My doctoral thesis (from the University of Kiel in 2003) was entitled Dynamics of exponential maps. It is available here and also from the University of Kiel and the Stony Brook thesis server.

Summary

The thesis covers a number of topics in the study of the family of complex exponential maps,
mathz\mapsto \exp(z)+\kappa, \qquad \kappa\in\mathbb{C}.math

Most of the results from the thesis have since been published in a series of papers:
  • Topological dynamics of exponential maps on their escaping sets contains the larger part of Chapter 3, as well as the early part of Chapter 4.
  • On nonlanding dynamic rays of exponential maps (Annales Academiae Scientiarum Fennicae) contains Theorem 3.8.3, and some extensions
  • Combinatorics of bifurcations in exponential parameter space (In: Transcendental dynamics and complex analysis. In honour of Noel Baker (Rippon and Stallard, eds)) contains the 'combinatorial' part of Chapter 5
  • Bifurcations in the space of exponential maps (Inventiones Mathematicae, w/ Dierk Schleicher) contains the proof of the "squeezing lemma" from Chapter 5 (with some additional applications)
  • A landing theorem for periodic rays of exponential maps (Proceedings of the AMS) - contains the results from Sections 5.13 and 5.14.
  • A question of Herman, Baker and Rippon concerning Siegel disks (Bulletin of the LMS) contains the result from Section 6.1
  • Classification of escaping exponential maps (with Förster and Schleicher, Proceedings of the AMS) contains Theorem 5.12.2.

Errata

There is a misstatement in Theorem 4.2.4. It should be assumed that the point z is not escaping. (For escaping points, there is an exception when the parameter is of satellite type.)