Hamiltonian integrable systems in a magnetic field and symplectic-Haantjes geometry
We investigate the geometry of classical Hamiltonian systems immersed in a magnetic field in three-dimensional (3D) 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)-t...
| Autores: | , , , |
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| Formato: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2024 |
| País: | España |
| Recursos: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repositorio: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:digital.csic.es:10261/379000 |
| Acesso em linha: | http://hdl.handle.net/10261/379000 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85209698783&doi=10.1098%2frspa.2024.0076&partnerID=40&md5=788596c1a87ece0f865253eab92355db |
| Access Level: | acceso abierto |
| Palavra-chave: | Haantjes geometry integrable systems magnetic systems Stäckel systems |
| Resumo: | We investigate the geometry of classical Hamiltonian systems immersed in a magnetic field in three-dimensional (3D) 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. In addition, the underlying Stäckel geometry is used to construct new families of integrable Hamiltonian models immersed in a magnetic field. © 2024 The Author(s). |
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