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Uniform perfectness of the attractor of bi-Lipschitz IFS 被引量：3

Uniform perfectness of the attractor of bi-Lipschitz IFS
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摘要 In this paper, we prove that the attractor of C1,a bi-Lipschitz IFS in R is uniformly perfect if it is not a singleton. Then we construct an example to show that this does not hold for C1 bi-Lipschitz IFS in Rn. In this paper, we prove that the attractor of C1, α bi-Lipschitz IFS in R is uniformly perfect if it is not a singleton. Then we construct an example to show that this does not hold for C1 bi-Lipschitz IFS in Rn.
作者 RUAN Huojun SUN Yeshun YIN Yongcheng
机构地区 Department of Mathematics
出处 《Science China Mathematics》 SCIE 2006年第4期433-438,共6页 中国科学：数学（英文版）
基金 supported by the National Natural Science Foundation of China(Grant Nos.10171090,10231040&10301027).
关键词 UNIFORM perfectness ITERATED FUNCTION systems. uniform perfectness, iterated function systems.
分类号 N [自然科学总论]
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参考文献8

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同被引文献14

  • 1WU Min.The multifractal spectrum of some Moran measures[J].Science China Mathematics,2005,48(8):1097-1112. 被引量：5
  • 2Min Wu.The multifractal spectrum of some moran measures[J]. Science in China Series A: Mathematics . 2005 (8)
  • 3Zhi-Ying Wen,Li-Feng Xi.Relations among whitney sets, self-similar arcs and quasi-arcs[J]. Israel Journal of Mathematics . 2003 (1)
  • 4Falconer K J,Marsh D T.Classification of quasi-circles by Hausdorff dimension. Nonlinearity . 1989
  • 5Cooper D,Pignataro T.On the shape of Cantor sets. J Diff Geom . 1988
  • 6Rao H,Ruan H J,Xi L F.Lipschitz equivalence of self-similar sets. C R Acad Sci Paris Ser I Math (Comptes Rendus Mathematique) . 2006
  • 7Hall P,,Heyde C C.Martingale Limit Theory and Its Application. . 1980
  • 8Falconer K J,Marsh D T.On the Lipschitz equivalence of Cantor sets. Mathematika . 1992
  • 9Rao H,Wen Z Y.A class of self-similar fractals with overlap structure. Adv in Appl Math . 1998
  • 10Petersen K.Ergodic Theory. . 1983

引证文献3

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Science China Mathematics
2006年 第4期

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