Generalized q-dimension of measures on Heisenberg self-affine sets in the Heisenberg group

被引：0
作者：
Miao, Jun Jie [1 ]
Wu, Xiaonan [1 ]
机构：
[1] E China Normal Univ, Dept Math, Shanghai Key Lab PMMP, Shanghai 200241, Peoples R China
来源：
NONLINEARITY | 2015年 / 28卷 / 08期
基金：
中国国家自然科学基金;
关键词：
self-affine; generalized q-dimension; Heisenberg group; SINGULARITY SPECTRUM; HAUSDORFF DIMENSION; SIERPINSKI CARPETS; FRACTALS; RECTIFIABILITY; SURFACES;
D O I：
10.1088/0951-7715/28/8/2939
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the generalized q-dimension of measures supported by Heisenberg self-affine sets in the Heisenberg group, and we obtain bounds for it which are valid for 'almost all' classes of affine contractions. In particular, when 1 < q <= 2, exact values are established for Heisenberg self-affine measures.
引用
收藏
页码：2939 / 2957
页数：19
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