数学杂志
數學雜誌
수학잡지
JOURNAL OF MATHEMATICS
2011年
5期
847-852
,共6页
Cantor集%迭代函数系%自相似集
Cantor集%迭代函數繫%自相似集
Cantor집%질대함수계%자상사집
Cantor set%iterated function system(IFS)%self-similar set
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.
本文研究瞭Cantor集和其併的自相似性.利用Cantor展式的方法,得到瞭關于Cantor集和迭代函數繫的一箇基本關繫:T∪(T+α)為自相似的噹且僅噹存在一箇非負整數n使得α=±(k2-k1)dn.進一步,若T∪(T+α)是自相似的,則它滿足開集條件.
본문연구료Cantor집화기병적자상사성.이용Cantor전식적방법,득도료관우Cantor집화질대함수계적일개기본관계:T∪(T+α)위자상사적당차부당존재일개비부정수n사득α=±(k2-k1)dn.진일보,약T∪(T+α)시자상사적,칙타만족개집조건.
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)dn.Moreover,if T ∪ (T + α) is a self-similar set,it satisfies the open set condition.
