Article contents
Group theoretic conditions for existence of robust relative homoclinic trajectories
Published online by Cambridge University Press: 26 July 2002
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.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 133 , Issue 1 , July 2002 , pp. 125 - 141
- Copyright
- 2002 Cambridge Philosophical Society
- 9
- Cited by