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  • Cited by 6
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Podvigina, Olga and Chossat, Pascal 2015. Simple heteroclinic cycles in ${\mathbb R}^4$. Nonlinearity, Vol. 28, Issue. 4, p. 901.

    Podvigina, Olga 2013. Classification and stability of simple homoclinic cycles in ${\mathbb R}^5$. Nonlinearity, Vol. 26, Issue. 5, p. 1501.

    Podvigina, Olga and Ashwin, Peter 2011. On local attraction properties and a stability index for heteroclinic connections. Nonlinearity, Vol. 24, Issue. 3, p. 887.

    Homburg, Ale Jan and Sandstede, Björn 2010.

    Sottocornola, Nicola 2005. Simple homoclinic cycles in low-dimensional spaces. Journal of Differential Equations, Vol. 210, Issue. 1, p. 135.

    Sottocornola, Nicola 2003. Robust homoclinic cycles in  4. Nonlinearity, Vol. 16, Issue. 1, p. 1.

  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 133, Issue 1
  • July 2002, pp. 125-141

Group theoretic conditions for existence of robust relative homoclinic trajectories

  • DOI:
  • Published online: 01 July 2002

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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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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