Let f(z) be a transcendental meromorphic functions. 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|U} lie in the derived set of P(f) and that if f~(np)|V → q(n → +∞) 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.
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