Integrable magnetic geodesic flows on lie groups |
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Authors: | A A Magazev I V Shirokov Yu A Yurevich |
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Institution: | (1) Irtysh Branch, Novosibirsk State Academy for Water Transport, Omsk, Russia;(2) Omsk State University, Omsk, Russia |
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Abstract: | On Lie group manifolds, we consider right-invariant magnetic geodesic flows associated with 2-cocycles of the corresponding Lie algebras. We investigate the algebra of the integrals of motion of magnetic geodesic flows
and also formulate a necessary and sufficient condition for their integrability in quadratures, giving the canonical forms
of 2-cocycles for all four-dimensional Lie algebras and selecting integrable cases.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 2, pp. 189–206, August, 2008. |
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Keywords: | Lie group Lie algebra cocycle magnetic geodesic flow integral of motion Poisson bracket |
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