The Multifractal Formalism for Measures, Review and Extension to Mixed Cases

被引：0

作者：

Mohamed Menceur ^{[1
]}

Anouar Ben Mabrouk ^{[2
,3
]}

Kamel Betina ^{[1
]}

机构：

[1] Algerba and Number Theory Laboratory, Faculty of Mathematics, University of Sciences and Technology Houari Boumediene

[2] Computational Mathematics Laboratory, Department of Mathematics, Faculty of Sciences

[3] Department of Mathematics, HIgher Institute of Applied Mathematics and Informatics, Street of Assad Ibn Alfourat, Kairouan University

来源：

Analysis in Theory and Applications | 2016年 / 32卷 / 04期

关键词：

Hausdorff measures; packing measures; Hausdorff dimension; packing dimension; renyi dimension; multifractal formalism; vector valued measures; mixed cases; Holderian measures; doubling measures; Borel-Cantelli; large deviations;

D O I：

暂无

中图分类号：

O189 [拓扑（形势几何学）];

学科分类号：

070104 ;

摘要：

The multifractal formalism for single measure is reviewed. Next, a mixed generalized multifractal formalism is introduced which extends the multifractal formalism of a single measure based on generalizations of the Hausdorff and packing measures to a vector of simultaneously many measures. Borel-Cantelli and Large deviations Theorems are extended to higher orders and thus applied for the validity of the new variant of the multifractal formalism for some special cases of multi-doubling type measures.

引用

页码：303 / 332

页数：30

共 50 条

[1] Complex multifractal measures and a generalized multifractal formalism
Jezewski, W
[J]. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2001, 298 (3-4) : 419 - 430
[2] Exceptions to the multifractal formalism for discontinuous measures
Riedi, RH
Mandelbrot, BB
[J]. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1998, 123 : 133 - 157
[3] A Multifractal Formalism for Hewitt–Stromberg Measures
Najmeddine Attia
Bilel Selmi
[J]. The Journal of Geometric Analysis, 2021, 31 : 825 - 862
[4] MULTIFRACTAL FORMALISM FOR INFINITE MULTINOMIAL MEASURES
RIEDI, RH
MANDELBROT, BB
[J]. ADVANCES IN APPLIED MATHEMATICS, 1995, 16 (02) : 132 - 150
[5] A Multifractal Formalism for Hewitt-Stromberg Measures
Attia, Najmeddine
Selmi, Bilel
[J]. JOURNAL OF GEOMETRIC ANALYSIS, 2021, 31 (01) : 825 - 862
[6] Correction: A Multifractal Formalism for Hewitt–Stromberg Measures
Najmeddine Attia
Bilel Selmi
[J]. The Journal of Geometric Analysis, 2022, 32
[7] A multifractal formalism for new general fractal measures
Achour, Rim
Li, Zhiming
Selmi, Bilel
Wang, Tingting
[J]. CHAOS SOLITONS & FRACTALS, 2024, 181
[8] Multifractal formalism for self-affine measures with overlaps
Qi-Rong Deng
Sze-Man Ngai
[J]. Archiv der Mathematik, 2009, 92 : 614 - 625
[9] On multifractal formalism for self-similar measures with overlaps
Julien Barral
De-Jun Feng
[J]. Mathematische Zeitschrift, 2021, 298 : 359 - 383
[10] Multifractal formalism for the inverse of random weak Gibbs measures
Yuan, Zhihui
[J]. STOCHASTICS AND DYNAMICS, 2020, 20 (04)

← 1 2 3 4 5 →