Mathematics

CLC number: O174.5

On Limiting Directions of Julia Sets of Entire Solutions of Complex Differential Equations

复微分方程整函数解的Julia集的极限方向

¹ School of Mathematical Sciences, Suzhou University of Science and Technology, Suzhou 215009, Jiangsu, China
² Information Construction and Management Center, Suzhou University of Science and Technology, Suzhou 215009, Jiangsu, China

^† Corresponding author. E-mail: alexehuang@sina.com

Received: 15 July 2023

Abstract

Assume that is a transcendental entire function. The ray is said to be a limiting direction of the Julia set of if there exists an unbounded sequence such that . In this paper, we mainly investigate the dynamical properties of Julia sets of entire solutions of the complex differential equations and , where is a differential polynomial in and its derivatives, and 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.

摘要

假设是一个超越整函数。如果存在无界序列使得,称射线是的Julia集的极限方向。本文主要研究复微分方程和整数解的Julia集的动力学性质, 其中是关于及其导数的微分多项式,并且、和是整函数。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。