华东师范大学学报(自然科学版) ›› 2011, Vol. 2011 ›› Issue (3): 54-58.

• 应用数学与基础数学 • 上一篇    下一篇

齐次三部分Cantor集的一个几何性质

李雪锋; 蒋 侃   

  1. 华东师范大学数学系, 上海 200241
  • 收稿日期:2010-10-01 修回日期:2011-01-01 出版日期:2011-05-25 发布日期:2011-05-25
  • 通讯作者: 李雪锋

Geometrical property of the three-part homogenous Cantor-set

LI Xue-feng; JIANG Kan   

  1. Department of Mathematics, East China Normal University, Shanghai 200241, China
  • Received:2010-10-01 Revised:2011-01-01 Online:2011-05-25 Published:2011-05-25
  • Contact: LI Xue-feng

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摘要： 令Cβ为压缩率为β∈(0,1/3)的齐次三部分Cantor集. 本文研究一个可视性问题:对给定的β∈(0,1/3),考虑是否存在过原点(0,0)斜率为λ的射线Lλ(λ∈(0,1)),使得其与集合Cβ× Cβ相交仅仅包含原点. 利用重正规化方法得到了一些结果.

关键词: 齐次三部分Cantor集, 仿射变换, 重正规化, 齐次三部分Cantor集, 仿射变换, 重正规化

Abstract: Let Cβ be the three-part homogenous cantor-set with ratio β∈(0,1/3). This paper studied a visibility problem: givenβ∈(0,1/3), is there a ray Lλ with slope λ∈(0,1) which goes through the origin (0,0) such that the intersection of Lλ and set Cβ× Cβ only contains the origin? Based on the method of renormalization, some results were obtained.

Key words: affine map, renormalization, three-part homogenous cantor-set, affine map, renormalization

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