대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제33권2호
  • /
  • Pages.459-471
  • /
  • 2018
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

RELATIVE MULTIFRACTAL SPECTRUM

  • 투고 : 2017.04.06
  • 심사 : 2017.08.04
  • 발행 : 2018.04.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

We obtain a relation between generalized Hausdorff and packing multifractal premeasures and generalized Hausdorff and packing multifractal measures. As an application, we study a general formalism for the multifractal analysis of one probability measure with respect to an other.

키워드

참고문헌

  1. J. Barral, Continuity of the multifractal spectrum of a random statistically self-similar measures, J. Theoret. Probab. 13 (2000), no. 4, 1027-1060. https://doi.org/10.1023/A:1007866024819
  2. J. Barral and B. M. Mandelbrot, Random multiplicative multifractal measures, Fractal Geometry and Applications, Proc. Symp. Pure Math., AMS, Providence, RI, 2004.
  3. L. Barreira and J. Schmeling, Sets of non-typical points have full topological entropy and full Hausdorff dimension, Israel J. Math. 116 (2000), no. 1, 29-70. https://doi.org/10.1007/BF02773211
  4. F. Ben Nasr, I. Bhouri, and Y. Heurteaux, The validity of the multifractal formalism: results and examples, Adv. Math. 165 (2002), no. 2, 264-284. https://doi.org/10.1006/aima.2001.2025
  5. P. Billingsley, Ergodic Theory and Information, Wiley, New York, 1965.
  6. G. Brown, G. Michon, and J. Peyriere, On the multifractal analysis of measures, J. Statist. Phys. 66 (1992), no. 3-4, 775-790. https://doi.org/10.1007/BF01055700
  7. H. Cajar, Billingsley dimension in probability spaces, Lecture notes in mathematics, vol. 892, Springer, New York, 1981.
  8. J. Cole, Relative multifractal analysis, Choas Solitons and Fractals 11 (2000), no. 14, 2233-2250. https://doi.org/10.1016/S0960-0779(99)00143-5
  9. M. Das, Local properties of self-similar measures, Illinois J. Math. 42 (1998), no. 2, 313-332.
  10. J. Levy Vehel and R. Vojak, Multifractal analysis of Choquet capacities, Adv. in Appl. Math. 20 (1998), no. 1, 1-43. https://doi.org/10.1006/aama.1996.0517
  11. B. Mandelbrot, Les Objects fractales: forme, hasard et dimension, Flammarion, 1975.
  12. B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman, 1982.
  13. L. Olsen, A multifractal formalism, Adv. Math. 116 (1995), no. 1, 82-196. https://doi.org/10.1006/aima.1995.1066
  14. R. Riedi and I. Scheuring, Conditional and relative multifractal spectra, Fractals 5 (1997), no. 1, 153-168.
  15. S. Wen and M. Wu, Relations between packing premeasure and measure on metric space, Acta Math. Sci. 27 (2007), no. 1, 137-144. https://doi.org/10.1016/S0252-9602(07)60012-5