{
  "id": "2401.16897",
  "version": "v2",
  "published": "2024-01-30T11:05:11.000Z",
  "updated": "2024-06-17T07:03:28.000Z",
  "title": "Hamiltonian integrable systems in a magnetic field and Symplectic-Haantjes geometry",
  "authors": [
    "Ondřej Kubů",
    "Daniel Reyes",
    "Piergiulio Tempesta",
    "Giorgio Tondo"
  ],
  "comment": "25 pages, no figures. Includes minor revisions enhancing clarity suggested by referees for Proceedings of Royal Society A and some additional comments",
  "categories": [
    "math-ph",
    "math.DG",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-06-17T07:03:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "magnetic field",
      "hamiltonian integrable systems",
      "symplectic-haantjes geometry",
      "systems admit non-trivial symplectic-haantjes manifolds",
      "three-dimensional riemannian configuration spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}