Counting Beta Expansions and the Absolute Continuity of Bernoulli Convolutions

Details Counting Beta Expansions and the Absolute Continuity of Bernoulli Convolutions Counting Beta Expansions and the Absolute Continuity of Bernoulli Convolutions

2012-03-26

arxiv.org/abs/1203.5698v1

Mathematics

Dynamical Systems

13 pages

Scientific paper

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.

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