Digit Frequencies and Bernoulli Convolutions
Publication date
2014-06-27
Authors
Kempton, Tom
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Document Type
Article
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Abstract
It is well known that when ββ is a Pisot number, the corresponding Bernoulli convolution νβνβ has Hausdorff dimension less than 11, i.e. that there exists a set AβAβ with νβ(Aβ)=1νβ(Aβ)=1 and dimH(Aβ)<1dimH(Aβ)<1. We show explicitly how to construct for each Pisot number ββ such a set AβAβ.
Keywords
Bernoulli convolutions, Beta-expansions, Ergodic theory
Citation
Kempton, T 2014, 'Digit Frequencies and Bernoulli Convolutions', Indagationes Mathematicae, vol. 25, no. 4, pp. 832-842. https://doi.org/10.1016/j.indag.2014.04.011