Review article. In: Nonlinear Instability, Chaos and Turbulence, Vol 2 , (L. Debnath and D. N. Riahi, eds.) Advances in Fluid Mechanics 25 WIT Press, Southampton, 2000, 79-109.
We consider mathematical issues concerning Ginzburg-Landau theory, by which we mean 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 Euclidean symmetries present in such systems.