DOI QR코드

DOI QR Code

CANTOR DIMENSION AND ITS APPLICATION

  • Baek, In-Soo (Department of Matematics, Pusan University of Foreign Studies)
  • Published : 2004.02.01

Abstract

We defined Cantor dimensions of a perturbed Cantor set, and investigated a relation between these dimensions and Hausdorff and packing dimensions of a perturbed Cantor set. In this paper, we introduce another expressions of the Cantor dimensions. Using these, we study some informations which can be derived from power equations induced from contraction ratios of a perturbed Cantor set to give its Hausdorff or packing dimension. This application to a deranged Cantor set gives us an estimation of its Hausdorff and packing dimensions, which is a generalization of the Cantor dimension theorem.

Keywords

weak local dimension;deranged Cantor set;Hausdorff dimension;packing dimension

References

  1. Real Anal. Exchange v.23 no.2 Dimensions of weakly convergent deranged Cantor sets
  2. Math. Proc. Cambridge Philos. Soc. v.91 Two definitions of fractional dimension C.Tricot https://doi.org/10.1017/S0305004100059119
  3. Real Analysis Exchange v.19 no.1 Dimensions of the perturbed Cantor set I.S.Baek
  4. Real Analysis Exchange v.26 no.2 Week local dimension on deranged Cantor set
  5. Techniques in fractal geometry
  6. Fractal geometry K.J.Falconer
  7. Acta Math. Hungar v.99 no.4 Hausdorff dimension of perturbed Cantor sets without some boundedness condition https://doi.org/10.1023/A:1024631512342