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Multifractal analysis of anisotropic and directional pointwise regularities for measures

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  • Ben Omrane, Ines

Abstract

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.

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  • Ben Omrane, Ines, 2024. "Multifractal analysis of anisotropic and directional pointwise regularities for measures," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    • Handle: RePEc:eee:chsofr:v:183:y:2024:i:c:s0960077924004867
    DOI: 10.1016/j.chaos.2024.114934
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    References listed on IDEAS

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    1. Arneodo, A. & Bacry, E. & Muzy, J.F., 1995. "The thermodynamics of fractals revisited with wavelets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 213(1), pages 232-275.
    2. Achour, Rim & Li, Zhiming & Selmi, Bilel & Wang, Tingting, 2024. "A multifractal formalism for new general fractal measures," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    3. DOUZI, Zied & SELMI, Bilel, 2016. "Multifractal variation for projections of measures," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 414-420.
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