Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지
DOI QR코드

DOI QR Code

THE DIMENSIONS OF THE MINIMUM AND MAXIMUM CYLINDRICAL LOCAL DIMENSION SETS

  • Baek, In-Soo (Department of Mathematics Busan University of Foreign Studies)
  • Received : 2014.04.16
  • Accepted : 2014.10.06
  • Published : 2015.02.15
Download PDF
⟨ Previous Next ⟩

Abstract

We compute the Hausdorff and packing dimensions of the cylindrical lower or upper local dimension set for a self-similar measure having different minimum and maximum of the local dimension on a self-similar set satisfying the open set condition.

Keywords

References

  1. I.-S. Baek, Relation between spectral classes of a self-similar Cantor set, J. Math. Anal. Appl. 292 (2004), no. 1, 294-302. https://doi.org/10.1016/j.jmaa.2003.12.001
  2. 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
  3. I. -S. Baek, The parameter distribution set for a self-similar measure, Bull. Kor. Math. Soc. 49 (2012), no. 5, 1041-1055. https://doi.org/10.4134/BKMS.2012.49.5.1041
  4. K. J. Falconer, Techniques in fractal geometry, John Wiley and Sons, 1997.
  5. L. Olsen and S. Winter, Normal and non-normal points of self-similar sets and divergence points of a self-similar measures, J. London Math. Soc. 67 (2003), no. 3, 103-122. https://doi.org/10.1112/S0024610702003630