Magnetic Flows on Homogeneous Spaces

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We consider magnetic geodesic flows of the normal metrics on a class of homogeneous spaces, in particular (co)adjoint orbits of compact Lie groups. We give the proof of the non-commutative integrability of flows and show, in addition, for the case of (co)adjoint orbits, the usual Liouville integrability by means of analytic integrals. We also consider the potential systems on adjoint orbits, which are generalizations of the magnetic spherical pendulum. The complete integrability of such system is proved for an arbitrary adjoint orbit of a compact semisimple Lie group.
21 pages, minor changes, final version, to appear in Commentarii Mathematici Helvetici

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Mathematical Physics, Differential Geometry, Exactly Solvable and Integrable Systems, 70H06, 37J35, 53D25

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http://salesiana.dossiersoluciones.com/handle/123456789/213321

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math-ph/0609005
 http://arxiv.org/abs/math-ph/0609005
 Comment. Math. Helv. 83 (2008), no. 3, 679-700

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