Exceptional digit frequencies and expansions in non-integer bases
Abstract
In this paper we study the set of digit frequencies that are realised by elements of the set of β-expansions. The main result of this paper demonstrates that as β approaches 1, the set of digit frequencies that occur amongst the set of β-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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