一类非自相似集的强正则性

Strong Regularily Property of Some Non-Similar Sets

给出了由压缩函数族Si(x)=xM+im,(M>m>1,i=0,1,2,…,m-1)通过限制某个Si出现的方式而产生的压缩不变集Eu,v.根据一个相关序列集个数的特征及连分数性质,证明了集Eu,v的盒维数与Hausdorff维数相等.

The contractive changeless et E u,v that ind uced form the contractive function series Si(x)=xM+im,(M >m>1,i=0,1,2,...,m-1) by restricting the producing model of a certain Si i s presented.According to the quantity characteristic of a correlative sequential set and the characteristic of continued fraction sequence,the Hausdorff dimensi on of E u,v is equal to the Box dimension of E u,v had been pr oved.