99-16   Berichtsreihe des Mathematischen Seminars der Universität Kiel

Walter Bergweiler:

The role of the Ahlfors five islands theorem in complex dynamics

The Ahlfors five islands theorem has become an important tool in complex dynamics. We discuss its role there, describing how it can be used to deal with a variety of problems. This includes questions concerning the Hausdorff dimension of Julia sets, the existence of singleton components of Julia sets, and the existence of repelling periodic points. We point out that for many applications a simplified version of the Ahlfors five islands theorem suffices, and we give an elementary proof of this version.

Mathematics Subject Classification (1991): 30C25, 30D05, 30D45, 58F23

Bibliographical note: Conform. Geom. Dyn. 4 (2000), 22-34 (elektronische Zeitschrift)

Keywords: Ahlfors theory, covering surface, island, Bloch principle, rescaling lemma, normal family, complex dynamics, Julia set, periodic point, Hausdorff dimension

Mail an Jens Burmeister
[Thu Feb 19 18:56:34 2009]