Project Details
Projekt
Geometry and dynamics of entire functions in the Speiser class
Applicant
Dr. Simon Albrecht
Subject Area
Mathematics
Term
from 2016 to 2017
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 321659528
Complex dynamics deals with the iteration of entire or rational maps f. Thereby, the Fatou set F(f) and the Julia set J(f) play an important role. The Fatou set consists of all points in which the iterates of f form a normal family in the sense of Montel. The Julia set is the complement of the Fatou set in the complex plane. It was observed that the Julia set consists of those points where the iterates behave in some sense chaotic. Julia sets often have a fractal shape. Hence, the intuitive concept of dimension is improper, and the notion of the Hausdorff dimension is used instead.In the case of transcendental entire functions, the Eremenko-Lyubich class B, which consists of those transcendental entire functions f whose set of singular values S(f) is bounded, and the Speiser class S, which consists of all transcendental entire functions f such that S(f) is finite, are of particular interest. Stallard showed that for a function f in the Eremenko-Lyubich class the Hausdorff dimension of J(f) is strictly larger than 1. Furthermore, she proved for any 1
DFG Programme
Research Fellowships
International Connection
United Kingdom
