Please wait a minute...
 北京大学期刊网　|　作者　　审稿人　　编委专家　　工作人员 首页　  |  　关于　  |  　浏览　  |  　投稿指南　  |  　新闻公告
 数学进展
 研究论文
 关于满足强分离开集条件的自相似集的Hausdorff测度 On the Hausdorff Measure of the Self-similar Sets Satisfying the Strong Separation Open Set Condition 许绍元,周作领 XU Shao-yuan, ZHOU Zuo-ling 中山大学数学与计算科学学院,中山大学岭南学院 广州,广东,510275 淮北煤炭师范学院数学系,淮北,安徽,235000,广州,广东,510275 (Math, and Sci. Comp. School, Zhongshan University, Guangzhou, Guangdong, 510275, P. R. China; Dept. of Math., Huaibei Coal Industry Teachers College, Huaibei, Anhui, 235000, P. R. China; Lingnan College, Zhongshan University, Guangzhou, Guangdong, 510275 收稿日期: 2005-10-25 出版日期: 2005-10-25
 114 浏览 引用导出
0
/   /   推荐
 摘要 设E是Rn中由相似压缩S1,S2,…,Sm所确定的满足开集条件的自相似集,其Hausdorff维数为s,其s-维Hausdorff测度记为Hs(E).利用部分估计原理得到了本文的主要结果:若E满足强分离开集条件,则在E中存在一个压缩拷贝串序列{Ui}和紧集U(|U|>0),使得Hs(U)等于|U|s,并且{Ui}按Hausdorff度量收敛到U,进而证明了由U可以构造一个数列,使得该数列正好收敛到Hs(E);另外,引入了自相似集的相似压缩不动点,得到了等式Hs(E∩U)=|U|s 成立的一个必要条件. 关键词 ： 自相似集,  Hausdorff测度与维数,  强分离开集条件,  Hausdorff度量,  相似压缩不动点 Abstract：For any E (?) Rn, denote by dimH(E) and Hs(E) the Hausdorff dimension and s-dimensional Hausdorff measure of E, where s is equal to dimH(E). Suppose E is the attractor of the IFS {S1,…,Sm} consisting of similarities. If E satisfies the strong separation open set condition (SSC), then there exists a series of contracting-copy-group {Ui} and a compact set U(|U| > 0) such that Hs(U) = |U|s and moreover, {Ui} converges to U with respect to Hausdorff metric. Besides, we introduce the concept of fixed point for the similar contraction mappings and obtain a necessary condition for the equality Hs(E ∩ U) = |U|s. Key words： HausdorfF measure and dimension    strong separation open set condition    Hausdorff metric    fixed point for the similar contraction mappings
 [1] 刘春苔. 广义有限型的注解[J]. 数学进展, 2019, 48(3): 343-351. [2] 许绍元. 关于自相似集的Hausdorff测度的一个判据及其应用[J]. 数学进展, 2002, 31(2): 157-162.
Viewed
Full text

Abstract

Cited

 © 2015-2017 北京大学图书馆 .