__Mathematical Foundations of
Ginzburg Landau Theory__

__ __

__Ian Melbourne__

University of Surrey, UK

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).