General Letters in Mathematics

Volume 8 - Issue 2 (3) | PP: 51 - 66 Language : English

Multifractal dimensions of vector-valued non-Gibbs measures

Bilel Selmi
Received Date Revised Date Accepted Date Publication Date
14/5/2020 1/6/2020 11/6/2020 12/7/2020
In the present work, we are concerned with some multifractal dimensions estimations of vector-valued measures in the framework of the so-called mixed multifractal analysis. We precisely consider some Borel probability measures that are no longer Gibbs and introduce some mixed multifractal generalizations of Hausdorff and packing dimensions of measures in a framework of relative mixed multifractal analysis. As an application, we are interested in the '-unidimensionality of those measures and to the calculus of its mixed multifractal Hausdorff and packing dimensions. In particular, we give a necessary and sufficient condition for the existence of the '-mixed multifractal Hausdorff and packing dimensions of a Borel probability measure. Finally, concrete examples satisfying the above property are developed.

How To Cite This Article
Selmi , B. (2020). Multifractal dimensions of vector-valued non-Gibbs measures . General Letters in Mathematics, 8 (2), 51-66, 10.31559/glm2020.8.2.3

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