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

Abstract

A Hopf-bifurcation scenario with symmetries is studied. Here, apart from the well known branches of periodic solutions, other bifurcation phenomena have to occur as it is shown in the second part of the paper using topological arguments. In this rst part of the paper we prove analytically that invariant tori with quasiperiodic motion bifurcate. The main methods used are orbit space reduction and singular perturbation theory.