bifurcation problem with symmetry group

Let Γ be a Lie group acting on a vector space V and let the system of ordinary differential equations


where g:n×n is smooth. Then g is called a bifurcation problem with symmetry group Γ if gx,λ(Γ) (where E(Γ) is the space of Γ-equivariant germs, at the origin, of C mappings of V into V) satisfying




where (dg)0,0 denotes the Jacobian Matrix evaluated at (0,0). [GSS]


  • GSS Golubitsky, Martin. Stewart, Ian. Schaeffer, G. David.: Singularities and Groups in Bifurcation Theory (Volume II). Springer-Verlag, New York, 1988.
Title bifurcation problem with symmetry group
Canonical name BifurcationProblemWithSymmetryGroup
Date of creation 2013-03-22 13:53:36
Last modified on 2013-03-22 13:53:36
Owner Daume (40)
Last modified by Daume (40)
Numerical id 6
Author Daume (40)
Entry type Definition
Classification msc 37G40