齐次三部分Cantor集的一个几何性质

Geometrical property of the three-part homogenous Cantor-set

令C_β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L_λ(λ∈(0,1)),使得其与集合C_β×C_β相交仅仅包含原点.利用重正规化方法得到了一些结果.

Let C_βbe the three-part homogenous cantor-set with ratioβ∈（0,1/3）.Thispaper studied a visibility problem：givenβ∈（0,1/3）,is there a ray L_λwith slopeλ∈（0,1）which goes through the origin（0,0）such that the intersection of L_λand set（C_β×C_β）only contains the origin？ Based on the method of renormalization,some results wereobtained.