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
PUZZLE AND PARAPUZZLE
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.