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DIMENSIONS OF A DERANGED CANTOR SET WITH SPECIFIC CONTRACTION RATIOS

Baek, In-Soo

  • 발행 : 2004.05.01

초록

We investigate a deranged Cantor set (a generalized Cantor set) using the similar method to find the dimensions of cookie-cutter repeller. That is, we will use a Gibbs measure which is a weak limit of a subsequence of discrete Borel measures to find the dimensions. The deranged Cantor set that will be considered is a generalized form of a perturbed Cantor set (a variation of the symmetric Cantor set) and a cookie-cutter repeller.

키워드

Cantor set;fractal dimensions;Gibbs measure

참고문헌

  1. L S. Baek, Dimensions of weakly convergent deranged Cantor set, Real Anal. Exchange 23 (1997/98), no. 2, 689-696.
  2. Fractal geometry K.J.Falconer
  3. Techniques in fractal geometry K.J.Falconer
  4. Real Anal. Exchange v.23 no.2 pp.689-696 Diemensions of weakly convergent deranged Cantor set I.S.Baek
  5. Real Anal. Exchange v.19 no.1 pp.269-273 Dimensions of the perturbed Cantor set I.S.Baek