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有限义性质下一类广义MORAN集的重分形分解(英文)

MULTIFRACTAL DECOMPOSITION OF CERTAIN GENERALIZED MORAN SETS UNDER THE FINITE INTERSECTION PROPERTY
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摘要 本文在一类广义 Moran集上定义了一种弱分离条件——有限交性质 ,并证明了重分形分解在此广泛的一类分形上仍然成立 .本文部分的推广了 Cawley和 Manlain的结果 . We defined a weak separation condition,the finite intersection property,on generalized Moran fractals by allowing appropriate overlapping on the construction and proved that multifractal formalism still holds for a larger class of fractals by using code mapping technique ,which extends part of Cawley's tesults.
作者 郭红文
出处 《数学杂志》 CSCD 北大核心 2001年第3期271-275,共5页 Journal of Mathematics
基金 the Doctoral Education Foundation of China
关键词 MORAN集 有限交性质 重分形分解 弱分离条件 分形 Moransets the finite intersection property multifractal decomposition
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参考文献4

  • 1[1]R. Cawley and R. D. Mauldin,Multifractal decompositions of Moran fractals[J]. Adv. Math. ,1992, 92:192~236.
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  • 3[3]K. J. Falconer. "The Geometry of Fractal Sets", Cambridge Tracts in Mathematics[M]. No. 85, Cambridge Univ. Press, New York/London, 1985.
  • 4[4]A. Schief, Separation properties for self-similar sets[J]. Proc. Amer. Math. Soc. , 1994, 122..111~115.
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