Doubling Property of Self-Affine Measures on Carpets of Bedford and McMullen

被引：0

作者：

Li, Hui ^{[1
]}

Wei, Chun ^{[2
]}

Wen, Shengyou ^{[1
]}

机构：

[1] Hubei Univ, Dept Math, Wuhan 430062, Peoples R China

[2] S China Univ Technol, Dept Math, Guangzhou 510641, Guangdong, Peoples R China

来源：

INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2016年 / 65卷 / 03期

关键词：

Self-affine carpet of Bedford-McMullen; self-affine measure; doubling property; HAUSDORFF DIMENSION; FRACTALS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the doubling property of measures on self-affine carpets of Bedford and McMullen. Let M be the family of such carpets, and let S is an element of M be a given carpet. We obtain an equivalent condition for a Borel measure to be doubling on S, and then consider self-affine measures on the carpet S. We encounter several cases; in each one, we obtain a complete characterization for doubling self-affine measures on S. In contrast with the fact that every self-similar carpet carries a doubling self similar measure, we found that there are self-affine carpets in M that do not carry any doubling self-affine measure. We give a geometric characterization for those "good" carpets.

引用

页码：833 / 865

页数：33

共 18 条

[1]

[Anonymous], 1984, THESIS

[2]

[Anonymous], 2014, FRACTAL GEOMETRY

[3] Hausdorff dimension of the limit sets of some planar geometric constructions [J].