Cantor集并的自相似性(英文)  

SELF-SIMILARITY OF UNIONS OF CANTOR SETS

作　　者：邓国泰[1] 刘春苔[2] 

机构地区：[1]华中师范大学数学与统计学学院,湖北武汉430079 [2]武汉工业学院数理科学系,湖北武汉430023

出　　处：《数学杂志》2011年第5期847-852,共6页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(10771082)

摘　　要：本文研究了Cantor集和其并的自相似性.利用Cantor展式的方法,得到了关于Cantor集和迭代函数系的一个基本关系:T∪(T+α)为自相似的当且仅当存在一个非负整数n使得α=±(k2-k1)dn.进一步,若T∪(T+α)是自相似的,则它满足开集条件.In this article,the authors study the self-similarity of the union of Cantor sets.By the Cantor expressions they get a basic relationship between Cantor sets and iterated function systems：T ∪ （T＋ α） is a self-similar set iff there exists a natural number n ≥ 0,such that α=±（k2-k1）d n.Moreover,if T ∪ （T＋ α） is a self-similar set,it satisfies the open set condition.

关 键 词：CANTOR集 迭代函数系 自相似集 

分 类 号：O174.1[理学—数学]