Singularities and Limit Functions in Iteration of Meromorphic Functions

Let f(z) be a transcendental meromorphic function. The paperinvestigates, using the hyperbolic metric, the relation betweenthe forward orbit P(f) of singularities of f^–1 and limitfunctions of iterations of f in its Fatou components. It ismainly proved, among other things, that for a wandering domainU, all the limit functions of {fⁿ|_U} lie in the derived setof P(f) and that if f^np|_V q(n +) for a Fatou component V, theneither q is in the derived set of S_p (f) or f^p(q) = q. As applicationsof main theorems, some sufficient conditions of the non-existenceof wandering domains and Baker domains are given.