一类康托集平移并的自相似结构

摘要

The concrete structure of the union of a- Cantor set and its translation from the self-similar set is discussed. Based on the series expression of the elements, the iterated function system with positive compression ratio is structured, and the sufficient and necessary condition is given for the union of the translation is a self- similar set. It is helpful for calculating, for example Hausdorff and Boxing etc., a%从自相似集的角度考虑一类康托集的平移并的具体结构.借助平移并的元素级数表达式,构造了压缩比为正值的迭代函数系统,给出了平移并为自相似集的充要条件,有利于计算Hausdorff维数、Boxing维数等各种分形维数.