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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2410.11343 |
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| _version_ | 1866908682578558976 |
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| author | Iooss, Gérard |
| author_facet | Iooss, Gérard |
| contents | A six-dimensional reversible normal form system occurs in B{é}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]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_11343 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Heteroclinic for a 6-dimensional reversible system occuring in orthogonal domain walls in convection Iooss, Gérard Mathematical Physics Classical Physics A six-dimensional reversible normal form system occurs in B{é}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]. |
| title | Heteroclinic for a 6-dimensional reversible system occuring in orthogonal domain walls in convection |
| topic | Mathematical Physics Classical Physics |
| url | https://arxiv.org/abs/2410.11343 |