On the multifractal measures: proportionality and dimensions of Moran sets

被引：2

作者：

Selmi, Bilel ^{[1
]}

Yuan, Zhihui ^{[2
]}

机构：

[1] Univ Monastir, Fac Sci Monastir, Dept Math, Probabil & Fractals Lab LR18ES17, Monastir 5000, Tunisia

[2] East China Univ Technol, Sch Sci, Nanchang 330013, Jiangxi, Peoples R China

来源：

RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO | 2023年 / 72卷 / 08期

基金：

中国国家自然科学基金;

关键词：

Multifractal analysis; Homogeneous Cantor sets; Hausdorff dimension; Packing dimension; Homogeneous Moran measures; SINGULARITY SPECTRUM;

D O I：

10.1007/s12215-023-00873-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：3949 / 3969

页数：21

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