Mixed multifractal densities for quasi-Ahlfors vector-valued measures

2021/03/09 by Adel Farhat, Farhat, Adel, Anouar Ben Mabrouk +1
Economics, Econometrics and Finance · Mathematics · #28A78 #28A80 #Complex Systems and Time Series Analysis #FOS: Mathematics #FOS: Physical sciences #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Metric Geometry (math.MG) #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2103.05246

openalex publication_date 2021/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present work, some density estimations associated with vector-valued quasi-Ahlfors measures are developed within the mixed multifractal analysis framework. The principle idea based on the fact that being quasi-Ahlfors is sufficient to conduct a mixed multifractal analysis for vector-valued measures. In the present work, we introduced a multifractal density for finitely many measures and showed that such density may be estimated well by means of the mixed multifractal measures. Such estimation induces an exact computation of the multifractal spectrum of the vector-valued quasi-Ahlfors measure.

Citations

• A mixed multifractal formalism for finitely many non Gibbs Frostman-like measures
• Mixed multifractal spectra of Birkhoff averages for non-uniformly expanding one-dimensional Markov maps with countably many branches

Related

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• A Mixed Generalized Multifractal Formalism For Vector Valued Measures
• A mixed multifractal formalism for finitely many non Gibbs Frostman-like measures
• On the multivariate multifractal formalism: examples and counter-examples
• Some Aspects of Multifractal analysis