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The following speakers have agreed to participate:


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)




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