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
收藏
页码：3949 / 3969
页数：21
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