Hamiltonian integrable systems in a magnetic field and Symplectic-Haantjes geometry
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910686187094016 |
|---|---|
| author | Kubů, Ondřej Reyes, Daniel Tempesta, Piergiulio Tondo, Giorgio |
| author_facet | Kubů, Ondřej Reyes, Daniel Tempesta, Piergiulio Tondo, Giorgio |
| contents | We investigate the geometry of classical Hamiltonian systems immersed in a magnetic field in three-dimensional Riemannian configuration spaces. We prove that these systems admit non-trivial symplectic-Haantjes manifolds, which are symplectic manifolds endowed with an algebra of Haantjes (1,1)-tensors. These geometric structures allow us to determine separation variables for known systems algorithmically; besides, the underlying Stäckel geometry is used to construct new families of integrable Hamiltonian models immersed in a magnetic field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_16897 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hamiltonian integrable systems in a magnetic field and Symplectic-Haantjes geometry Kubů, Ondřej Reyes, Daniel Tempesta, Piergiulio Tondo, Giorgio Mathematical Physics Differential Geometry Exactly Solvable and Integrable Systems We investigate the geometry of classical Hamiltonian systems immersed in a magnetic field in three-dimensional Riemannian configuration spaces. We prove that these systems admit non-trivial symplectic-Haantjes manifolds, which are symplectic manifolds endowed with an algebra of Haantjes (1,1)-tensors. These geometric structures allow us to determine separation variables for known systems algorithmically; besides, the underlying Stäckel geometry is used to construct new families of integrable Hamiltonian models immersed in a magnetic field. |
| title | Hamiltonian integrable systems in a magnetic field and Symplectic-Haantjes geometry |
| topic | Mathematical Physics Differential Geometry Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2401.16897 |