Group theoretic conditions for existence of robust relative homoclinic trajectories

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Group theoretic conditions for existence of robust relative homoclinic trajectories

Please use this identifier to cite or link to this item: http://hdl.handle.net/10036/18980

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Title: Group theoretic conditions for existence of robust relative homoclinic trajectories
Author: Ashwin, Peter
Montaldi, James
Citation: 133 (1), pp. 125-141
Publisher: Cambridge University Press
Journal: Mathematical Proceedings of the Cambridge Philosophical Society
Date Issued: 2002
URI: http://hdl.handle.net/10036/18980
DOI: 10.1017/S0305004101005801
Links: http://journals.cambridge.org/action/displayAbstract?aid=114041
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: Article
Description: 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
Keywords: heteroclinic cyclessymmetry
ISSN: 0305-0041


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