数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (1): 97-107.doi: 10.1016/S0252-9602(16)30118-7

• 论文 • 上一篇    下一篇

LIMITING DIRECTIONS OF JULIA SETS OF ENTIRE SOLUTIONS TO COMPLEX DIFFERENTIAL EQUATIONS

王珺1, 陈宗煊2   

  1. 1. School of Mathematical Sciences, Fudan University, Shanghai 200433, China;
    2. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
  • 收稿日期:2015-11-04 出版日期:2017-02-25 发布日期:2017-02-25
  • 通讯作者: Zongxuan CHEN,E-mail:chzx@vip.sina.com E-mail:chzx@vip.sina.com
  • 作者简介:Jun WANG,E-mail:majwang@fudan.edu.cn
  • 基金资助:

    The work was supported by Shanghai Center for Mathematical Sciences, China Scholarship Council (201206105015), National Science Foundation of China (11171119, 11001057, 11571049) and Natural Science Foundation of Guangdong Province in China (2014A030313422).

LIMITING DIRECTIONS OF JULIA SETS OF ENTIRE SOLUTIONS TO COMPLEX DIFFERENTIAL EQUATIONS

Jun WANG1, Zongxuan CHEN2   

  1. 1. School of Mathematical Sciences, Fudan University, Shanghai 200433, China;
    2. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
  • Received:2015-11-04 Online:2017-02-25 Published:2017-02-25
  • Contact: Zongxuan CHEN,E-mail:chzx@vip.sina.com E-mail:chzx@vip.sina.com
  • About author:Jun WANG,E-mail:majwang@fudan.edu.cn
  • Supported by:

    The work was supported by Shanghai Center for Mathematical Sciences, China Scholarship Council (201206105015), National Science Foundation of China (11171119, 11001057, 11571049) and Natural Science Foundation of Guangdong Province in China (2014A030313422).

摘要:

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.

关键词: limiting direction, Julia set, entire function, linear differential equation, deficiency

Abstract:

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.

Key words: limiting direction, Julia set, entire function, linear differential equation, deficiency