DOI QR코드

DOI QR Code

THE PARAMETER DISTRIBUTION SET FOR A SELF-SIMILAR MEASURE

  • Received : 2011.06.02
  • Published : 2012.09.30

Abstract

The parameter lower (upper) distribution set corresponds to the cylindrical lower or upper local dimension set for a self-similarmeasure on a self-similar set satisfying the open set condition.

Keywords

Hausdorff dimension;packing dimension;self-similar set;distribution set;local dimension set

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, Derivative of the Riesz-Nagy -Takacs function, Bull. Korean Math. Soc. 48 (2011), no. 2, 261-275. https://doi.org/10.4134/BKMS.2011.48.2.261
  3. I.-S. Baek, The derivative and moment of the generalized Riesz-Nagy-Takacs function, preprint.
  4. 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
  5. R. Cawley and R. D. Mauldin, Multifractal decompositions of Moran fractals, Adv. Math. 92 (1992), no. 2, 196-236. https://doi.org/10.1016/0001-8708(92)90064-R
  6. G. A. Edgar, Measure, Topology, and Fractal Geometry, Springer Verlag, 1990.
  7. M. Elekes, T. Keleti, and A. Mathe, Self-similar and self-affine sets; measures of the intersection of two copies, Ergodic Theory Dynam. Systems 30 (2010), no. 2, 399-440. https://doi.org/10.1017/S0143385709000121
  8. K. J. Falconer, Techniques in Fractal Geometry, John Wiley and Sons, 1997.
  9. W. Li, An equivalent definition of packing dimension and its application, Nonlinear Anal. Real World Appl. 10 (2009), no. 3, 1618-1626. https://doi.org/10.1016/j.nonrwa.2008.02.004
  10. M. Moran, Multifractal components of multiplicative set functions, Math. Nachr. 229 (2001), 129-160. https://doi.org/10.1002/1522-2616(200109)229:1<129::AID-MANA129>3.0.CO;2-L
  11. L. Olsen, A multifractal formalism, Adv. Math. 116 (1995), no. 1, 82-196. https://doi.org/10.1006/aima.1995.1066
  12. 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
  13. A. Schief, Separation properties for self-similar sets, Proc. Amer. Math. Soc. 122 (1994), no. 1, 111-115. https://doi.org/10.1090/S0002-9939-1994-1191872-1

Cited by

  1. THE DIMENSIONS OF THE MINIMUM AND MAXIMUM CYLINDRICAL LOCAL DIMENSION SETS vol.28, pp.1, 2015, https://doi.org/10.14403/jcms.2015.28.1.29
  2. SPECTRAL CLASSES AND THE PARAMETER DISTRIBUTION SET vol.30, pp.3, 2015, https://doi.org/10.4134/CKMS.2015.30.3.221

Acknowledgement

Supported by : National Research Foundation of Korea(NRF)