| 超整函数族Julia集的Hausdorff维数 |
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| 引用本文： | 杨存基. 超整函数族Julia集的Hausdorff维数[J]. 数学学报, 2010, 53(1): 187-198 |
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| 作者姓名： | 杨存基 |
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| 作者单位： | 大理学院数学与计算机学院; |
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| 基金项目： | 国家自然科学基金资助项目(10801134) |
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| 摘 要： | Stallard曾经用一族特殊的整函数说明了:超越整函数的Julia集的Hausdorff维数可以无限接近1.本文证明了该函数族的随机迭代的Julia集的Hausdorff维数也可无限接近于1.另一方面,对任意自然数M及任意实数d∈(1,2),本文给出了M个元素的整函数族其随机迭代的Julia集的Hausdorff维数等于d.
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| 关 键 词： | 函数族 随机迭代 Julia集 Hausdorf维数 |
| 收稿时间： | 2008-03-18 |
Hausdorff Dimensions of Julia Sets of Families of Transcendental Entire Functions |
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| Cun Ji YANG School of Mathematical , Computer,Dali University,Dali ,P.R.China. Hausdorff Dimensions of Julia Sets of Families of Transcendental Entire Functions[J]. Acta Mathematica Sinica, 2010, 53(1): 187-198 |
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| Authors: | Cun Ji YANG School of Mathematical Computer Dali University Dali P.R.China |
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| Affiliation: | School of Mathematical and Computer, Dali University, Dali 671003, P. R. China |
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| Abstract: | By a family of transcendental entire functions, Stallard shows that the Hausdorff dimensions of Julia sets of those functions have greatest lower bound equal to one.We prove that the Hausdorff dimensions of Julia sets of two families of transcendental entire functions have greatest lower bound equal to one. On the other hand, for any d∈(1, 2), we prove that there exists a family of transcendental entire functions with Hausdorff dimension equal to d. |
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| Keywords: | family of functions random dynamical system Julia sets Hausdorf dimension |
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