2 Number Theory

Authors: Simon Baker

Abstract

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

Keywords

beta-expansions growth rate dimension theory exponential growth Feng and Sidorov

Cite

@article{arxiv.1208.6195,
  title  = {The growth rate and dimension theory of beta-expansions},
  author = {Simon Baker},
  journal= {arXiv preprint arXiv:1208.6195},
  year   = {2013}
}

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