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Journal of the London Mathematical Society Advance Access originally published online on February 20, 2008
Journal of the London Mathematical Society 2008 77(2):405-423; doi:10.1112/jlms/jdm118
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© 2008 London Mathematical Society

On multiply connected wandering domains of meromorphic functions

P. J. Rippon and G. M. Stallard

Department of Mathematics
The Open University
Walton Hall
Milton Keynes
MK7 6AA
United Kingdom
g.m.stallard@open.ac.uk

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)subV, then f maps each component of {partial} U onto a component of the boundary of V in Formula. 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.

2000 Mathematics Subject Classification 30D05, 37F10.

Received July 20, 2006; revised October 2, 2007; published online February 20, 2008.


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