Generalized heteroclinic cycles in spherically invariant systems and their pertubations
- Chossat, Pascal
- Guyard, Frédéric
- Lauterbach, Reiner
In this paper we want to investigate the effects of forced symmetry breaking perturbations, see LAUTERBACH & ROBERTS , as well as [28, 31], on the heteroclinic cycle which was found in the ℓ = 1, ℓ = 2 mode interaction by ARMBRUSTER & 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. The main problem is to find a selection principle, that is to give a mechanism which enables the physical system to select one particular heteroclinic cycle on this generalized heteroclinic cycle. After that 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.