ON THE DIMENSION OF SELF-AFFINE SETS AND MEASURES WITH OVERLAPS

被引：11

作者：

Barany, Balazs ^{[1
,2
]}

Michalrams ^{[3
]}

Simon, Karoly ^{[4
]}

机构：

[1] Budapest Univ Technol & Econ, MTA BME Stochast Res Grp, POB 91, H-1521 Budapest, Hungary

[2] Univ Warwick, Math Inst, Coventry CV4 7AL, W Midlands, England

[3] Polish Acad Sci, Inst Math, Ul Sniadeckich 8, PL-00656 Warsaw, Poland

[4] Budapest Univ Technol & Econ, Inst Math, Dept Stochast, POB 91, H-1521 Budapest, Hungary

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2016年 / 144卷 / 10期

基金：

英国工程与自然科学研究理事会;

关键词：

Self-affine measures; self-affine sets; Hausdorff dimension; HAUSDORFF DIMENSION; FRACTALS; ATTRACTORS;

D O I：

10.1090/proc/13121

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we consider diagonally affine, planar IFS Phi = {S-i(x, y)=(alpha(i)x + t(i,1), beta(i)y + t(i,2))}(i=1)(m). Combining the techniques of Hochman and Feng and Hu, we compute the Hausdorff dimension of the self-affine attractor and measures and we give an upper bound for the dimension of the exceptional set of parameters.

引用

页码：4427 / 4440

页数：14

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