Geometrical property of the three-part homogenous Cantor-set
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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.
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关键词:
- 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. -
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