摘要
Let f be an entire function. A point Zo is called a critical point of f if f′（zo） = O, and f（zo） is called a critical value （or an algebraic singularity） of f. Next a ∈ C is said to be an asymptotic value （or a transcendental singularity） of f if there exists a curve Г ： [0, 1） → C such that limt→1 F（t） = ∞ and limt→1（f o Г）（t） = a. In this paper we find relations between the asymptotic values of f, 9 and f o 9, relations between critical points of f, 9 and f o 9 and also in the case when the two functions f and 9 are semi-conjugated with another entire function.
Let f be an entire function. A point Zo is called a critical point of f if f′（zo） = O, and f（zo） is called a critical value （or an algebraic singularity） of f. Next a ∈ C is said to be an asymptotic value （or a transcendental singularity） of f if there exists a curve Г ： [0, 1） → C such that limt→1 F（t） = ∞ and limt→1（f o Г）（t） = a. In this paper we find relations between the asymptotic values of f, 9 and f o 9, relations between critical points of f, 9 and f o 9 and also in the case when the two functions f and 9 are semi-conjugated with another entire function.
基金
This paper is a main talk on the <International Conference at Analysis in Theory and Applications>held in Nanjing, P. R. China, July, 2004.
