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Group theoretic conditions for existence of robust relative homoclinic trajectories

Published online by Cambridge University Press:  26 July 2002

PETER ASHWIN  and
JAMES MONTALDI
PETER ASHWIN
Affiliation:
School of Mathematical Sciences, Laver Building, University of Exeter, Exeter EX4 4QE.
JAMES MONTALDI
Affiliation:
CNRS-INLN, 1361 route des Lucioles, 06560 Valbonne, France.
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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

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