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An algebraic criterion for symmetric Hopf bifurcation. (English) Zbl 0788.58038
From the authors’ abstract: “The equivariant Hopf bifurcation theorem states that bifurcating branches of periodic solutions with certain symmetry exist when the fixed-point subspace of the subgroup of symmetries is two-dimensional. We show that there is a group-theoretic restriction on the subgroup of symmetries in order for that subgroup to have a two-dimensional fixed-point subspace in any representation. We illustrate this technique for all irreducible representations of SO(3) on the space V of spherical harmonics for even”.
MSC:
37G99Local and nonlocal bifurcation theory
34C23Bifurcation (ODE)
34C25Periodic solutions of ODE
37C80Symmetries, equivariant dynamical systems