Forced symmetry breaking perturbations for periodic solutions

Abstract

Using the formalism defined by R. Lauterbach and M. Roberts, we develop a geometric approach for the problem of forced symmetry breaking for periodic orbits in G-equivariant systems of ODE's. We show that this problem can be studied as the perturbation of the identity mapping on the double coset space L backslash G/K where K is the maximal subgroup of G acting on the periodic orbit and L the symmetry of the perturbation. We exhibit some example where this kind of symmetry breaking allows to show the existence of heteroclinic cycles between periodic solutions. (orig.)