Graduate School in Nonlinear Science

Sponsored by the Danish Research Academy

MIDIT                               OFD                           CATS
Modelling, Nonlinear Dynamics       Optics and Fluid Dynamics     Chaos and Turbulence Studies
and Irreversible Thermodynamics     Risø National Laboratory      Niels Bohr Institute and 
Technical University of Denmark     Building 128                  Department of Chemistry
Building 321                        P.O. Box 49                   University of Copenhagen 
DK-2800 Lyngby                      DK-4000 Roskilde              DK-2100 Copenhagen Ø
Denmark                             Denmark                       Denmark


It is a beautiful combinatorial game discovered by Branner & Hubbard in the context of cubic maps and then transferred by Yoccoz to the quadratic set up. The idea is to cut the Julia set or the Mandelbrot set into pieces, describe their combinatorics in dynamical terms and then study their conformal geometry. What makes this theory special compared to the usual Markov coding is the presence of the critical point. What makes it tractable is conformal invariance or quasi-invariance of different geometric parameters. It is a key to many problems, including the rigidity and renormalization problems.