065  Berichtsreihe des Mathematischen Seminars der Universität Kiel  
Walter Bergweiler, Alexandre Eremenko:Direct singularities and completely invariant domains of entire functionsLet 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

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