Rippon, P. J. and Stallard, G. M.
On multiply connected wandering domains of meromorphic functions.
Journal of the London Mathematical Society, 77(2) pp. 405–423.
We describe conditions under which a multiply connected wandering domain of a transcendental meromorphic function with a finite number of poles must be a Baker wandering domain, and we discuss the possible eventual connectivity of Fatou components of transcendental meromorphic functions. We also show that if f is meromorphic, U is a bounded component of F(f) and V is the component of F(f) such that F(U) is contained in V, then f maps each component of the boundary of U onto a component of the boundary of V in C^. We give examples which show that our results are sharp; for example, we prove that a multiply connected wandering domain can map to a simply connected wandering domain, and vice versa.
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