Pascal Chossat and Michael Field.
Geometric analysis of the effect of symmetry breaking
perturbations on an O(2) invariant homoclinic cycle
Using ideas based on blowing up, we give a geometric analysis
of the effect of symmetry breaking perturbations on an O(2)-invariant
homoclinic cycle previously studied by Armbruster, Holmes and
Guckenheimer. We present numerical evidence to suggest that, at resonant
points, breaking symmetry to a reflectional subgroup of O(2)
may lead to chaotic dynamics.