摘要
若自相似迭代函数系{φj}jm=1(满足φj(x)=ρjRjx+bj,bj∈Rd,其中0<ρj<1,Rj为d×d正交矩阵)关于不变开集Ω满足有限型条件,K是迭代函数系{φj}jm=1生成的自相似集.但是,Ω与K的交集可能为空集.本文用构造方法证明存在一个不变开集U,使得U∩K≠φ,且迭代函数系{φj}jm=1关于不变开集U也满足有限型条件.
If self-similar IFS {φj}^mj=1（ which satisfies： φj（x）=ρjRjx＋bj,bj∈R^d , where 0 〈 ρj 〈 1 , and Rj are orthonormal d×d matrices） satisfies finite type condition with respect to the invariant open set Ω. The invariant set K is generated by IFS {φj}^mj=1. Since the intersection of Ω and K may be empty. We prove that there exists an invariant open set U such that U∩K≠φ, and IFS {φj}^mj=1 also satisfies finite type condition with respect to the invariant open set U by a constructive method.
出处
《山西师范大学学报（自然科学版）》
2009年第3期20-23,共4页
Journal of Shanxi Normal University(Natural Science Edition)
关键词
迭代函数系
自相似集
不变开集
有限型条件
iterated function systems
self-similar sets
invariant open set
finite type condition
