线性微分方程整函数解的Julia集的径向分布

研究了线性微分方程f⁽(n))+A_n-2f⁽(n-2))+…+A₀(z)f=0整函数解的Julia集的径向分布,其中n≥2,A_j(z)(j=0,1,…,n-2)是具有有限下级的整函数,得到了这类方程线性无关解的乘积的Julia集的径向分布的下界.     

线性微分方程亚纯解的Julia集的径向分布

本文研究了线性微分方程f(n)+An-1f(n-1)+···+A1f+A0f=0亚纯解的动力学性质,其中n≥2,Ai(z)(i=0,1,···,n-1)是具有有限下级的亚纯函数.利用亚纯函数的Nevanlinna值分布理论,获得了一定条件下方程亚纯解的Julia集的径向分布的下界,推广了相关文献的结果.     

复线性微分方程解的增长性的几个结果

本文研究了复线性微分方程解的增长性问题.利用两类具有某种渐进增长性质的函数作为线性微分方程的系数,讨论了两类二阶线性微分方程解的增长性,获得了方程解为无穷级.这些结果推广了先前的一些结果.     

整函数的值分布与Julia集

本文证明了一个较为广泛的值分布定理.用它可以直接改进若干用不同方法建立起来的复迭理论中的结果.     

Julia集的连续性 *

给出了k >1次有理函数空间的Julia集连续性的充分必要条件 .     

Julia集的生成

该文运用Hausdorff意义下的极限研究了有理动力系统的Julia集, 用新的思路证明了几个关于Julia集的定理. 为计算机作Julia集提供了更多的理论根据.     

一类无穷下级整函数的Julia集的径向分布

主要研究方程f"(z)+A(z)f'(z)+B(z)f(z)=0(A(z)),B(z)为整函数)的解、解的多项式或微分多项式这些具有无穷下级的整函数的Julia集的径向分布问题.     

有限个有理函数的随机复动力系统的Julia集

本文讨论有限个有理函数生成的随机复动力系统，得到Julia集有内点的充分条件和必要条件．证明了对任意的正数，可以构造有限个多项式，彼此的Julia集之间的距离大干L，但J(f1，…，fm)含有内点但不是全平面。     

Julia集的拓扑复杂性

研究有理函数及整函数Julia集的拓扑结构,刻画了有理函数Julia集的复杂性,展示了整函数在Fatou集上的动力学性质对其Julia集拓扑复杂性的影响.     

填充Julia集与Mandelbrot集的面积与直径

本文用单叶函数中的面积定理及Ｇａｒａｂｅｄｉａｎ－Ｓｃｈｉｆｆｅｒ不等式的有关推论，给出了求多项式的填充Ｊｕｌｉａ集及Ｍａｎｄｅｌｂｒｏｔ集面积的方法及直径的上界估计，从而给Ａ．Ｄｏｕａｄｙ所提的有关问题一个回答。     

Logarithmic derivatives of solutions to linear differential equations

Given an ordinary differential field of characteristic zero, it is known that if and satisfy linear differential equations with coefficients in , then is algebraic over . We present a new short proof of this fact using Gröbner basis techniques and give a direct method for finding a polynomial over that satisfies. Moreover, we provide explicit degree bounds and extend the result to fields with positive characteristic. Finally, we give an application of our method to a class of nonlinear differential equations.

     

Limiting directions of julia sets of entire solutions to complex differential equations

In this paper, we mainly investigate the dynamical properties of entire solutions of complex differential equations. With some conditions on coefficients, we prove that the set of common limiting directions of Julia sets of solutions, their derivatives and their primitives must have a definite range of measure.     

Oscillation of Solutions of Linear Differential Equations

This paper is devoted to studying the growth problem, the zeros and fixed points distribution of the solutions of linear differential equations f″＋e^-zf′＋Q（z）f=F（z）,whereQ（z）≡h（z）e^cz and c∈R.     

On subnormal solutions of second order linear periodic differential equations

In this paper, we investigate the existence and the form of subnormal solution for a class of second order periodic linear differential equations, estimate the growth properties of all solutions, and answer the question raised by Gundersen and Steinbart.     

Zero distribution of solutions of complex linear differential equations determines growth of coefficients

It is shown that the exponent of convergence λ(f) of any solution f of with entire coefficients A₀(z), …, A_k?2(z), satisfies λ(f) ? λ ∈ [1, ∞) if and only if the coefficients A₀(z), …, A_k?2(z) are polynomials such that for j = 0, …, k ? 2. In the unit disc analogue of this result certain intersections of weighted Bergman spaces take the role of polynomials. The key idea in the proofs is W. J. Kim’s 1969 representation of coefficients in terms of ratios of linearly independent solutions. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

有限迭代级整系数线性微分方程解的性质

研究了有限迭代级整系数的复线性微分方程,应用Nevalinna和Ahlfors的角域理论,得到了有关解的迭代级,零点迭代收敛指数以及角域中的零点分布的结果．     

Continuity of Julia sets

A sufficient and necessary condition is given for the continuity of Julia sets in the space of all rational maps with degreek>1. Project supported by the National Natural Science Foundation of China (Grant No. 19871002).     

一类二阶非齐次线性微分方程解的复振荡

研究了一类二阶非齐次线性微分方程f″+Ae~(az~n)f′+(B_1e~(bz~n)+B_0e~(dz~n))f=F(z)解的增长性和零点分布,其中F为级小于n的非零整函数,A,B1,B0为非零多项式.在复数a,b,d满足一定条件下,得到该方程的每一个解的超级和二级零点收敛指数的精确估计.