ON THE SINGULARITIES OF COMPOSITION OF ENTIRE FUNCTIONS

Let f be an entire function. A point zo is called a critical point of f if f’(zo) = 0, 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 lim t→1 FFFFFFF(t) = ∞ and lim t→1(f o Г)(t) = a. In this paper we find relations between the asymptotic values of f, g and fog, relations between critical points of f, g and f o g and also in the case when the two functions f and g are semi-conjugated with another entire function.