Resumen de On the Gibbs Properties of Bernoulli Convolutions Related to ß-Numeration in Multinacci Bases

Eric Olivier, Nikita Sidorov, Alain Thomas

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