Heteroclinic for a 6-dimensional reversible system occuring in orthogonal domain walls in convection - Archive ouverte HAL
Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2023

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].
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Dates et versions

hal-04233495 , version 1 (09-10-2023)
hal-04233495 , version 2 (20-12-2023)
hal-04233495 , version 3 (03-05-2024)
hal-04233495 , version 4 (25-06-2024)
hal-04233495 , version 5 (29-07-2024)
hal-04233495 , version 6 (07-08-2024)
hal-04233495 , version 7 (17-09-2024)

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  • HAL Id : hal-04233495 , version 2

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Gérard Iooss. Heteroclinic for a 6-dimensional reversible system occuring in orthogonal domain walls in convection. 2023. ⟨hal-04233495v2⟩
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