B. Selmi, N. Yu. Svetova, “On the Mutual multifractal analysis for some non-regular Moran measures”, Probl. Anal. Issues Anal., 2023, Volume 12(30), Issue 1,Pages <nobr>46

On the Mutual multifractal analysis for some non-regular Moran measures

B. Selmi^a, N. Yu. Svetova^b

^a Analysis, Probability and Fractals Laboratory LR18ES17, Faculty of sciences of Monastir, Department of mathematics, 5000-Monastir-Tunisia
^b Petrozavodsk State University, 33 Lenina pr., Petrozavodsk 185910, Russia

Abstract: In this paper, we study the mutual multifractal Hausdorff dimension and the packing dimension of level sets $K(\alpha, \beta)$ for some non-regular Moran measures satisfying the so-called Strong Separation Condition. We obtain sufficient conditions for the valid multifractal formalisms of such measures and discuss examples.

Keywords: fractal/multifractal dimensions, Moran sets, non-regular Moran measures.

UDC: 517.518.1

MSC: 28A20, 28A75, 28A78, 28A80, 49Q15

Received: 04.09.2022
Revised: 10.12.2022
Accepted: 06.12.2022

Language: English

DOI: 10.15393/j3.art.2023.12310