Generalized heteroclinic cycles in spherically invariant systems and their perturbations

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 Benard problem, which was the initial motivation for this work.