03-11   Berichtsreihe des Mathematischen Seminars der Universität Kiel

Walter Bergweiler, Alexandre Eremenko:

Meromorphic functions with two completely invariant domains

Dedicated to the memory of Professor I.N.Baker

We show that if a meromorphic function has two completely invariant Fatou components and only finitely many critical and asymptotic values, then its Julia set is a Jordan curve. However, even if both domains are attracting basins, the Julia set need not be a quasicircle. We also show that all critical and asymptotic values are contained in the two completely invariant components. This need not be the case for functions with infinitely many critical and asymptotic values.

Electronic Print: Front for the Mathematics ArXiv

Mathematics Subject Classification (1991): 30D05; 30D30

Mail an Jens Burmeister
[Thu Feb 19 18:56:36 2009]