Counting Beta Expansions and the Absolute Continuity of Bernoulli Convolutions
Dynamical Systems
2012-03-27 v1 Number Theory
Abstract
We study the typical growth rate of the number of words of length n which can be extended to beta-expansions of x. In the general case we give a lower bound for the growth rate, while in the case that the Bernoulli convolution associated to parameter beta is absolutely continuous we are able to give the growth rate precisely. This gives new necessary and sufficient conditions for the absolute continuity of Bernoulli convolutions.
Cite
@article{arxiv.1203.5698,
title = {Counting Beta Expansions and the Absolute Continuity of Bernoulli Convolutions},
author = {Tom Kempton},
journal= {arXiv preprint arXiv:1203.5698},
year = {2012}
}
Comments
13 pages