Group theoretic conditions for existence of robust relative homoclinic trajectories

Details Group theoretic conditions for existence of robust relative homoclinic trajectories Group theoretic conditions for existence of robust relative homoclinic trajectories

2002-01-29

arxiv.org/abs/math/0201288v1

Mathematics

Dynamical Systems

18 pages. To appear in Math Proc Camb Phil Soc (2002)

Scientific paper

10.1017/S0305004101005801

We consider robust relative homoclinic trajectories (RHTs) for equivariant vector fields. We give some conditions on the group and representation that imply existence of equivariant vector fields with such trajectories. Using these result 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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