LIMITING DIRECTION AND BAKER WANDERING DOMAIN OF ENTIRE SOLUTIONS OF DIFFERENTIAL EQUATIONS

doi:10.1016/S0252-9602(16)30072-8

数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (5): 1331-1342.doi: 10.1016/S0252-9602(16)30072-8

LIMITING DIRECTION AND BAKER WANDERING DOMAIN OF ENTIRE SOLUTIONS OF DIFFERENTIAL EQUATIONS

王珺¹, 陈宗煊²

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:2015-06-08 出版日期:2016-10-25 发布日期:2016-10-25
通讯作者: Zongxuan CHEN,majwang@fudan.edu.cn E-mail:majwang@fudan.edu.cn
作者简介:Jun WANG,majwang@fudan.edu.cn
基金资助:
The work was supported by Shanghai Center for Mathematical Science China Scholarship Council (201206105015), the National Science Foundation of China (11171119, 11001057, 11571049) and the Natural Science Foundation of Guangdong Province in China (2014A030313422).

LIMITING DIRECTION AND BAKER WANDERING DOMAIN OF ENTIRE SOLUTIONS OF DIFFERENTIAL EQUATIONS

Jun WANG¹, Zongxuan CHEN²

1. School of Mathematical Sciences, Fudan University, Shanghai 200433, China;
2. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China

Received:2015-06-08 Online:2016-10-25 Published:2016-10-25
Contact: Zongxuan CHEN,majwang@fudan.edu.cn E-mail:majwang@fudan.edu.cn
Supported by:
The work was supported by Shanghai Center for Mathematical Science China Scholarship Council (201206105015), the National Science Foundation of China (11171119, 11001057, 11571049) and the Natural Science Foundation of Guangdong Province in China (2014A030313422).

摘要/Abstract

摘要：

In this paper, we mainly investigate entire solutions of complex differential equations with coefficients involving exponential functions, and obtain the dynamical properties of the solutions, their derivatives and primitives. With some conditions on coefficients, for the solutions, their derivatives and their primitives, we consider the common limiting directions of Julia set and the existence of Baker wandering domain.

关键词: limiting direction, Baker wandering domain, entire function, linear differential equation

Abstract:

Key words: limiting direction, Baker wandering domain, entire function, linear differential equation

中图分类号:

34M10

王珺, 陈宗煊. LIMITING DIRECTION AND BAKER WANDERING DOMAIN OF ENTIRE SOLUTIONS OF DIFFERENTIAL EQUATIONS[J]. 数学物理学报(英文版), 2016, 36(5): 1331-1342.

Jun WANG, Zongxuan CHEN. LIMITING DIRECTION AND BAKER WANDERING DOMAIN OF ENTIRE SOLUTIONS OF DIFFERENTIAL EQUATIONS[J]. Acta mathematica scientia,Series B, 2016, 36(5): 1331-1342.

参考文献

[1] Abramowitz M, Stegun I A. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. National Bureau of Standards Applied Mathematics Series 55, Washington, 1964
[2] Baker I N. Sets of non-normality in iteration theory. J London Math Soc, 1965, 40:499-502
[3] Baker I N. The domains of normality of an entire function. Ann Acad Sci Fenn Ser A I Math, 1975, 1:277-283
[4] Baker I N. An entire function which has wandering domains. J Aust Math Soc Ser A, 1976, 22:173-176
[5] Baker I N. Wandering domian in the iteration of entire functions. Proc Lond Math Soc, 1984, 49(3):563-576
[6] Bellman R. Stability Theory of Differential Equations. New Yok:McGraw-Hill Press, 1953
[7] Bergweiler W. Iteration of meromorphic functions. Bull Amer Math Soc, 1993, 29:151-188
[8] Chen Z X, Yang C C. Some further results on the zeros and growthes of entire solutions of second order linear differential equations. Kodai Math J, 1999, 22(2):273-285
[9] Glldberg A A, Ostrovskii I V. Value Distribution of Meromorphic Functions. Translations of Mathematical Monographs 236. Amer Math Soc, 2008
[10] Gundersen G. Estimates for the logarithmic derivative of a meromorphic function, plus similar estimates. J Lond Math Soc, 1988, 37(2):88-104
[11] Hayman W K. Meromorphic Functions. Oxford:Clarendon Press, 1964
[12] Huang Z G, Wang J. On the radial distribution of Julia sets of entire solutions of f^(k)+A^(z)f=0. J Math Anal Appl, 2012, 387:1106-1113
[13] Huang Z G, Wang J. Fatou sets of entire solutions of linear differential equations. J Math Anal Appl, 2014, 409:275-281
[14] Huang Z G, Wang J. On limit directions of Julia sets of entire solutions of linear differential equations. J Math Anal Appl, 2014, 409:478-484
[15] Laine I. Nevanlinna Theory and Complex Differential Equations. Berlin:Walter de Gruyter, 1993
[16] Markushevich A I. Theory of Functions of a Complex Variable, Vol Ⅱ. rev. ed. Englewood Cliffs:PrenticeHall, 1965
[17] Polyanin A D, Zaitsev V F. Handbook of Exact Solutions for Ordinary Differential Equations. 2nd ed. Boca Raton:Chapman and Hall/CRC Press, 2003
[18] Qiao J Y. Stable domains in the iteration of entire functions (in Chinese). Acta Math Sinica, 1994, 37:702-708
[19] Qiao J Y. On limiting directions of Julia sets. Ann Acad Sci Fenn Math, 2001, 26:391-399
[20] Qiu L, Wu S J. Radial distributions of Julia sets of meromorphic functions. J Austral Math Soc, 2006, 81(3):363-368
[21] Xiao L P, Chen Z X. On a problem in complex oscillation theory of periodic higher order linear differential equations. Acta Math Sci, 2010, 30B(4):1291-1300
[22] Yang L. Value Distribution Theory. Berlin:Springer-Verlag Press, 1993
[23] Zheng J H, Wang S, Huang Z G. Some properties of Fatou and Julia sets of transcendental meromorphic functions. Bull Austral Math Soc, 2002, 66:1-8
[24] Zheng J H. On uniformly boundary of stable domians in iteration of meromorphic functions Ⅱ. Math Proc Cambridge Phil Soc, 2002, 132:531-544
[25] Zheng J H. On the multiply connected Fatou components in iteration of meromorphic functions. J Math Anal Appl, 2006, 313:24-37
[26] Zheng J H. Value Dictribution of Meromorphic Functions. TUP-Springer Project, Beijing:Tsinghua University Press and Springer Press, 2010
[27] Zheng J H. Dynamics of Transcendental Meromorphic Functions (in Chinese). Monograph of Tsinghua University. Beijing:Tsinghua University Press, 2006

LIMITING DIRECTION AND BAKER WANDERING DOMAIN OF ENTIRE SOLUTIONS OF DIFFERENTIAL EQUATIONS

LIMITING DIRECTION AND BAKER WANDERING DOMAIN OF ENTIRE SOLUTIONS OF DIFFERENTIAL EQUATIONS

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