Two first weeks
Pierre Coullet: Dynamical Systems
Geometry of dynamical systems (2 hours)
Normal forms (2 hours)
Bifurcations (2 hours)
Qualitative analysis of one-dimensional stationary patterns (3 hours)
Gerard Iooss : bifurcations in reversible systems and Application to "Spatial dynamics".
1. Reduction of the dynamics to a center manifold.
2. Normal forms and Elementary reversible bifurcations.
3. Basic examples - Elliptic pb in strips - one-dimensional patterns.
4. Application to travelling waves in lattices (Fermi-Pasta-Ulam, Klein-Gordon,..)
5. Application to travelling water waves.
Lorenz Kramer: Amplitude Equations
From Normal Forms to Amplitude Equations (2 hours)
Variational case: the real Ginzburg-Landau Equation (2 hours)
Nonvariational case: the Complex Ginzburg-Landau Equation (2 hours)
Fronts and other coherent structures (2 hours)
Len Pismen:The Dynamics of Reaction Diffusion Systems
Symmetry-breaking bifurcations in RD systems (2 hours)
Stationary structures in RD systems with separated scales (2 hours)
Instabilities of stationary structures (2 hours)
Spiral waves (3 hours)
The following 5 weeks are devoted to research. Visitors will deliver seminars and mini-courses.
The topis which will be covered during the research session include
Ocean Waves (A. Newell, A. Provenzale)
Growth (M. Benamar)
Forest Fires (F. Williams)
Orientation dynamics in anisotropic fluids (A. Buka)
Cardiac Arythmia (A. Karma, A. Pumir)
Elasticity and Plasticity (B. Odoli, Y. Pomeau)
Vegetation Patterns (R. Lefever)
Explosions, Detonations and Flames (P. Clavin)
I. S. Aronson, Y. Couder, M. C. Cross, A. A. Golovin, L. Mahadevan, J. Prost, Z. Racz and R. Toral
The last week is devoted to the review of the presentation of the junior's works (5 talks a day)