Multifractal analysis of anisotropic and directional pointwise regularities for measures

The usual multifractal analysis for measures studies isotropic pointwise regularity. It does not take into account behaviors that may differ when measured in coordinate axes directions. In this paper, we focus on anisotropic and directional pointwise regularities for Borel probability measures on R2...

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Bibliographic Details
Published in:Chaos, solitons and fractals solitons and fractals, 2024-06, Vol.183, p.114934, Article 114934
Main Author: Ben Omrane, Ines
Format: Article
Language:English
Subjects:
Anisotropic and pointwise directional regularities for measures
Dimension print
Multifractal analysis for measures
Self-affine invariant measures
Self-affine Sierpinski Sponges
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Summary:The usual multifractal analysis for measures studies isotropic pointwise regularity. It does not take into account behaviors that may differ when measured in coordinate axes directions. In this paper, we focus on anisotropic and directional pointwise regularities for Borel probability measures on R2. We will investigate general upper bound results about the dimension prints of the fractal sets of anisotropic regularities and irregularities, and iso-level directional regularity. We apply our results for selfaffine invariant measures on R2 supported by selfaffine Sierpinski Sponges. We show different directional multifractal phenomena. We finally obtain lower bound results about the dimension prints of the fractal sets of anisotropic regularities and irregularities for the measure product of two Borel probability measures on R that have Frostman measures at states q1 and q2 respectively.
ISSN:0960-0779
1873-2887
DOI:10.1016/j.chaos.2024.114934