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Integrability of the magnetic geodesic flow on the sphere with a constant 2-form (2506.23312v1)
Published 29 Jun 2025 in math.DG, math-ph, math.DS, math.MP, and nlin.SI
Abstract: We prove a recent conjecture of Dragovic et al arXiv2504.20515 stating that the magnetic geodesic flow on the standard sphere $Sn\subset \mathbb R{n+1}$ whose magnetic 2-form is the restriction of a constant 2-form from $\mathbb{R}{n+1}$ is Liouville integrable. The integrals are quadratic and linear in momenta.