Permutable functions concerning differential equations

Journal of the Australian Mathematical Society

X. Hua¹ 

[1] R. Vaillancourt

关键词: primary 30D05;    37F10;    37F50;    secondary 34A20;   

DOI  :  10.1017/S1446788700037988

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

Let f and g be two permutable transcendental entire functions. Assume that f is a solution of a linear differential equation with polynomial coefficients. We prove that, under some restrictions on the coefficients and the growth of f and g, there exist two non-constant rational functions R1 and R2 such that R1 (f) = R(g). As a corollary, we show that f and g have the same Julia set: J(f) = J(g). As an application, we study a function f which is a combination of exponential functions with polynomial coefficients. This research addresses an open question due to Baker.

【 授权许可】

Unknown