Simon Baker
Published 2017-11-28Version 1
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.
Universal $β$-expansions
Digit frequencies and self-affine sets with non-empty interior
Non-uniform expansions of real numbers
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