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统计自相似集的重分形分解 被引量：3

Multifractal Decomposition of Statbtically Self-Similar Sets
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摘要 设K是由Graf定义的统计自相似集.本文构造了一支撑在K上的随机测 度p,并研究了结合P的K的重分形分解,得到了分形谱函数f(α)的表达式. Let K be statistical self-similar set defined by Graf. In this paper, we construct a random measure p which is supported by K, and study the multifractal decomposition for K with ρ. Under such a decomposition, we obtain the expression of the spectrum function f(α).
作者 余旌胡 胡迪鹤
机构地区 中国科学院武汉物理与数学研究所 武汉大学数学与统计学院
出处 《数学学报（中文版）》 SCIE CSCD 北大核心 2003年第3期507-512,共6页 Acta Mathematica Sinica：Chinese Series
基金 国家自然科学基金资助项目(10671066)
关键词 统计自相似集 重分形分解 谱函数 Statistical self-similar sets Multifractal decomposition Spectrum function
分类号 O141.3 [理学—基础数学] O211.6 [理学—概率论与数理统计]
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参考文献6

  • 1Mandelbort B., Negative fractal dimension and multifractals, Physics A, 1990, 163: 306-315.
  • 2Cawley R., Mauldin R. D., Multifractal decomposition of Moran fractals, Adv.Math., 1992, 92: 196-236.
  • 3Falconer K. J., Random fractals, Math. Proc. Camb. Phil. Soc., 1987, 100: 559-582.
  • 4Mauldin R. D., Williams S. C., Random recursive constructions: asymptotic geometric and topological properties, Tran. Amer. Math. Soc., 1986, 295: 325-346.
  • 5Graf S., Statistically serf-similar fractal, Prob. Theor. Rel. Fields, 1987, 74: 357-392.
  • 6Falconer K. J., The multifractal spectrum of statistically self-similar measure, J. of Theor Prob., 1994, 7(3):681-702.

同被引文献13

  • 1Mandelbort B. Itermittent Turbulence in Self-similar Casades: Divergence of High Moments and Dimension of the Carrer. J. Fluid Mech., 1974, 62: 331-358.
  • 2Falconer K J. The Multifractal Spectrum of Statistically Self-similar Measure. J. of Theor. Prob,1994, 3: 618-702.
  • 3Arbeiter M and Patzschke N. Random Self-similar Multifractals. Math. Nachr., 1996, 181: 5-42.
  • 4Liang J R, Wang X T and Ren F Y. On Three Open Questions Proposed by Falconer. Progress innatural science, progress in natural science, 1999, 9(3): 180-188.
  • 5Graf S. Statistically Self-similar Fractal. Prob. Theor. Rel. Fields, 1987, 74:357-392.
  • 6Cawley R and Mauldin R D. Multifractal Decompositions of Moran Fractals. Adv. Math., 1992,92: 196-236.
  • 7Mauldin R D and Williams S C. Random Recursive Constructions: Asymptotic Geometric and Topological Properties. Tran. Amer. Math. Soc., 1986,295: 325-346.
  • 8Arbeiter M,Patzsehke N. Random self-similar multifraetals[J]. Math Naehr, 1996,181:5.
  • 9Mauldin R D,Williams S C. Random recursive constructions: asymptotic geometric and topological properties[J]. Tran Amer Math Soc, 1986,295 ( 1 ) : 325.
  • 10徐赐文.多型随机递归集关于统计自相似测度的Multifractal分解[J].数学年刊（A辑）,2000,1(1):109-122. 被引量：2

引证文献3

二级引证文献7

数学学报（中文版）
2003年 第3期

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