The paper proves complete integrability of homogeneous exact magnetic flows on spheres in all dimensions via a Lax representation.
Integrability of the magnetic geodesic flow on the sphere with a constant 2-form
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abstract
We prove a recent conjecture of Dragovic et al arXiv2504.20515 stating that the magnetic geodesic flow on the standard sphere $S^n\subset \mathbb R^{n+1}$ 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.
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A Lax representation and integrability of homogeneous exact magnetic flows on spheres in all dimensions
The paper proves complete integrability of homogeneous exact magnetic flows on spheres in all dimensions via a Lax representation.