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arXiv · 1804.09034

A mixed multifractal formalism for finitely many non Gibbs Frostman-like measures

Mohamed Menceur·Anouar Ben Mabrouk
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Abstract

The multifractal formalism for measures hold whenever the existence of corresponding Gibbs-like measures supported on the singularities sets holds. In the present work we tried to relax such a hypothesis and introduce a more general framework of mixed (and thus single) multifractal analysis where the measures constructed on the singularities sets are not Gibbs but controlled by an extra-function allowing the multifractal formalism to hold. We fall on the classical case by a particular choice of such a function.

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Mohamed Menceur, Anouar Ben Mabrouk. 2018-04-21. A mixed multifractal formalism for finitely many non Gibbs Frostman-like measures. https://arxiv.org/abs/1804.09034

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