On limit directions of Julia sets of entire solutions of linear differential equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:409

Article

Huang, Zhi-Gang¹  Wang, Jun² 

[1] Suzhou Univ Sci & Technol, Sch Math & Phys, Suzhou 215009, Peoples R China

[2] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

关键词: Limit direction;    Entire function;    Julia set;    Linear differential equation;   

DOI  :  10.1016/j.jmaa.2013.07.026

来源: Elsevier

【 摘 要 】

This paper is devoted to studying the limit directions of Julia sets of solutions of f((n)) + A(n-1)(z)f((n-1)) + center dot center dot center dot + A(0)(z)f = 0, where n (>= 2) is an integer and A(j)(z) (j = 0, 1, ... , n-1) are entire functions of finite lower order. With some additional conditions on coefficients, we know that every non-trivial solution f(z) of such equations has infinite lower order, and prove that the limit directions of Julia sets of f(z) must have a definite range of measure. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free