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Pré-Publication, Document De Travail Année : 2006

phase transitions for the multifractal analysis of self-similar measures

Résumé

We study the multifractal analysis of a class of self-similar measures with overlaps. This class, for which we obtain explicit formulae for the L^q spectrum tau(q) as well as the singularity spectrum f(alpha), is sufficiently large to point out new phenomena concerning the multifractal structure of self-similar measures. We show, that unlike the classical quasi-Bernoulli case, the L^q spectrum can have an arbitrarely large number of non-differentiability points (phase transitions). These singularities occur only for the negative values of q and yield to measures that do not satisfy the multifractal formalism. The weak quasi-Bernoulli property is the key point of most of the arguments.
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hal-00022128 , version 1 (03-04-2006)

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Benoit Testud. phase transitions for the multifractal analysis of self-similar measures. 2006. ⟨hal-00022128⟩
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