Browse > Article
http://dx.doi.org/10.4134/CKMS.2004.19.4.683

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)
Publication Information
Communications of the Korean Mathematical Society / v.19, no.4, 2004 , pp. 683-689 More about this Journal
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
correlation dimension; Cantor-like set; overlaps;
Citations & Related Records
연도 인용수 순위
  • Reference
1 W. Chin, B. Hunt and J. A. Yorke, Correlation dimension for iterated function systems, Trans. Amer. Math. Soc. 349 (1997), 1783-1796.   DOI   ScienceOn
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.   DOI
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.   DOI
6 K. Simon, Exceptional set and multifractal analysis, Period. Math. Hungar. 37 (1998), 121-125.   DOI
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.