复微分方程整函数解的Julia集的极限方向

doi:10.6040/j.issn.1671-9352.0.2023.193

摘要/Abstract

摘要： 利用Phragmén-Lindelöf 指标函数以及完全正规增长整函数的性质研究微分方程f ⁽ⁿ⁾+P_n-1(z)f ^(n-1)+… +P0(z)f=0和f ″+A(z)f '+B(z)f=0整函数解的Julia集的极限方向,获得方程无穷级整函数解及其导数和原函数的公共Julia集的极限方向集测度的下界估计,其中n≥2, P_j(z)(j=1,2,…,n-1)是整函数, P0(z)、A(z)和B(z)为完全正规增长的整函数。

关键词: 复微分方程, Julia 集的极限方向, Phragmén-Lindelö, f 指标函数, 完全正规增长

Abstract: The Julia limiting directions of entire solutions of complex differential equations f ⁽ⁿ⁾+P_n-1(z)f ^(n-1)+… +P0(z)f=0 and f ″+A(z)f '+B(z)f=0 are studied by using Phragmén-Lindelöf indicator function and the properties of the completely regular growth functions, the lower bound of the measure of the set of common Julia limiting directions of the derivatives and primitives of infinite order entire solutions of the equations mentioned above is obtained, where n≥2, P_j(z)(j=1,2,…,n-1) are entire functions, P0(z), A(z) and B(z) are entire functions of completely regular growth.

Key words: complex differential equation, the limiting direction of Julia set, Phragmén-Lindelö, f indicator function, completely regular growth

中图分类号:

O174.52

向旭旭,刘建明,王钦,欧阳瑞琦. 复微分方程整函数解的Julia集的极限方向[J]. 《山东大学学报(理学版)》, 2024, 59(12): 73-78.

XIANG Xuxu, LIU Jianming, WANG Qin, OUYANG Ruiqi. Julia limiting directions of entire solutions of complex differential equations[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(12): 73-78.

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