Intendierte Lernergebnisse
The listener will be equipped with a solid knowledge on the classical field of Complex Analysis and the basics in the area of Complex Dynamics. The latter field studies the behavior of iteration of meromorphic functions.
Lehrmethodik
Presentation at the blackboard, computer simulations
Inhalt/e
Simply connected domains (Homotopies, holomorphic logarithms and roots, analytical continuation)Families of holomorphic functions (Basics, Theorem of Bloch, Theorem of Schottky, Little and Great Theorems of Montel and Picard, Riemann mapping theorem)Holomorphic dynamical systems (Basics, Julia and Fatou sets, hyperbolic points, non- hyperbolic points, exceptional points and Julia sets, periodic orbits and Julia sets, Mandelbrot sets)
Erwartete Vorkenntnisse
Basics of Complex Analysis. In fact, the lecture directly connects to my course "Funktionentheorie".The course is also suitable for BSc students. No previous knowledge on Dynamical Systems is required.
Literatur
L. Ahlfors: Complex analysis, McGraw-Hill, 1953A. Beardon: Iteration of rational functions: Complex analytic dynamical systems, Springer, 1991J. Milnor: Dynamics in one complex variable (3rd ed.), Princeton University Press, 2006R. Remmert: Theory of complex functions, Springer, 1990 (readers familiar with the language should consult the German versions "Funktionentheorie 1" and "Funktionentheorie 2" (beide mit Georg Schumacher))