Julia Limiting Directions of Entire Solutions of Complex Differential Equations
Julia Limiting Directions of Entire Solutions of Complex Differential Equations
复制标题
复微分方程全解的Julia极限方向
DOI：
10.1007/s10473-021-0415-7
复制
发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Chengchun Zhang
中科院分区：
文献类型：
--
作者：
Jun Wang;Xiao Yao;Chengchun Zhang
对于整函数或亚纯函数f，若在Julia集上存在一个无界序列{zn}满足arg zn = θ，则称θ ∈ [0，2 π）为Julia极限方向.本文的主要结果是关于P（z，f）+ F（z）fs = 0的整体解f，其中P（z，f）是f的微分多项式，其整体增长系数小于整体超越函数F的整体增长系数，整数s不超过P（z，f）中所有微分单项式的最小次数。我们观察到f的Julia极限方向部分来自于F快速增长的方向。
For entire or meromorphic function f, a value θ ∈ [0,2π) is called a Julia limiting direction if there is an unbounded sequence {z_n} in the Julia set satisfying arg z_n = θ. Our main result is on the entire solution f of P(z, f) + F(z)f~s = 0,where P(z, f) is a differential polynomial of f with entire coefficients of growth smaller than that of the entire transcendental F, with the integer s being no more than the minimum degree of all differential monomials in P(z,f). We observe that Julia limiting directions of f partly come from the directions in which F grows quickly.