Integration of geodesic flows on homogeneous spaces: the case of a wild lie group

Details Integration of geodesic flows on homogeneous spaces: the case of a wild lie group Integration of geodesic flows on homogeneous spaces: the case of a wild lie group

2007-03-21

arxiv.org/abs/math-ph/0703064v1

Theoretical and Mathematical Physics, 136(3): 1212-1224 (2003)

Physics

Mathematical Physics

18 pages, 1 figure

Scientific paper

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.

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