On combinatorics and core entropy of transcendental entire functions
speaker: Dierk Schleicher (Universite' de Marseilles)abstract: We describe the dynamics of post-singularly finite transcendental entire functions, reporting on work by and with David Pfrang, Roman Chernov, Bernhard Reinke, Malte Hassler, and Sergey Shemyakov. We show that every such function has a Homotopy Hubbard Tree that allows to distinguish different maps within any given parameter space from each other. Via these Hubbard trees, one can define “core entropy” as a measure of complexity of the dynamics. Unlike topological entropy, we show that core entropy is always finite. For certain families of maps such as exponential maps, the entropy is always uniformly bounded (for exponential maps, by log 2). For other families, such as the cosine family, there is no uniform bound throughout the family. We also discuss how to define core entropy for transcendental entire functions that are not postsingularly finite.
timetable:
Wed 29 May, 11:30 - 12:20, Aula Dini
<< Go back