A Lax representation and integrability of homogeneous exact magnetic flows on spheres in all dimensions

Published 29 Jun 2025 in nlin.SI, math-ph, math.DS, and math.MP | (2506.23299v1)

Abstract: We consider motion of a material point placed in a constant homogeneous magnetic field restricted to the sphere $S^{n-1}$. We provide a Lax representation of the equations of motion for arbitrary $n$ and prove integrability of those systems in the Liouville sense. The integrability is provided via first integrals of degree one and two.

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Integrability of homogeneous exact magnetic flows on spheres for all dimensions

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