Hausdorff dimension of planar self-affine sets and measures with overlaps

被引：13

作者：

Hochman, Michael ^{[1
,2
]}

Rapaport, Ariel ^{[1
,3
,4
]}

机构：

[1] Hebrew Univ Jerusalem, Einstein Inst Math, Edmond J Safra Campus, Jerusalem, Israel

[2] Inst Adv Study, 1 Einstein Dr, Princeton, NJ 08540 USA

[3] Ctr Math Sci, Wilberforce Rd, Cambridge CB3 0WA, England

[4] Technion, Dept Math, Haifa, Israel

来源：

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2022年 / 24卷 / 07期

基金：

美国国家科学基金会;

关键词：

Hausdorff dimension; self-affine set; self-affine measure; Lyapunov dimension; LEDRAPPIER-YOUNG FORMULA; EQUAL HAUSDORFF; BOX;

D O I：

10.4171/JEMS/1127

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that if mu is a self-affine measure in the plane whose defining IFS acts totally irreducibly on RP1 and satisfies an exponential separation condition, then its dimension is equal to its Lyapunov dimension. We also treat a class of reducible systems. This extends our previous work on the subject with Barany to the overlapping case.

引用

页码：2361 / 2441

页数：81

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