2021/03/07 by Adel Farhat, Farhat, Adel, Anouar Ben Mabrouk +1
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #28A78 #28A80 #Chaos control and synchronization #Complex Systems and Time Series Analysis #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2103.05466
openalex publication_date 2021/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The multifractal formalism for measures in its original formulation is checked for special classes of measures such as doubling, self-similar, and Gibbs-like ones. Out of these classes, suitable conditions should be taken into account to prove the validity of the multifractal formalism. In the present work, a large class of measures satisfying a weak condition known as quasi Ahlfors is considered in the framework of mixed multifractal analysis. A joint multifractal analysis of finitely many quasi Ahlfors probability measures is developed. Mixed variants of multifractal generalizations of Hausdorff and packing measures, and corresponding dimensions are introduced. By applying convexity arguments, some properties of these measures and dimensions are established. Finally, an associated multifractal formalism is introduced and proved to hold for the class of quasi Ahlfors measures.