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...

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Detalles Bibliográficos
Autores: Kubů, O., Reyes, D., Tempesta, P., Tondo, G.
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2024
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/379000
Acceso en línea: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
Palabra clave:Haantjes geometry
integrable systems
magnetic systems
Stäckel systems
Descripción
Sumario: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).