WIAS Preprint No. 233, (1996)

Forced symmetry breaking perturbations for periodic solutions



Authors

  • Guyard, Fréderic
  • Lauterbach, Reiner
    ORCID: 0000-0002-9310-3177

2010 Mathematics Subject Classification

  • 34C25 34C37 58F35

Keywords

  • Forced symmetry breaking, periodic solution, orbit space, heteroclinic cycles

Abstract

Using the formalism defined by R. Lauterbach and M. Roberts [21], 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.

Appeared in

  • Nonlinearity, 10 (1997), pp. 291-310

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