复微分方程整函数解的Julia集的极限方向
On Limiting Directions of Julia Sets of Entire Solutions of Complex Differential Equations
夏欣 1张颖 2黄志刚1
作者信息
- 1. 苏州科技大学数学科学学院,江苏苏州 215009
- 2. 苏州科技大学信息建设与管理中心,江苏苏州 215009
- 折叠
摘要
假设是一个超越整函数.如果存在无界序列argz=θ∈[0,2π]使得lim rn→∞ arg zn=θ,称射线arg z=θ∈[0,2π]是f的Julia集的极限方向.本文主要研究复微分方程F(z)fn(z)+P(z,f)=0和fn+A(z)P(z,f)=h(z)整数解的Julia集的动力学性质,其中P(zf)是关于f及其导数的微分多项式,并且F(z)、A(z)和h(z)是整函数.我们证明了上述两个方程的系数的Petrenko偏差与整数解的极限方向的测度之间存在密切关系.
Abstract
Assume thatfis a transcendental entire function.The ray argz=θ∈[0,2π]is said to be a limiting direction of the Julia set J(f)of f if there exists an unbounded sequence{zn}⊆J(f)such that lim rn→∞ arg zn=θ.In this paper,we mainly investigate the dynamical proper-ties of Julia sets of entire solutions of the complex differential equations F(z)fn(z)+P(z,f)=0,and fn+A(z)P(z,f)=h(z),where P(z,f)is a differential polynomial in fand its derivatives,F(z),A(z)and h(z)are entire functions.We demonstrate the existence of close relationships Petrenko's deviations of the coefficients and the measures of limiting directions of entire solutions of the above two equations.
关键词
Julia集/极限方向/整函数/Petrenko偏差Key words
Julia set/limiting direction/entire function/Petrenko's deviation引用本文复制引用
基金项目
National Natural Science Foundation of China(11971344)
出版年
2024
NETL
NSTL
万方数据