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)f(z) and proved, among others, that if f(z)f(z) has a Baker wandering domain U, then for all sufficiently large n  , fn(U)fn(U) contains a round annulus whose module tends to infinity as n→∞n→∞ and so for some 0