弱分离条件下的自共形迭代函数系统

武志容, 叶远灵

数学学报 ›› 2011, Vol. 54 ›› Issue (6) : 881-892.

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中国科学院数学与系统科学研究院期刊网
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数学学报 ›› 2011, Vol. 54 ›› Issue (6) : 881-892. DOI: 10.12386/A2011sxxb0089
论文

弱分离条件下的自共形迭代函数系统

    武志容, 叶远灵
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Self-Conformal IFS with the WSC

    Zhi Rong WU, Yuan Ling YE
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文章历史 +

摘要

开集条件是分形几何的一个重要概念, 弱分离条件 (WSC) 在研究有重叠的迭代函数系统(IFS)中扮演着重要角色. 本文考虑满足弱分离条件的自共形迭代函数系统,并给出确定其不变集的Hausdorff维数的一种方式.  

Abstract

The open set condition is an important concept in fractal geometry. And, the weak separation condition (WSC) plays an important role in the study of iterated function systems (IFS) with overlaps. In this paper, we consider self-conformal IFS satisfying the WSC, and we present a way to determine the Hausdorff dimension of the invariant set relevant.  

关键词

自共形迭代函数系统 / 开集条件 / 弱分离条件 / Hausdorff维数

Key words

self-conformal IFS / open set condition / weak separation condition / Hausdorff dimension

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武志容, 叶远灵. 弱分离条件下的自共形迭代函数系统. 数学学报, 2011, 54(6): 881-892 https://doi.org/10.12386/A2011sxxb0089
Zhi Rong WU, Yuan Ling YE. Self-Conformal IFS with the WSC. Acta Mathematica Sinica, Chinese Series, 2011, 54(6): 881-892 https://doi.org/10.12386/A2011sxxb0089

参考文献

[1] Hutchinson J. E., Fractals and self-similarity, Indiana Univ. Math. J., 1981, 30: 713-747.

[2] Fan A. H., Lau K. S., Iterated function system and Ruelle operator, J. Math. Anal. Appl., 1999, 231: 319-344.

[3] Lau K. S., Ngai S. M., Multifractal measures and a weak Separation condition, Adv. Math., 1999, 141: 45-96.

[4] Ye Y. L., Multifractal of self-conformal measures, Nonlinearity, 2005, 18: 2111-2133.

[5] Lau K. S., Ngai S. M., Wang X. Y., Separation conditions for conformal iterated function systems, Monatshefte Für Mathematik, 2009, 156: 325-355.

[6] Falconer K., Sub-self-similar sets, Trans. Amer. Math. Soc., 1995, 347: 3121-3129.

[7] Chen E. C., Xiong J. C., Hausdorff dimension of sub-self-similar sets, Journal of University of Science and Technology of China, 2004, 34: 535-542.

[8] Mcclure M., Vallin R. W., The Borel structure of the collections of sub-self-similar sets and super-self-similar sets, Acta Math. Univ. Comenianae, 2000, 69: 145-149.

[9] Liu H., Hausdorff Dimension of Sub-Self-Conformal Sets, Guangzhou: Master Degree Thesis of South China Normal University, 2006.

[10] Wu Z. R., Contractive Conformal Iterated Function System and Weak Separation Condition, Guangzhou: Master Degree Thesis of South China Normal University, 2008.

[11] Ye Y. L., Separation properties for self-conformal sets, Studia Math., 2002, 152: 33-44.

[12] Zerner M. P. W., Weak separation properties for self-similar sets, Proc. Amer. Math. Soc., 1996, 124: 3529-3539.

[13] Falconer K., Dimensions and measures of quasi self-similar sets, Proc. Amer. Math. Soc., 1989, 106: 543-554.
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