Integrability of the magnetic geodesic flow on the sphere with a constant 2-form
Bolsinov A.V. Konyaev A.Y. Matveev V.S.
2025World Scientific
International Journal of Geometric Methods in Modern Physics
2025
In this paper, we prove a recent conjecture of [V. Dragovi´c, B. Gaji´c and B. Jovanovi´c, Integrability of homogeneous exact magnetic flows on spheres, Regul. Chaotic Dyn. 30(4) (2025) 582–597, doi:10.1134/S1560354725040082] stating that the magnetic geodesic flow on the standard sphere Sn ⊂ Rn+1 whose magnetic 2-form is the restriction of a constant 2-form from Rn+1 is Liouville integrable. The integrals are quadratic and linear in momenta.
finite-dimensional integrable systems , Killing tensors , magnetic geodesics , Neumann system , orthogonal separation of variables , Quadratic in momenta integrals
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School of Mathematics, Loughborough University, LE11 3TU, United Kingdom
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Faculty of Mechanics and Mathematics, Moscow State University, Moscow Center for Fundamental and Applied Mathematics, Moscow, 119992, Russian Federation
Institut für Mathematik, Friedrich Schiller Universität Jena, Jena, 07737, Germany
School of Mathematics
Institute of Mathematics and Mathematical Modeling
Faculty of Mechanics and Mathematics
Institut für Mathematik
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Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026