k-自相似映射的结构及其应用  

Structures of k-self-similar mappings and applications

作　　者：张海妮[1] 李建林[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《陕西师范大学学报（自然科学版）》2009年第1期6-10,共5页Journal of Shaanxi Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(10571113)

摘　　要：研究了内积空间上k-自相似映射的结构与k-自相似映射列{An}的收敛性,并给出了相关的应用,证明了内积空间X上的映射A是一个k-自相似映射当且仅当存在X上的实线性等距U及常向量b,使得Ax=kUx+b(x∈X);给出了X上k-自相似映射列{An}的逐点收敛性的三个等价刻画;作为应用,证明了:若{In}是欧氏空间(Rp,ρ)上的一列自相似压缩迭代映射系且收敛于一个自相似压缩迭代映射系I,则In的吸引子(即自相似集)S(In)依分形空间K(X)上的Hausdorff度量收敛于I的吸引子S(I).The constructions of k-self-similar mappings on an inner product space and the convergence os sequences of k-self-similar mappings are discussed and some applications are given.It is proved firstly that a mapping A on an inner product space X is k-self-similar if and only if there exist a positive number k and a real linear isometry U on X and a vector b such that Ax=kUx+b for all x∈X.Three equivalent characterizations for a sequence {An} of k-self-similar mappings on X to be convergent are obtained.As appl...

关 键 词：k-自相似映射 等距算子 自相似压缩映射 吸引子 收敛性 

分 类 号：O174[理学—数学]