On the Gibbs properties of Bernoulli convolutions related to β-numeration in multinacci bases
Eric Olivier, Nikita Sidorov, Alain Thomas
Abstract
We consider infinitely convolved Bernoulli measures (or simply Bernoulli convolutions) related to the β-numeration. A matrix decomposition of these measures is obtained in the case when β is a PV number. We also determine their Gibbs properties for β being a multinacci number, which makes the multifractal analysis of the corresponding Bernoulli convolution possible.
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