一类平面自相似集的共形维数  

Conformal dimension of a class of plane self-similar sets

作　　者：张田莉 杨红霞 ZHANG Tianli;YANG Hongxia(Faculty of Mathematics and Statistics,Hubei Key Laboratory of Applied Mathematics,Hubei University,Wuhan 430062,China)

机构地区：[1]湖北大学数学与统计学学院,应用数学湖北省重点实验室,湖北武汉430062

出　　处：《湖北大学学报（自然科学版）》2023年第6期858-864,共7页Journal of Hubei University：Natural Science

摘　　要：设A={1,2,3,4}为一有限集,给定一族生成方式{S_(i)}_(i∈A).设对任意的a∈(0,1/4),T_(a)是以0,1和1/2+2ai为顶点的闭三角形.从T_(a)出发,定义一类平面自相似集X_(a),主要证明该类自相似集X_(a)的共形维数为1,并且不是拟对称极小集.Let A={1,2,3,4}be a nite set,given a family of generation modes{S_(i)}_(i∈A).Let T_(a)be a closed triangle with vertices 0,1 and 1/2+2a i for any a∈(0,1/4).In this paper,starting from T_(a),we defined a class of plane self-similar set X_(a),we mainly prove that the conformal dimension of this kind of self-similar set X_(a)is 1 and it is not a quasisymmetric minimal set.

关 键 词：共形维数 拟对称极小集 自相似集 

分 类 号：O174.12[理学—数学]