A selection of a weak KAM solution of the sub-riemannian Mañé Lagrangian
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917481192357888 |
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| author | Juárez, Iker Martínez Morgado, Héctor Sánchez |
| author_facet | Juárez, Iker Martínez Morgado, Héctor Sánchez |
| contents | For a sub-riemannian structure on the torus, satisfying the Hörmander condition, we consider the Mañé Lagrangian associated to a horizontal vector field. Assuming that the Aubry set consists in a finite number of static classes, we show that the invariant measure, for the horizontal stochastic perturbation of the flow of the vector field, determines a particular weak KAM solution of the Lagrangian, as the perturbation tends to zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_10335 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A selection of a weak KAM solution of the sub-riemannian Mañé Lagrangian Juárez, Iker Martínez Morgado, Héctor Sánchez Dynamical Systems 37J51, 60F10, 49L25, 53C17 For a sub-riemannian structure on the torus, satisfying the Hörmander condition, we consider the Mañé Lagrangian associated to a horizontal vector field. Assuming that the Aubry set consists in a finite number of static classes, we show that the invariant measure, for the horizontal stochastic perturbation of the flow of the vector field, determines a particular weak KAM solution of the Lagrangian, as the perturbation tends to zero. |
| title | A selection of a weak KAM solution of the sub-riemannian Mañé Lagrangian |
| topic | Dynamical Systems 37J51, 60F10, 49L25, 53C17 |
| url | https://arxiv.org/abs/2401.10335 |