Generalized Dimensions of Self-Affine Sets with Overlaps

被引：0

作者：

Ma, Guanzhong ^{[1
]}

Luo, Jun ^{[2
]}

Zhou, Xiao ^{[2
]}

机构：

[1] Anyang Normal Univ, Sch Math & Stat, Anyang 455000, Peoples R China

[2] Chongqing Univ, Coll Math & Stat, Chongqing 401331, Peoples R China

来源：

FRACTAL AND FRACTIONAL | 2024年 / 8卷 / 12期

关键词：

generalized dimension; self-affine set; overlap; FTC; pseudo-norm; SEPARATION PROPERTIES; HAUSDORFF DIMENSION;

D O I：

10.3390/fractalfract8120722

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Two decades ago, Ngai and Wang introduced a well-known finite type condition (FTC) on the self-similar iterated function system (IFS) with overlaps and used it to calculate the Hausdorff dimension of self-similar sets. In this paper, inspired by Ngai and Wang's idea, we define a new FTC on self-affine IFS and obtain an analogous formula on the generalized dimensions of self-affine sets. The generalized dimensions raised by He and Lau are used to estimate the Hausdorff dimension of self-affine sets.

引用

页数：12

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