The magnetic geodesic flow on a homogeneous symplectic manifold

We prove the noncommutative integrability of the magnetic geodesic flow defined by the Kirillov form on a coadjoint orbit of a compact semi-simple 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.