INVARIANT DOMAINS AND SINGULARITIES

Let U be an invariant component of the Fatou set of an entire transcen dental function f such that the iterates of f tend to infinity in U. L et P(f) be the closure of the set of the forward orbits of all critica l and asymptotic values of f. We show that there exists a sequence p(n ) is an element of P(f) such that (p(n), U) = o(\p(n)\), where dist(., .) denotes Euclidean distance. On the other hand, we give an example w here dist(P(f),U) > 0. In this example, U is bounded by a Jordan curve .