Variational formula related to the self-affine Sierpinski carpets

被引：0
|
作者：
Gui, Yongxin [1 ]
Li, Wenxia [2 ]
Xiao, Dongmei [3 ]
机构：
[1] HuBei Univ Sci & Technol, Sch Math & Stat, Xianning 437100, Peoples R China
[2] E China Normal Univ, Shanghai Key Lab PMMP, Dept Math, Shanghai 200241, Peoples R China
[3] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China
来源：
MATHEMATISCHE NACHRICHTEN | 2015年 / 288卷 / 5-6期
基金：
中国国家自然科学基金;
关键词：
Self-affine Sierpinski carpet; digit frequency; group frequency; Hausdorff dimension; Primary: 28A80; Secondary: 28A78; HAUSDORFF DIMENSION; SETS; FRACTALS; MCMULLEN; BEDFORD;
D O I：
10.1002/mana.201400210
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider those subsets of the self-affine Sierpinski carpets that are the union of an uncountable number of sets each of which consists of the points with their location codes having prescribed group frequencies. It is proved that their Hausdorff dimensions equal to the supremum of the Hausdorff dimensions of the sets in the union. The main advantage is that we treat these subsets in a unified manner and the value of the Hausdorff dimensions do not need to be guessed a priori.
引用
收藏
页码：593 / 603
页数：11
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