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arXiv · 1912.10987

Computing Garsia Entropy for Bernoulli Convolutions with Algebraic Parameters

Kevin G. Hare·Tom Kempton·Tomas Persson·Nikita Sidorov
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Abstract

We introduce a parameter space containing all algebraic integers $\beta\in(1,2]$ that are not Pisot or Salem numbers, and a sequence of increasing piecewise continuous function on this parameter space which gives a lower bound for the Garsia entropy of the Bernoulli convolution $\nu_{\beta}$. This allows us to show that $\mathrm{dim}_\mathrm{H} (\nu_{\beta})=1$ for all $\beta$ with representations in certain open regions of the parameter space.

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Kevin G. Hare, Tom Kempton, Tomas Persson, Nikita Sidorov. 2019-12-23. Computing Garsia Entropy for Bernoulli Convolutions with Algebraic Parameters. https://arxiv.org/abs/1912.10987

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