2006.247: Group theoretic conditions for existence of robust relative homoclinic trajectories

2006.247: Peter Ashwin and James Montaldi (2002) Group theoretic conditions for existence of robust relative homoclinic trajectories. Mathematical Proceedings of the Cambridge Philosophical Society, 133 (1). pp. 125-141. ISSN 0305-0041

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DOI: 10.1017/S0305004101005801

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.

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