The Hausdorff dimension of the projections of self-affine carpets

被引：18

作者：

Ferguson, Andrew ^{[1
]}

Jordan, Thomas ^{[2
]}

Shmerkin, Pablo ^{[3
,4
]}

机构：

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

[2] Univ Bristol, Dept Math, Bristol BS8 1TW, Avon, England

[3] Univ Manchester, Sch Math, Manchester M13 9PL, Lancs, England

[4] Univ Manchester, Ctr Interdisciplinary Computat & Dynam Anal, Manchester M13 9PL, Lancs, England

来源：

FUNDAMENTA MATHEMATICAE | 2010年 / 209卷 / 03期

基金：

英国工程与自然科学研究理事会;

关键词：

Hausdorff dimension; orthogonal projection; self-affine carpet; SETS;

D O I：

10.4064/fm209-3-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the orthogonal projections of a large class of self-affine carpets, which contains the carpets of Bedford and McMullen as special cases. Our main result is that if Lambda is such a carpet, and certain natural irrationality conditions hold, then every orthogonal projection of Lambda in a non-principal direction has Hausdorff dimension min(gamma, 1), where gamma is the Hausdorff dimension of Lambda. This generalizes a recent result of Peres and Shmerkin on sums of Cantor sets.

引用

页码：193 / 213

页数：21

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