Hopf-bifurcation in systems with spherical symmetry. I: Invariant tori (Q1356003)

The Hopf bifurcation with \(O(3)\) symmetry is studied. In the first part, the author investigates the bifurcation of invariant tori applying the analytic technique. The basic methods are orbit space reduction, Poincaré series, invariants and equivariants, the usage of the structure of isotropy subgroups, normal forms technique, singular perturbation theory. Mainly the case of ten-dimensional representation of \(\Gamma= O(3)\times S^1\) on the space \(V_2\oplus iV_2\) of homogeneous harmonic polynomials of degree two is considered. The existence of invariant tori and results about their stability are obtained. In the introduction a detailed review of preceding results is given.