Multifractal dimensions of vector-valued non-Gibbs measures

Volume 8, Issue 2, Article 3 - 2020

Authors: Bilel Selmi

Copyright © 2020 . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Abstract

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

B. Selmi, Multifractal dimensions of vector-valued non-Gibbs measures, Gen.Lett. Math., 8(2) (2020), 51-66, https://doi.org/10.31559/glm2020.8.2.3