On multiply-connected Fatou components in iteration of meromorphic functions

Let f :C →Cˆ 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→∞and so for some 0