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

RENORMALIZATION CONJECTURES AND THEOREMS

The "Feigenbaum Universality Law" discovered about 20 years ago and heuristically explained by the Renormalization Conjectures has fascinated both physicists and mathematicians. Physically, it gives a prediction of the transition parameter from "laminar" to "turbulent" regimes. Mathematically, it happened to be a deep problem on the borderline of dynamics, analysis and geometry. Methods of holomorphic dynamics turned out to be of crucial importance. The "dynamical part" of the problem was handled in 85 - 95 in the works of Sullivan and McMullen. The "parameter part" was recently handled by the author.