Multiscale self-affine Sierpinski carpets

被引：12
作者：
Gui, Yongxin [1 ,2 ]
Li, Wenxia [1 ]
机构：
[1] E China Normal Univ, Dept Math, Shanghai 200241, Peoples R China
[2] Xianning Coll, Dept Math, Xianning 437005, Peoples R China
来源：
NONLINEARITY | 2010年 / 23卷 / 03期
基金：
中国国家自然科学基金;
关键词：
HAUSDORFF DIMENSION; SETS; MCMULLEN; BEDFORD;
D O I：
10.1088/0951-7715/23/3/003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The well-known self-affine Sierpinski carpets, first studied by McMullen and Bedford independently, are constructed geometrically by repeating a single action according to a given pattern. In this paper, we extend them by randomly choosing a pattern from a set of patterns with different scales in each step of their construction process. The Hausdorff and box dimensions of the resulting limit sets are determined explicitly and the sufficient conditions for the corresponding Hausdorff measures to be positive finite are also obtained.
引用
收藏
页码：495 / 512
页数：18
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