Group theoretic conditions for existence of robust relative homoclinic trajectories

Peter Ashwin, James Montaldi

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    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.© 2002 Cambridge Philosophical Society.
    Original languageEnglish
    Pages (from-to)125-141
    Number of pages16
    JournalMathematical Proceedings of the Cambridge Philosophical Society
    Issue number1
    Publication statusPublished - 2002


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