Title:Dynamics of exponential maps

Author:Lasse Rempe

URN:NBN:urn:nbn:de:gbv:8-diss-7816

Faculty:Faculty of Mathematics and Natural Sciences
DDC:510 Mathematics

Date of thesis defense:2003-07-08

Referent:Prof. Dr. Walter Bergweiler
second reviewer(s) :Prof. Dr. Alexandre Eremenko, Prof. Dr. Dierk Schleicher

Description:This thesis contains several new results about the dynamics of exponential maps $z\mapsto \exp(z)+\kappa$. In particular, we prove that periodic external rays of exponential maps with nonescaping singular value always land. This is an analog of a theorem of Douady and Hubbard for polynomials. We also answer a question of Herman, Baker and Rippon by showing that the boundary of an unbounded exponential Siegel disk always contains the singular value. In addition to the presentation of new results, the thesis also aims to give an overview of the current state of knowledge on the dynamics of exponential maps.

Keywords:Exponentialabbildung , dynamical systems, dynamische Systeme, function theory, Funktionentheorie, holomorphic dynamics, holomorphe Dynamik, exponential maps, Exponentialabbildungen, Julia set, Juliamenge

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