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山东大学学报(理学版) ›› 2016, Vol. 51 ›› Issue (2): 85-88.doi: 10.6040/j.issn.1671-9352.0.2015.188

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复微分方程解的导数的Julia集的径向分布

张国威   

  1. 安阳师范学院数学与统计学院, 河南 安阳 455000
  • 收稿日期:2015-04-22 出版日期:2016-02-16 发布日期:2016-03-11
  • 作者简介:张国威(1981— ), 男, 博士, 讲师, 研究方向为复分析. E-mail:herrzgw@foxmail.com
  • 基金资助:
    国家自然科学基金资助项目(11426035);河南省高等学校重点科研项目(15A110008)

Radial distribution of Julia sets of derivatives of solutions to complex differential equations

ZHANG Guo-wei   

  1. School of Mathematics and Statistics, Anyang Normal University, Anyang, 455000, Henan, China
  • Received:2015-04-22 Online:2016-02-16 Published:2016-03-11

摘要: 进一步研究了一些复微分方程的整函数解的导数的Julia集的径向分布, 证明了它的径向分布的集合中含有区间并找到了区间长度的下界。

关键词: 导数, 径向分布, 复微分方程, Julia集

Abstract: The radial distributions of Julia sets of derivatives of entire solutions to some complex differential equations are studied. We obtain their radial distributions include intervals, of which lower bound also can be found.

Key words: derivative, complex differential equation, radial distribution, Julia set

中图分类号: 

  • O174.52
[1] GOLDBERG A A, OSTROVSKII I V. Value distribution of meromorphic function, Translations of Mathematical Monographs series[M]. Providence: American Mathematical Society, 2008, vol 236.
[2] LAINE I. Nevanlinna theory and complex differential equations[M]. Berlin: Walter de Gruyter, 1993.
[3] 仪洪勋,杨重骏. 亚纯函数唯一性理论[M]. 北京:科学出版社,2003. YI Hongxun, YANG Chunchung. Uniqueness theory of meromorphic functions[M]. Beijing: Science Press, 2003.
[4] BERGWEILER W. Iteration of meromorphic functions[J]. Bulletin of the American Mathematical Society(N S), 1993, 29:151-188.
[5] 郑建华. 亚纯函数动力系统[M]. 北京: 清华大学出版社,2006. ZHENG Jianhua. Dynamics of meromorphic functions[M]. Beijing: Tsinghua University Press, 2006.
[6] ZHENG Jianhua, WANG Sheng, HUANG Zhigang. Some properties of Fatou and Julia sets of transcendental meromorphic functions[J]. Bulletin of the Australian Mathematical Society, 2002, 66:1-8.
[7] BAKER I N. Sets of non-normality in iteration theory[J]. Journal of the London Mathematical Society, 1965, 40:499-502.
[8] 乔建永. 整函数迭代的稳定集[J]. 数学学报, 1994, 37(5):702-708. QIAO Jianyong. Stable domains in the iteration of entire functions[J]. Acta Mathematica Sinica, Chinese Series, 1994, 37(5):702-708.
[9] QIAO Jianyong. On limiting directions of Julia set[J]. Annales Academiæ Scientiarum Fennicæ Mathematica, 2001, 26:391-399.
[10] QIU Ling, WU Shengjian. Radial distributions of Julia sets of meromorphic functions[J]. Journal of the Australian Mathematical Society, 2006, 81(3):363-368.
[11] WANG Sheng. On radial distributions of Julia sets of meromorphic functions[J]. Taiwanese Journal of Mathematics, 2007, 11(5):1301-1313.
[12] HUANG Zhigang, WANG Jun. On the radial distribution of Julia sets of entire solutions of f (n)+A(z)f=0[J]. Journal of Mathematical Analysis and Applications, 2012, 387:1106-1113.
[13] HUANG Zhigang, WANG Jun. On limit directions of Julia sets of entire solutions of linear differential equations[J]. Journal of Mathematical Analysis and Applications, 2014, 409:478-484.
[14] 张国威,丁杰,杨连中. 复线性微分方程解的导数的Julia集的径向分布[J]. 中国科学:A辑 数学,2014, 4(6):693-700. ZHANG Guowei, DING Jie, YANG Lianzhong. Radial distribution of Julia sets of derivatives of solutions of complex linear differential equations[J]. Scientia Sinica Mathematica: Series A Mathematica, 2014, 44(6):693-700.
[15] MISIUREWICZ M. On iterates of ez[J]. Ergodic Theory Dynamical Systems, 1981, 1:103-106.
[16] BAKER I N. The domains of normality of an entire function[J]. Annales Academiæ Scientiarum Fennicæ Series A I Mathematica, 1975, 1:277-283.
[17] WANG Shupei. On the sectorial oscillation theory of f ″+Af=0[J]. Annales Academiæ Scientiarum Fennicæ Series A I Mathematica Dissertationes, 1994, 92:293-312.
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