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arXiv · 1208.6195

The growth rate and dimension theory of beta-expansions

Simon Baker
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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.

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Simon Baker. 2012-10-15. The growth rate and dimension theory of beta-expansions. https://arxiv.org/abs/1208.6195

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