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MP: Theoretische und Mathematische Grundlagen der Physik

MP VI: HV VI

MP VI.1: Hauptvortrag

Mittwoch, 28. März 2001, 15:00–16:00, HS VIII

Dynamics of Iterated Entire Maps — •Dierk Schleicher — Mathematisches Institut, Universität München

In the last two decades, there has been enormous progress in iteration theory of holomorphic maps; among the more spectacular results are universality phenomena and an understanding of renormalization in the dynamics of iteration. These results concern iterated rational maps, i.e. maps with finite degree on the Riemann sphere and in particular polynomials.
In our talk, we will discuss iterated entire transcendental maps: this theory is still in its infancy, but the dynamics has several rather surprising features from points of view of topology, measure, and dimension theory. We will explain some of these features and argue that they might be typical for transcendental iteration theory.