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__Patterns, Nonlinear Dynamics and Applications - PANDA__

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__First meeting: Pattern formation in applications I: Monday 17th December
2001, DAMTP, Cambridge__

Ian Melbourne |
*Validity and universality of the Ginzburg-Landau equation* |

Abstract:

We consider mathematical issues concerning Ginzburg-Landau theory, including
the validity, universality, and structure of reduced equations near criticality
in spatially extended systems. The extraction of Ginzburg-Landau
equations (variously known as amplitude, modulation and envelope equations)
is part of this theory.

We pay particular attention to the (noncompact) Euclidean symmetries
present in such systems, stressing the analogy with Landau theory (where
the symmetry group is finite) and equivariant bifurcation theory (where
the symmetry group is compact).