Magnetic Flows on Homogeneous Spaces

Details Magnetic Flows on Homogeneous Spaces Magnetic Flows on Homogeneous Spaces

2006-09-02

arxiv.org/abs/math-ph/0609005v2

Comment. Math. Helv. 83 (2008), no. 3, 679-700

Physics

Mathematical Physics

21 pages, minor changes, final version, to appear in Commentarii Mathematici Helvetici

Scientific paper

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.

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