DOI QR코드

DOI QR Code

MULTIFRACTAL SPECTRUM IN A SELF-SIMILAR ATTRACTOR IN THE UNIT INTERVAL

  • Baek, In-Soo (DEPARTMENT OF MATHEMATICS PUSAN UNIVERSITY OF FOREIGN STUDIES)
  • Published : 2008.10.31

Abstract

We study the multifractal spectrum of two dimensionally indexed classes whose members are distribution sets of a self-similar attractor in the unit interval.

Keywords

References

  1. I. S. Baek, Relation between spectral classes of a self-similar Cantor sets, J. Math. Anal. Appl. 292 (2004), no. 1, 294-302 https://doi.org/10.1016/j.jmaa.2003.12.001
  2. I. S. Baek, Dimensions of distribution sets in the unit interval, Commun. Korean Math. Soc. 22 (2007), no. 4, 547-552 https://doi.org/10.4134/CKMS.2007.22.4.547
  3. I. S. Baek, Dimensions of the subsets in the spectral classes of a self-similar Cantor set, Journal of Applied Mathematics and Informatics 26 (2008), no. 3-4, 733-738
  4. I. S. Baek, Characteristic multifractal in a self-similar Cantor set, Journal of the Chungcheong Math. Soc. 21 (2008), no. 2, 157-163
  5. I. S. Baek, Multifractal characterization of the Riesz-Nagy-Takacs function, preprint.
  6. I. S. Baek, L. Olsen, and N. Snigireva, Divergence points of self-similar measures and packing dimension, Adv. Math. 214 (2007), no. 1, 267-287 https://doi.org/10.1016/j.aim.2007.02.003
  7. K. J. Falconer, The Fractal Geometry, John Wiley and Sons, 1990
  8. K. J. Falconer, Techniques in Fractal Geometry, John Wiley and Sons, 1997
  9. H. H. Lee and I. S. Baek, A note on equivalent interval covering systems for packing dimension of R, J. Korean Math. Soc. 28 (1991), no. 2, 195-205
  10. L. Olsen and S. Winter, Normal and non-normal points of self-similar sets and divergence points of self-similar measures, J. London Math. Soc. 67 (2003), no. 2, 103-122 https://doi.org/10.1112/S0024610702003630

Cited by

  1. SINGULARITY ORDER OF THE RIESZ-NÁGY-TAKÁCS FUNCTION vol.30, pp.1, 2015, https://doi.org/10.4134/CKMS.2015.30.1.007