Geodesic
Integrable magnetic geodesic flows on Lie groups
Teoretičeskaâ i matematičeskaâ fizika, Tome 156 (2008) no. 2, pp. 189-206

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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.
Mots-clés : Lie group, Poisson bracket.
Keywords: Lie algebra, cocycle, magnetic geodesic flow, integral of motion 
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     author = {A. A. Magazev and I. V. Shirokov and Yu. A. Yurevich},
     title = {Integrable magnetic geodesic flows on {Lie} groups},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
     volume = {156},
     number = {2},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2008_156_2_a2/}
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A. A. Magazev; I. V. Shirokov; Yu. A. Yurevich. Integrable magnetic geodesic flows on Lie groups. Teoretičeskaâ i matematičeskaâ fizika, Tome 156 (2008) no. 2, pp. 189-206. http://geodesic.mathdoc.fr/item/TMF_2008_156_2_a2/