一类平面自相似集的共形维数

Conformal dimension of a class of plane self-similar sets

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.