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.
Original language | English |
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Pages (from-to) | 1–31 |
Journal | Monatshefte fur Mathematik |
Volume | 190 |
Issue number | 1 |
Early online date | 13 Jun 2019 |
DOIs | |
Publication status | Published - 1 Sept 2019 |
Keywords
- Expansions in non-integer bases
- Digit frequencies
- Bernoulli convolutions