On multiply-connected Fatou components in iteration of meromorphic functions

摘要

Let f : C -> (C) over cap to be a transcendental meromorphic function with at most finitely many poles. We mainly investigated the existence of the Baker wandering domains of f (z) and proved, among others, that if f (z) has a Baker wandering domain U, then for all sufficiently large n, f(n)(U) contains a round annulus whose module tends to infinity as n -> infinity and so for some 0 < d < 1, M-c(r,a,f)(d) <= m(c)(r,a,f), r is an element of G, where G is a set of positive numbers with infinite logarithmic measure. Therefore, we give out several criterion conditions for non-existence of the Baker wandering domains. (c) 2005 Elsevier Inc. All rights reserved.