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On the Gibbs properties of Bernoulli convolutions related to $\beta$-numeration in multinacci bases

Eric Olivier·Nikita Sidorov·Alain Thomas
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Abstract

We consider infinitely convolved Bernoulli measures (or simply Bernoulli convolutions) related to the $\beta$-numeration. A matrix decomposition of these measures is obtained in the case when $\beta$ is a PV number. We also determine their Gibbs properties for $\beta$ being a multinacci number, which makes the multifractal analysis of the corresponding Bernoulli convolution possible.

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Eric Olivier, Nikita Sidorov, Alain Thomas. 2004-11-12. On the Gibbs properties of Bernoulli convolutions related to $\beta$-numeration in multinacci bases. https://arxiv.org/abs/math/0411278

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