Forced symmetry breaking perturbations for periodic solutions
- Guyard, Fréderic
- Lauterbach, Reiner
2010 Mathematics Subject Classification
- 34C25 34C37 58F35
- Forced symmetry breaking, periodic solution, orbit space, heteroclinic cycles
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 LG/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.
- Nonlinearity, 10 (1997), pp. 291-310