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Generalized Heteroclinic Cycles in Spherically Invariant Systems and Their Perturbations

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Summary.

In this paper we want to investigate the effects of forced symmetry-breaking perturbations—see Lauterbach & Roberts [29], as well as [28], [31]—on the heteroclinic cycle which was found in the l = 1 , l = 2 mode interaction by Armbruster and Chossat [1], [12] and generalized by Chossat and Guyard [25], [14]. We show that this cycle is embedded in a larger class of cycles, which we call a generalized heteroclinic cycle (GHC). After describing the structure of this set, we discuss its stability. Then the persistence under symmetry-breaking perturbations is investigated. We will discuss also the application to the spherical Bénard problem, which was the initial motivation for this work.

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Authors and Affiliations

  1. Institut Non Linéaire de Nice (CNRS et Université de Nice), 1361 Route des Lucioles, Sophia-Antipolis-06560 Valbonne, France, FR

    P. Chossat

  2. Weierstraß Institute for Applied Analysis and Stochastics, Mohrenstraß e 39, D-10117 Berlin, Germany, DE

    F. Guyard & R. Lauterbach

Authors
  1. P. Chossat
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  2. F. Guyard
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  3. R. Lauterbach
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Additional information

Received March 11, 1997; first revision received October 10, 1997; second revision received April 13, 1998; accepted July 16, 1998

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Chossat, P., Guyard, F. & Lauterbach, R. Generalized Heteroclinic Cycles in Spherically Invariant Systems and Their Perturbations. J. Nonlinear Sci. 9, 479–524 (1999). https://doi.org/10.1007/s003329900077

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  • DOI: https://doi.org/10.1007/s003329900077

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