Journal of East China Normal University(Natural Sc ›› 2011, Vol. 2011 ›› Issue (3): 54-58.

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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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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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