1/6-Cantor集的顶点的球密度计算

The Computation of Densities of Vertexes on One Sixth Cantor Set

本文研究自相似集E的顶点的上、下球密度计算问题,其中E是由作用于闭区间[0,1]上的3个压缩比为1/6的相似压缩函数生成.通过在区间[0,1]上引入一个以E为支撑的自相似测度,然后利用该自相似测度定义某点处的上、下球密度.结合E的自相似结构,将上、下球密度的计算问题转变成计算闭区间[1/6,1]上密度函数的最大值和最小值问题,从而得到集合E上各顶点的上、下球密度的精确值.

This paper is about the computation of densities of vertexes on self-similar set E, where E is generated by three functions on interval[0,1] with contraction ratio 1/6 A self-similar measure μ with support E is defined, and the upper spherical density and lower spherical density are defined with respect to this mea- sure. By the similarity of E, the exact values of spherical densities are obtained by the maximum of density function on interval [1/6,1].