Heteroclinic for a 6-dimensional reversible system occuring in orthogonal domain walls in convection
Résumé
A six-dimensional reversible normal form system occurs in Bénard-Rayleigh convection between parallel planes, when we look for domain walls intersecting orthogonally (see Buffoni et al [1]). We prove analytically the existence, local uniqueness, and analyticity in parameters, of a heteroclinic connection between two equilibria, each corresponding to a system of convective rolls. We prove that the 3-dimensional unstable manifold of one equilibrium, intersects transversally the 3-dimensional stable manifold of the other equilibrium, both manifolds lying on a 5-dimensional invariant manifold. We also study the linearized operator along the heteroclinic, allowing to prove (in another paper) the persistence under perturbation, of the heteroclinic obtained in [1].
Origine | Fichiers produits par l'(les) auteur(s) |
---|