Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

프랙탈과 다중프랙탈의 연구

  • 백인수 (부산외국어대학교 수학과)
  • Published : 2006.07.01
Download PDF
⟨ Previous Next ⟩

Abstract

자연현상의 복잡한 대상의 연구에서 출발한 프랙탈의 연구는 물리학에서 특히 열역학에서의 기법을 활용한 다중프랙탈의 연구로까지 그 영역이 확대되었다. 이 논문에서는 프랙탈과 다중프랙탈의 여러 가지 성질과 그 응용에 대한 최근 결과를 소개한다

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, preprint
  3. R. Cawley and R. D. Mauldin, Multifractal decomposition of Moran fractals, Adv. Math. 92 (1992), 196-236 https://doi.org/10.1016/0001-8708(92)90064-R
  4. G. A. Edgar, Measure, Topology and Fractal Geometry, Springer Verlag, 1990
  5. K. J. Falconer, The geometry of fractal sets, Cambridge University Press, 1985
  6. K. J. Falconer, Fractal Geometry, John Wiley and Sons, 1990
  7. K. J. Falconer, Techniques in fractal geometry, John Wiley and Sons, 1997
  8. F. Hausdorff, Dimension und ausress, Mass. Math. Ann. 79 (1919), 157-179
  9. G. Julia, Sur l'iteratioti des fonctions rationnelles, J. Math. Pure Appl. 7 (1918), no. 4, 47-245
  10. B. B. Mandelbrot, Les Object Fractals: Forme, Hasard et Dimension, Flammarion, 1975
  11. B. B. Mandelbrot, The fractal geometry of Nature, W. H. Freeman and Company, 1982
  12. P. M. Mattila, The geometry of sets and measures in Euclidean spaces, Cambridge University Press, 1995
  13. S. Ngai and Y. Wang, Hausdorff dimension of self-similar sets with overlaps, J. London Math. Soc. 63 (2001), no. 2, 655-672 https://doi.org/10.1017/S0024610701001946
  14. 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
  15. D. Rand, The singularity spectrum f(a) for cookie-cutters, Ergodic Th. Dynam. Sys. 9 (1989), 527-541
  16. C. A. Rogers, Dimension prints, Mathematika 35 (1988), 1-27 https://doi.org/10.1112/S0025579300006239
  17. X. Sun, H. Chen, Z. Wu, and Y. Yuan, Multifractal analysis of Hang Seng index in Hong Kong stock market, Physica A, Statistical mechanics and its applications 291 (2001), no. 1, 553-562 https://doi.org/10.1016/S0378-4371(00)00606-3
  18. C. Tricot, Two definitions of fractional dimension, Math. Proc. Cambridge Philo. Soc. 91 (1982), 54-74