A SYSTEMATIC STUDY OF HETEROCLINIC CYCLES IN DYNAMICAL-SYSTEMS WITH BROKEN SYMMETRIES

Let X be a Banach space or a manifold and G a compact Lie group acting on X. We study G-equivariant (semi) flows on X in the context of forc ed symmetry breaking. After applying small symmetry breaking perturbat ions, certain generic invariant manifolds of the above Bows persist sl ightly changed. We obtain necessary and sufficient conditions for the existence of heteroclinic cycles on the perturbed manifolds. Applicati ons are given for the case G=SO(3).