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arXiv · 1711.10397

Exceptional digit frequencies and expansions in non-integer bases

Simon Baker
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Abstract

In this paper we study the set of digit frequencies that are realised by elements of the set of $\beta$-expansions. The main result of this paper demonstrates that as $\beta$ approaches $1,$ the set of digit frequencies that occur amongst the set of $\beta$-expansions fills out the simplex. As an application of our main result, we obtain upper bounds for the local dimension of certain biased Bernoulli convolutions.

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Simon Baker. 2017-11-28. Exceptional digit frequencies and expansions in non-integer bases. https://arxiv.org/abs/1711.10397

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