A joint multifractal analysis of vector valued non Gibbs measures

Mohamed Menceur and Anouar Ben Mabrouk

Chaos, Solitons & Fractals, 2019, vol. 126, issue C, 203-217

Abstract: The multifractal formalism for measures holds 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 joint 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. An answer to a question raised in [2] on which gauge function φ shall we get a finite, infinite or zero value of Hμ,φq,t(K) for the singularities set K is provided.

Keywords: Hausdorff and packing measures; Hausdorff and packing dimensions; Multifractal formalism; Mixed cases; Hölderian measures (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:126:y:2019:i:c:p:203-217

DOI: 10.1016/j.chaos.2019.05.010

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