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A topological classification of integrable geodesic flows on the two- dimensional sphere with an additional integral quadratic in the momenta. (English) Zbl 0802.58044
A topological classification is given up to topological equivalence of Liouville foliations of all Riemannian metrics on a 2-sphere, having integrable geodesic flows with an additional integral quadratic in the momenta. The classification is computable and the formula for calculating the complexity of the flow is straightforward.

##### MSC:
 37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) 53D25 Geodesic flows in symplectic geometry and contact geometry 37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
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