A relative multifractal analysis

Khelifi, Mounir; Lotfi, Hela; Samti, Amal; Selmi, Bilel

doi:10.1016/j.chaos.2020.110091

Cited by 17 publications

(4 citation statements)

References 24 publications

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“…3. All the above results hold if we replace the centered δ−coverings (δ−packings) by the centered ν − δ−coverings (ν − δ−packings) and we suppose that the measure ν satis es the following condition For any < λ < given, there exists δ > , such that if ν (B(x, r) [14] for a systematic discussion of these measures. 4.…”

Section: Lemmamentioning

confidence: 96%

The mutual singularity of the relative multifractal measures

Douzi

Selmi

2021

Nonautonomous Dynamical Systems

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Section: Lemmamentioning

confidence: 96%

The mutual singularity of the relative multifractal measures

Douzi

Selmi

2021

Nonautonomous Dynamical Systems

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“…The last closest work to our's is developed in [28]. However, the main difference is that the authors there considered the multifractal formalism for a measure relatively to another one controlled by the diameter of the covering elements.…”

Section: Recent Related Work and Motivationsmentioning

confidence: 99%

Mixed multifractal densities for quasi-Ahlfors vector-valued measures

Farhat¹,

Mabrouk²

2021

Preprint

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In the present work, some density estimations associated to vector-valued quasi-Ahlfors measures are developed within the mixed multifractal analysis framework. The principle idea reposes 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 multifractal spectrum of the vector-valued quasi-Ahlfors measure.

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“…This means that, we somehow forget the geometric structure of X and focus instead on the properties of the measure µ. The set X is thus partitioned into α-level sets X µ (α) relatively to the regularity exponent of µ (see for example [1,2,9,21,22,23,27,31,39,40,42,43]). In the present work, we will be interested to the development of a mixed multifractal analysis of finitely many measures.…”

Section: Introductionmentioning

confidence: 99%

On the mixed multifractal formalism for vector-valued measures

Selmi

Mabrouk

2022

Proyecciones (Antofagasta)

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The multifractal formalism for vector-valued measures holds when-ever the existence of corresponding Gibbs-like measures, supported on the singularities sets holds. We tried through this article to improve a result developed by Menceur et al. in [29] and to suggest a new sufficient condition for a valid mixed multifractal formalism for vector-valued measures. We describe a necessary condition of validity for the formalism which is very close to the sufficient one.

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A relative multifractal analysis

Cited by 17 publications

References 24 publications

The mutual singularity of the relative multifractal measures

The mutual singularity of the relative multifractal measures

Mixed multifractal densities for quasi-Ahlfors vector-valued measures

On the mixed multifractal formalism for vector-valued measures

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