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On the multifractal measures and dimensions of image measures on a class of Moran sets

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  • Attia, Najmeddine
  • Selmi, Bilel

Abstract

On a Moran set meeting the strong separation requirement, we examine a family of multifractal Hausdorff and packing measures and dimensions in this study. Let φ∗π be the image measure of ergodic Borel probability measure π and measurable function φ. Entropy is used to calculate the formula for the dimension of the multifractal measure of φ∗π. Moreover, some statistical interpretations, on a class of Moran sets, of the dimensions and corresponding geometrical measures are also supported. Finally, a specific illustration of a measure that satisfies the aforementioned criteria is created.

Suggested Citation

  • Attia, Najmeddine & Selmi, Bilel, 2023. "On the multifractal measures and dimensions of image measures on a class of Moran sets," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:chsofr:v:174:y:2023:i:c:s0960077923007191
    DOI: 10.1016/j.chaos.2023.113818
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    References listed on IDEAS

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    1. Douzi, Zied & Selmi, Bilel, 2019. "Regularities of general Hausdorff and packing functions," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 240-243.
    2. Najmeddine Attia & Bilel Selmi, 2023. "On the Fractal Measures and Dimensions of Image Measures on a Class of Moran Sets," Mathematics, MDPI, vol. 11(6), pages 1-14, March.
    3. Khelifi, Mounir & Lotfi, Hela & Samti, Amal & Selmi, Bilel, 2020. "A relative multifractal analysis," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    4. DOUZI, Zied & SELMI, Bilel, 2016. "Multifractal variation for projections of measures," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 414-420.
    5. Dai, Meifeng & Jiang, Ying, 2009. "The equivalence of multifractal measures on cookie-cutter-like sets," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1408-1415.
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