| 具有共形迭代函数系统有理函数Julia集的性质 |
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| 引用本文： | 庄伟.具有共形迭代函数系统有理函数Julia集的性质[J].数学杂志,2007,27(2):177-180. |
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| 作者姓名： | 庄伟 |
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| 作者单位： | 北京石油化工学院数理部,北京,102617 |
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| 摘 要： | 本文研究了几何有限有理函数的复解析动力性质.利用Markov划分与共形迭代函数系统的理论,获得了几何有限有理函数Julia集的性质.如有理函数是几何有限的,且Julia集是连通的,则Julia集的Hausdorff维数为1当且仅当Julia集为一圆周或直线的一段.
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| 关 键 词： | Julia集 Hausdorff维数 Markov划分 共形迭代函数系统 |
| 文章编号： | 0255-7797（2007）02-0177-04 |
| 修稿时间： | 2004-08-262005-06-30 |
THE PROPERTY OF THE JULIA SET OF RATIONAL FUNCTIONS WITH CONFORMAL ITERATED FUNCTION SYSTEM |
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| ZHUANG Wei.THE PROPERTY OF THE JULIA SET OF RATIONAL FUNCTIONS WITH CONFORMAL ITERATED FUNCTION SYSTEM[J].Journal of Mathematics,2007,27(2):177-180. |
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| Authors: | ZHUANG Wei |
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| Institution: | Dept. of Math. and Physics, Beijing Institute of Petrochemical Technology, Beijing 102617, China |
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| Abstract: | In this paper, we study the dynamics of the geometrically finite rational functions. By the theory of Markov partitions and the conformal iterated function system, we obtain the property of the Julia set of the geometrically finite rational functions. We prove that if the Julia set is connected, then the Hausdorff dimension of the Julia set equals 1 if and only if the Julia set is an arc of a circle or a straight line. |
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| Keywords: | Julia set Hausdorff dimension Markov partitions conformal iterated function system |
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