| 超越整函数半群的Julia集的连通性 |
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| 引用本文： | 黄志刚.超越整函数半群的Julia集的连通性[J].清华大学学报(自然科学版),2004,44(3):366-368. |
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| 作者姓名： | 黄志刚 |
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| 作者单位： | 清华大学,数学科学系,北京,100084;苏州科技大学,应用数学系,苏州,215009 |
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| 摘 要： | 考察了由一族超越整函数生成的半群的的动力学性质,其中半群运算是函数的复合。运用Fatou-Julia理论,研究了上述定义的半群的Julia集的连通性,得到上述定义的半群的Julia集在复平面内为连通的几个条件。同时,还给出了上述定义半群的Julia集并上无穷点在Riemann球面内为连通的两个条件。
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| 关 键 词： | 复动力系统 半群 超越整函数 连通性 Julia集 |
| 文章编号： | 1000-0054(2004)03-0366-03 |
| 修稿时间： | 2003年1月13日 |
Connectivity of Julia sets of transcendental semigroups |
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| HUANG Zhigang.Connectivity of Julia sets of transcendental semigroups[J].Journal of Tsinghua University(Science and Technology),2004,44(3):366-368. |
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| Authors: | HUANG Zhigang |
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| Abstract: | This paper analyzes the dynamic properties of semigroups generated by a family of transcendental entire functions with the semigroup operation being functional composition. Fatou-Julia theory was used to investigate the connectivity of the Julia set of these semigroups as a subset of the complex plane. Conditions were defined to connect the Julia set of the semigroup. After adding a point representing infinity to the Julia set, two sufficient conditions were specified for the Julia set to be connected as a subset of a Riemann sphere. |
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| Keywords: | complex dynamics semigroup transcendental entire function connectivity Julia set |
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