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

THE MANDELBROT SET AND ITS LITTLE COPIES

The Mandelbrot set M is a bifurcation diagram of the complex quadratic family. Its beautiful and rich structure continues to fascinate people. In the beginning of the 80's, Douady and Hubbard undertook a deep combinatorial study of this set which explained many of its features observed on computer pictures. In particular, they developed a theory of little Mandelbrot copies inside M based on the theory of quadratic-like maps. This theory laid down a foundation for the renormalization theory in the complex plane.