On multiply connected wandering domains of meromorphic functions

• Autores: Phillip J. Rippon, Gwyneth M. Stallard
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 77, Nº 2, 2008, págs. 405-423
• Idioma: inglés
• DOI: 10.1112/jlms/jdm118
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• Resumen

  • 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)V, then f maps each component of U onto a component of the boundary of V in . 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.