On the Gibbs properties of Bernoulli convolutions related to β-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 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. © Springer-Verlag 2005.
    Original languageEnglish
    Pages (from-to)145-174
    Number of pages29
    JournalMonatshefte für Mathematik
    Volume145
    Issue number2
    DOIs
    Publication statusPublished - Jun 2005

    Keywords

    • β-numeration
    • Bernoulli convolution
    • Continued fraction
    • Infinite matrix product
    • PV number
    • Weak Gibbs measure

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