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
收藏
页码：833 / 865
页数：33
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