三分康托集与其两个平移交的维数

华东师范大学学报(自然科学版) ›› 2010, Vol. 2010 ›› Issue (5): 91-95.

三分康托集与其两个平移交的维数

张云秀

南京林业大学应用数学系, 南京 210037

收稿日期:2009-12-01 修回日期:2010-04-01 出版日期:2010-09-25 发布日期:2010-09-25
通讯作者: 张云秀

Dimension of the intersection of the Cantor ternary set with its two translations

ZHANG Yun-xiu

Department of Applied Mathematics, Nanjing Forest University, Nanjing 210037, China

Received:2009-12-01 Revised:2010-04-01 Online:2010-09-25 Published:2010-09-25
Contact: ZHANG Yun-xiu

摘要/Abstract

摘要： C为三分康托集, 考虑何时交集C\cap (C+t)\cap (C+s) 非空, 计算出当交集非空时 (t,s) 的 Hausdorff 维数. 证明了: 对于平面上几乎处处的(t,s), dim_H C\cap (C+t)\cap (C+s)=0. 利用Moran集的相关结论得到当交集非空时dim_H C\cap (C+t)\cap (C+s)的表达式.

关键词: 三分康托集, 交集, 端点, 莫朗集, 三分康托集, 交集, 端点, 莫朗集

Abstract: Let C be the Cantor ternary set. The condition of the intersection C\cap (C+t)\cap (C+s)\neq\emptyset was considered and the Hausdorff dimension of (t,s) was computed when the intersection was nonempty. A conclusion was proved: dim_H C\cap (C+t)\cap (C+s)=0 for a.e. (t,s)\in{\bf R}\times {\bf R}. Then by a related result of Moran set, the expression of dim_H C\cap (C+t)\cap (C+s) was investigated.

Key words: intersection, end-points, Moran sets, Cantor ternary set, intersection, end-points, Moran sets

中图分类号:

O174.12

张云秀. 三分康托集与其两个平移交的维数[J]. 华东师范大学学报(自然科学版), 2010, 2010(5): 91-95.

ZHANG Yun-xiu. Dimension of the intersection of the Cantor ternary set with its two translations[J]. Journal of East China Normal University(Natural Sc, 2010, 2010(5): 91-95.