Rippon, P. J. and Stallard, G. M.
(2008).
On multiply connected wandering domains of meromorphic functions.
*Journal of the London Mathematical Society*, 77(2) pp. 405–423.

## Abstract

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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