|Affiliations:||Mathematical Institute of the Serbian Academy of Sciences and Arts||Title:||Magnetic flows on homogeneous spaces||Journal:||Commentarii Mathematici Helvetici||Volume:||83||Issue:||3||First page:||679||Last page:||700||Issue Date:||1-Jan-2008||Rank:||M21||ISSN:||0010-2571||DOI:||10.4171/CMH/139||Abstract:||
We consider magnetic geodesic flows of the normal metrics on a class of homogeneous spaces, in particular adjoint orbits of compact Lie groups. We give the proof of the noncommutative integrability of flows and show, in addition, for the case of 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.
|Keywords:||Compatible poisson brackets | Magnetic flows | Non-commutative integrability||Publisher:||European Mathematical Society||Project:||Serbian Ministry of Science, Project 144014 “Geometry and Topology of Manifolds and Integrable Dynamical Systems”|
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