一类康托集平移并的自相似结构  

The Self-Similar Structure of a Cantor Set on the Translation Union

作　　者：李艳晓[1] 张永胜[1] 袁可红[1] 

机构地区：[1]洛阳理工学院数理系,河南洛阳471023

出　　处：《河南科学》2011年第10期1151-1154,共4页Henan Science

基　　金：河南省杰出青年基金(104100510018);河南省高校科技创新人才支持计划(2008HASTIT029);河南省教育厅科技攻关项目(2007520033)

摘　　要：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.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 I-Iausdorff and Boxing etc., all sorts of fractal dimension.

关 键 词：自相似集 迭代函数系统 平移并 

分 类 号：O174[理学—数学]