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Group theoretic conditions for existence of robust relative homoclinic trajectories
University of Exeter; CNRS-INLN, Valbonne, France.
Mathematical Proceedings of the Cambridge Philosophical Society
Cambridge University Press
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.
Copyright © 2002 Cambridge Philosophical Society. This article appeared in Mathematical Proceedings of the Cambridge Philosophical Society 133: 1 (2002), pp. 125-141 and may be found at http://journals.cambridge.org/action/displayAbstract?aid=114041
133 (1), pp. 125-141