SINGULARITIES AND LIMIT FUNCTIONS IN ITERATION OF MEROMORPHIC FUNCTIONS

Let f(z) be a transcendental meromorphic function. The paper investigates, using the hyperbolic metric, the relation between the forward orbit P(f) of singularities of f^{-1} and limit functions of iterations of f in its Fatou components. It is mainly proved, among other things, that for a wandering domain U , all the limit functions of \{f^n\vert_U\} lie in the derived set of P(f) and that if f^{np}\vert_V\rightarrow q(n\rightarrow +\infty) for a Fatou component V , then either q is in the derived set of S_p(f) or f^p (q) = q . As applications of main theorems, some sufficient conditions of the non-existence of wandering domains and Baker domains are given.