复动力学性质在复微分方程理论中的应用研究

Complex differential equations and complex dynamics are important research contents in complex analysis, this project is a combination of both the fields. By introduction the dynamical properties to the coefficients of a complex differential equations, which related to Br ü ck conjecture, we consider to study the growth of this equation. Thus, we provide a new way to solve the Br ü ck conjecture. In addition, for the entire solutions and their derivatives of a class of linear differential equations, we consider the radial distribution of the Julia sets, the multiple connectivity of the components of the Fatou sets and other dynamical properties of them. This topic put forward and solve, will help to deepen complex differential equations and complex dynamics connections.

复微分方程与复动力系统都是复分析中的重要研究内容，本项目研究的是两者相结合的领域。拟考虑对和Brück猜想相关的线性复微分方程的系数引入动力学性质，来研究此方程解的增长性问题，从而为Brück猜想的解决提供一种新的思路。另外，还考虑一类线性复微分方程的解及其导数的Julia集的径向分布，Fatou集的多连通性等动力学性质。本课题的提出与解决，将有助于深化复微分方程与复动力系统的联系。

复微分方程与复动力系统都是复分析中的重要研究内容，本项目研究的是两者相结合的领域。我们主要研究了几类复微分方程解的动力学性质，包括解的Julia集的径向分布，解的导数的Julia集的径向分布，解的牛顿迭代法的Julia集的径向分布等等，找到了这些径向分布的下界。本课题的完成，将有助于深化复微分方程与复动力系统的联系。