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arXiv · 2410.11343

Heteroclinic for a 6-dimensional reversible system occuring in orthogonal domain walls in convection

Gérard Iooss
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Abstract

A six-dimensional reversible normal form system occurs in B{\'e}nard-Rayleigh convection between parallel planes, when we look for domain walls intersecting orthogonally (see Buffoni et al [1]). On the truncated system, 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 [9]) the persistence under reversible perturbation, of the heteroclinic obtained in [1].

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Gérard Iooss. 2024-10-15. Heteroclinic for a 6-dimensional reversible system occuring in orthogonal domain walls in convection. https://arxiv.org/abs/2410.11343

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