Exceptional digit frequencies and expansions in non-integer bases
Dynamical Systems
2017-11-29 v1 Number Theory
Abstract
In this paper we study the set of digit frequencies that are realised by elements of the set of -expansions. The main result of this paper demonstrates that as approaches the set of digit frequencies that occur amongst the set of -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.
Cite
@article{arxiv.1711.10397,
title = {Exceptional digit frequencies and expansions in non-integer bases},
author = {Simon Baker},
journal= {arXiv preprint arXiv:1711.10397},
year = {2017}
}