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On the multifractal measures: proportionality and dimensions of Moran sets

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Abstract

The aim of this work is to discuss the proportionality of the multifractal measures. We will prove that the ratio of the multifractal measures is bounded. In addition, for a class of homogeneous Cantor sets, we find an explicit formula for their multifractal Hausdorff and packing function dimensions and discuss some interesting examples.

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Acknowledgements

The referees’ constructive criticism and recommendations on the text are appreciated by the authors. The authors would like to thank Professor De-Jun Feng for the reference [10] and Professors Lars Olsen and Jinjun Li for useful discussions while writing this manuscript. The first author is supported by Analysis, Probability & Fractals Laboratory (No: LR18ES17). The second author is supported by the National Natural Science Foundation of China (Grant No. 12061006) and Natural Science Foundation of Jiangxi (Grant No. 20212BAB201002).

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Authors and Affiliations

  1. Analysis, Probability and Fractals Laboratory: LR18ES17, Department of Mathematics, Faculty of Sciences of Monastir, University of Monastir, Monastir, 5000, Tunisia

    Bilel Selmi

  2. School of Science, East China University of Technology, Nanchang, 330013, Jiangxi, People’s Republic of China

    Zhihui Yuan

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  1. Bilel Selmi
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  2. Zhihui Yuan
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Correspondence to Zhihui Yuan.

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Selmi, B., Yuan, Z. On the multifractal measures: proportionality and dimensions of Moran sets. Rend. Circ. Mat. Palermo, II. Ser 72, 3949–3969 (2023). https://doi.org/10.1007/s12215-023-00873-9

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