EVENT DETAILS AND ABSTRACT

Title: Combinatorics, kneading theory and Hubbard trees for complex quadratic maps
Speaker: Professor Henk Bruin
Speaker Info: Caltech
Brief Description:
Special Note: Please note unusual day.
Abstract:

Kneading theory is the theory of symbolic dynamics of continuous interval maps and is as such well-understood. For complex maps, even as "simple" as $z \mapsto z^2 + c$, several symbolic questions remained open. In this talk we (joint work with Dierk Schleicher, Munich) try to complete the picture, and explore the relation between kneading invariants, external angles, Hubbard trees and branchpoints on Julia sets.

Although a symbolic description alone seems insufficient to determine the geometry (Hausdorff dimension, local connectivity) of Julia sets and the Mandelbrot set, we are able to prove statements about the distribution of harmonic measure on the Mandelbrot set and the prevalence of Collet-Eckmann maps.