Hamiltonian Hopf bifurcation with symmetry

Studies Hamiltonian Hopf bifurcation in the presence of a compact symmetry group G. The author classifies the expected actions of G and show that near four-dimensional fixed point subspaces of subgroups of G*Si the bifurcation of periodic solutions is diffeomorphic to the standard Hamiltonian Hopf bifurcation in two degrees of freedom. Examples are given of O(2), SO(2) and SU(2) symmetry. Furthermore it is shown that Hamiltonian Hopf bifurcation with SO(2) symmetry occurs in the Euler-Poisson equations for the Lagrange rigid body motion.