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arXiv · 2506.23299

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

Vladimir Dragović·Borislav Gajić·Božidar Jovanović
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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 and prove complete integrability of those systems for any $n$. The integrability is provided via first integrals of degree one and two.

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Vladimir Dragović, Borislav Gajić, Božidar Jovanović. 2025-06-29. A Lax representation and integrability of homogeneous exact magnetic flows on spheres in all dimensions. https://arxiv.org/abs/2506.23299

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