대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제16권1호
  • /
  • Pages.95-102
  • /
  • 2001
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지

CORRELATION DIMENSIONS OF CANTOR SETS WITH OVERLPS

  • Lee, Mi-Ryeong (Department of Mathematics, College of Natural Science, Kyungpook National University)
  • 발행 : 2001.01.01
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초록

We consider a Cantor set with overlaps Λ in R$^1$. We calculate its correlation dimension with respect to the push-down measure on Λ comparing with its similarity dimension.

키워드

참고문헌

  1. Mathematical Founddations and Applications Fractal Geometry K. Falconer
  2. Phy. v.8D The infinite number of generalized dimensions of fractals and strange attractors H. G. E. Hentschel and Itamar Procaccia
  3. Indiana Math. J. v.30 Fractals and self-similarity J. E. Hutchinson
  4. Hiroshima Math. J. v.25 On loosely self-similar sets S. Ikeda
  5. Kyungpook Math. J. v.40 The correlation dimensions of loosely self-similar sets M. R. Lee;H. H. Lee
  6. Hyperbolicity and Sensitive chaotic Dynamics at Homochnic Bifurcations J. Palis;F. Takens
  7. Funda. Math. v.155 Correlation dimension for self-similar Cantor sets with overlaps K. Simon;B. Solomyak