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On the Gibbs Properties of Bernoulli Convolutions Related to β-Numeration in Multinacci Bases

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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.

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Authors and Affiliations

  1. Université de Provence, Marseille, France

    Eric Olivier

  2. The University of Manchester, UK

    Nikita Sidorov

  3. Centre de Mathématiques et d’Informatique, Marseille, France

    Alain Thomas

Authors
  1. Eric Olivier
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  2. Nikita Sidorov
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  3. Alain Thomas
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Additional information

Supported by a HK RGC grant and a CUHK Postdoctoral Fellowship.

Supported by the EPSRC grant no GR/R61451/01.

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Olivier, E., Sidorov, N. & Thomas, A. On the Gibbs Properties of Bernoulli Convolutions Related to β-Numeration in Multinacci Bases. Mh Math 145, 145–174 (2005). https://doi.org/10.1007/s00605-005-0298-z

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  • DOI: https://doi.org/10.1007/s00605-005-0298-z

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