06-5   Berichtsreihe des Mathematischen Seminars der Universität Kiel

Walter Bergweiler, Alexandre Eremenko:

Direct singularities and completely invariant domains of entire functions

Let f be a transcendental entire function and let a be a complex number. Suppose that a is a critical value of f or that the inverse function of f has a direct singularity over a. We show that if D is a simply connected domain which does not contain a, then the full preimage of D is disconnected. Conversely, we show that if a is not a critical value and if the inverse function of f does not have a direct singularity over a, then there exists a simply connected domain not containing a whose full preimage is connected.

Electronic Print:Front for the Mathematics ArXiv

Mathematics Subject Classification (1991): 30D20

Mail an Jens Burmeister
[Thu Feb 19 18:56:37 2009]