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.
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.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2010年第1期187-198,共12页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金资助项目(10801134)
