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- Title
Group theoretic conditions for existence of robust relative homoclinic trajectories.
- Authors
ASHWIN, PETER; MONTALDI, JAMES
- Abstract
We consider robust relative homoclinic trajectories (RHTs) for G-equivariant vector fields. We give some conditions on the group and representation that imply existence of equivariant vector fields with such trajectories. Using these results we show very simply that abelian groups cannot exhibit relative homoclinic trajectories. Examining a set of group theoretic conditions that imply existence of RHTs, we construct some new examples of robust relative homoclinic trajectories. We also classify RHTs of the dihedral and low order symmetric groups by means of their symmetries.
- Subjects
GROUP theory; EXISTENCE theorems; VECTOR fields; MATHEMATICAL symmetry; PERTURBATION theory; SPACE trajectories; SET theory; MANIFOLDS (Mathematics)
- Publication
Mathematical Proceedings of the Cambridge Philosophical Society, 2002, Vol 133, Issue 1, p125
- ISSN
0305-0041
- Publication type
Article
- DOI
10.1017/S0305004101005801