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随机递归结构的重分形分解 被引量:1

Multifractal Decompositions Of Random Recursive Constructions
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摘要 设μ为支撑于随机递归结构K上的无穷乘积测度,K(ω)≠φ。本文研究K关于测度μ的重分形分解,并讨论了谱维f(α)的性质。 Let K be a random fracal set resulting from random recursive constructions,μ be an infinite product random measure supppported on K. In this paper,we have disscussed the multifactal decomposition for K with measure μ, and disscussed the properties of dimension spectrum f(α).
作者 苏峰 赵兴球
出处 《应用概率统计》 CSCD 北大核心 1997年第2期113-119,共7页 Chinese Journal of Applied Probability and Statistics
基金 湖北省自然科学基金
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同被引文献7

  • 1Dryakhlov, A.V. and Tempelman, A.A., On Hausdorff dimension of random fractals, New York J. Math., 7(2001), 99-115.
  • 2Cawley, R. and Mauldin, R.D., Multifractal decompositions of Moran fractals, Adv. Math., 92(1992), 196-236.
  • 3Falconer, K.J., The multifractal spectrum of statistically self-similar measure, J. of Theor. Prob., 3(1994), 618-702.
  • 4Arbeiter, M. and Patzschke, N., Random self-similar multifractals, Math. Nachr., 181(1996), 5-42.
  • 5Edgar, G.A. and Mauldin, R.D., Multifractal decomposition of digraph recursive fractals, Proc. Lon- don Math. Soc., 65(3)(1992), 604-628.
  • 6Mauldin, R.D. and Williams, S.C., Random recursive constructions: asymptotic geometric and topo- logical properties, Trans. Amer. Math. Soc., 295(1986), 325-346.
  • 7TEMPELMAN, A.A., Dimension of random fractal in metric spaces, (Russian) Teor. Veroyatnost. i Primeen, 44(1999), 589-616; translation in Theory Probab. Appl., 44(2000), 537-557.

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