Geodesic
Integration of Geodesic Flows on Homogeneous Spaces: The Case of a Wild Lie Group
Teoretičeskaâ i matematičeskaâ fizika, Tome 136 (2003) no. 3, pp. 365-379

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We obtain necessary and sufficient conditions for the integrability in quadratures of geodesic flows on homogeneous spaces $M$ with invariant and central metrics. The proposed integration algorithm consists in using a special canonical transformation in the space $T^*M$ based on constructing the canonical coordinates on the orbits of the coadjoint representation and on the simplectic sheets of the Poisson algebra of invariant functions. This algorithm is applicable to integrating geodesic flows on homogeneous spaces of a wild Lie group.
Mots-clés : Lie group, Poisson bracket.
Keywords: Lie algebra, homogeneous space, geodesic flow, invariant operator 
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     author = {A. A. Magazev and I. V. Shirokov},
     title = {Integration of {Geodesic} {Flows} on {Homogeneous} {Spaces:} {The} {Case} of a {Wild} {Lie} {Group}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {365--379},
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     volume = {136},
     number = {3},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2003_136_3_a1/}
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A. A. Magazev; I. V. Shirokov. Integration of Geodesic Flows on Homogeneous Spaces: The Case of a Wild Lie Group. Teoretičeskaâ i matematičeskaâ fizika, Tome 136 (2003) no. 3, pp. 365-379. http://geodesic.mathdoc.fr/item/TMF_2003_136_3_a1/