Ondřej Kubů, Daniel Reyes, Piergiulio Tempesta, Giorgio Tondo
Published 2024-01-30, updated 2024-06-17Version 2
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 St\"ackel geometry is used to construct new families of integrable Hamiltonian models immersed in a magnetic field.
Comments: 25 pages, no figures. Includes minor revisions enhancing clarity suggested by referees for Proceedings of Royal Society A and some additional comments
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