The magnetic geodesic flow on a homogeneous symplectic manifold
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- Efimov, D.I. Sib Math J (2005) 46: 83. doi:10.1007/s11202-005-0009-y
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We prove the noncommutative integrability of the magnetic geodesic flow defined by the Kirillov form on a coadjoint orbit of a compact semisimple Lie group. This implies that on a simply-connected homogeneous symplectic manifold the magnetic geodesic flow, defined by the homogeneous symplectic form and some metric, is integrable in the noncommutative sense.