000K utf8 1100 $c2003 1500 eng 2050 urn:nbn:de:gbv:8-diss-7816 3000 Rempe, Lasse 4000 Dynamics of exponential maps$hChristian-Albrechts-Universität zu Kiel [Rempe, Lasse] 4030 Kiel$nChristian-Albrechts-Universität zu Kiel 4209 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. 4950 https://nbn-resolving.org/urn:nbn:de:gbv:8-diss-7816$xR$3Volltext$534 4961 https://macau.uni-kiel.de/receive/diss_mods_00000781 5051 510 5550 dynamical systems 5550 dynamische Systeme 5550 Exponentialabbildung 5550 Exponentialabbildungen 5550 exponential maps 5550 function theory 5550 Funktionentheorie 5550 holomorphe Dynamik 5550 holomorphic dynamics 5550 Juliamenge 5550 Julia set