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

As part of its 1999 spring programme the "Danish Graduate School in Nonlinear Science" organizes a five day Ph.D. course by Professor Mikhail Lyubich, State University of New York at Stony Brook, USA. The course is entitled "Real and Complex Dynamics". Professor Lyubich has been elected as the "European Mathematical Society" Lecturer of 1999. His series of lectures are given in three places in Europe, see http://www.emis.de/etc/lecture.html for further information.

Abstract
Real and complex one-dimensional dynamics have been in the focus of research for the past 20 years. The ideas of dynamics, statistical physics, geometric function theory and hyperbolic geometry (supported by computer experiments) came together to reveal many rich and fascinating structures. As a result, several central problems have been recently resolved. Among them are the proofs of the real Rigidity Conjecture, the Feigenbaum Universality Conjecture and the Regular or Stochastic Conjecture. Altogether it gives a complete picture of dynamics in the real quadratic family.

• The Mandelbrot set and its little copies
• Rigidity Conjectures and Theorems
• Puzzle and parapuzzle
• Renormalization Conjectures and Theorems
• Real quadratic family: A complete picture

Organizer
Bodil Branner, Department of Mathematics, Technical University of Denmark.

Another Ph.D. course in Dynamics
In parallel the DCAMM International Graduate Research School in Applied Mechanics organizes a Ph.D. course entitled "Hamiltonian Mechanics with applications", see http://www.fam.dtu.dk/html/booklet99.html#course". It is possible to participate in both Ph.D. courses.

Preliminary programme
Professor Lyubich lectures are scheduled for 10:45 - 12:30 each day.

Coffee/tea break from 10:15 to 10:45 Lunch break from 12:30 to 13:30

Social programme
Several joint activities will be announced.

Registration
Registration is free. Accommodations will be made available for foreign participants in nearby housing facilities. Danish participants are expected to cover their own living expenses.

Grants
A number of grants are available to contribute to the travel and living expenses of the foreign students. Applications including a short CV and a recommendation from the supervisor should be sent to the correspondence address below no later than May 15, 1999. Applicants will be notified immediately after this deadline if support can be provided.

Deadlines
Applications for grants and housing: May 15, 1999. Final registration: June 7, 1999.

Correspondence to
Kirsten Krasilnikoff
Department of Mathematics
Technical University of Denmark
DK-2800 Lyngby, Denmark
Phone: +45 45 25 30 33
Fax: +45 45 88 13 99
E-mail: K.Krasilnikoff@mat.dtu.dk