Dimensions of a class of self-affine Moran sets

被引：6

作者：

Gu, Yifei ^{[1
]}

Miao, Jun Jie ^{[1
]}

机构：

[1] East China Normal Univ, Sch Math Sci, 500 Dongchuan Rd, Shanghai 200241, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2022年 / 513卷 / 01期

关键词：

Self-affine set; Moran set; Box-counting dimension; Packing-dimension; Hausdorff dimension; Assouad dimension; HAUSDORFF DIMENSION; FRACTALS;

D O I：

10.1016/j.jmaa.2022.126210

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the paper, we define a class of fractals named "self-affine Moran sets", which are the generalization of classic Moran sets. Simply to say, we replace similarity mappings by affine mappings in the definition of Moran construction. We investigate the packing dimension, upper and lower box-counting dimension and Assouad dimension of these sets and give the dimension formulas. We also study Hausdorff dimension of such sets, we find some sufficient conditions for the Hausdorff dimension formula.(c) 2022 Elsevier Inc. All rights reserved.

引用

页数：24

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