Multifractal formalism for self-affine measures with overlaps

被引：3

作者：

Deng, Qi-Rong ^{[1
]}

Ngai, Sze-Man ^{[2
]}

机构：

[1] Fujian Normal Univ, Dept Math, Fuzhou 350007, Peoples R China

[2] Georgia So Univ, Dept Math Sci, Statesboro, GA 30460 USA

来源：

ARCHIV DER MATHEMATIK | 2009年 / 92卷 / 06期

关键词：

Self-affine measure; multifractal formalism; dimension spectrum; L(q)-spectrum; iterated function system with overlaps; asymptotic weak separation condition; L-Q-SPECTRUM; CONFORMAL MEASURES; BERNOULLI CONVOLUTIONS; EXCEPTIONAL PHENOMENA; SINGULARITY SPECTRUM; SIERPINSKI CARPETS; GIBBS MEASURES; FRACTALS; DECOMPOSITIONS; DIMENSION;

D O I：

10.1007/s00013-009-2969-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that for a class of self-affine measures defined by an expanding matrix whose eigenvalues have the same modulus, the L(q)-spectrum tau(q) is differentiable for all q > 0. Furthermore, we prove that the multifractal formalism holds in the region corresponding to q > 0.

引用

页码：614 / 625

页数：12

共 31 条

[1] [Anonymous], 1985, COURSE 88
[2] Multifractal analysis of Birkhoff averages on 'self-affine' symbolic spaces
Barral, Julien
Mensi, Mounir
[J]. NONLINEARITY, 2008, 21 (10) : 2409 - 2425
[3] Gibbs measures on self-affine Sierpinski carpets and their singularity spectrum
Barral, Julien
Mensi, Mounir
[J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2007, 27 : 1419 - 1443
[4] MULTIFRACTAL DECOMPOSITIONS OF MORAN FRACTALS
CAWLEY, R
MAULDIN, RD
[J]. ADVANCES IN MATHEMATICS, 1992, 92 (02) : 196 - 236
[5] Self-affine measures and vector-valued representations
Deng, Qi-Rong
He, Xing-Gang
Lau, Ka-Sing
[J]. STUDIA MATHEMATICA, 2008, 188 (03) : 259 - 286
[6] DENG QR, 2005, THESIS CHINESE U HON
[7] EDGAR GA, 1992, P LOND MATH SOC, V65, P604
[8] Falconer K., 1997, Techniques in fractal geometry
[9] Gibbs properties of self-conformal measures and the multifractal formalism
Feng, De-Jun
[J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2007, 27 : 787 - 812
[10] Feng DJ, 2005, ASIAN J MATH, V9, P473

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