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Local bifurcation theory for PDE's was developed in the early sixties in order to analyze hydrodynamical instabilities on a rigorous mathematical basis.
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equivariant branching lemma, homoclinic cycle, forced symmetry breaking, relative periodic orbits, isotropy types, projected vector field, transverse bifurcation, relative equilibria, equivariant bifurcation theory, heteroclinic cycle, invariant sphere, principal stratum, resonant bifurcation, maximal isotropy, equivariant systems, bifurcation equation, equivariant structure, fixed point subspace, normal hyperbolicity, branching lemmas, complex irreducible representations, equivariant vector fields, absolutely irreducible representation, bifurcating solutions, center manifold reduction
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