Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

DIMENSION FOR A CANTOR-LIKE SET WITH OVERLAPS

  • Lee, Mi-Ryeong (Department of Mathematics Kyungpook National University) ;
  • Park, Jung-Ju (Department of Mathematics Kyungpook National University) ;
  • Lee, Hung-Hwan (Department of Mathematics Kyungpook National University)
  • Published : 2004.10.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper we define a Cantor-like set K with overlaps in R$^1$. We find the correlation dimension of the set K without two conditions: the control of placements of basic sets constructing K and the thickness of K being greater than 1.

Keywords

References

  1. W. Chin, B. Hunt and J. A. Yorke, Correlation dimension for iterated function systems, Trans. Amer. Math. Soc. 349 (1997), 1783-1796. https://doi.org/10.1090/S0002-9947-97-01900-4
  2. K. Falconer, Techniques in Fractal Geometry, Mathematical Foundations and Applications, John Wiley & Sons 1997.
  3. M. R. Lee, Correlation dimensions of Cantor sets with overlaps, Commun. Korean Math. Soc. 15 (2000), 293-300.
  4. Y. Peres and B. Solomyak, Existence of $L^q$ dimensions and entropy dimension for self-conformal measures, Indiana Univ. Math. J. 49 (2000), no. 4, 1603-1621. https://doi.org/10.1512/iumj.2000.49.1851
  5. T. D. Sauer and J. A. Yorke, Are the dimensions of a set and its images equal under typical smooth functions ?, Ergodic Theory Dynam. Systems 17 (1997), 941-956. https://doi.org/10.1017/S0143385797086252
  6. K. Simon, Exceptional set and multifractal analysis, Period. Math. Hungar. 37 (1998), 121-125. https://doi.org/10.1023/A:1004786605015
  7. K. Simon, Multifractals and the dimension of exceptions, Real Anal. Exchange 27 (2001/02), no. 1, 191-207.
  8. K. Simon and B. Solomyak, Correlation dimension for self-similar Cantor sets with overlaps, Fund. Math. 155 (1998), no. 3, 293-300.