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Isomorphisms of geodesic flows on quadrics. (English) Zbl 1229.37096

Summary: We consider several well-known isomorphisms between Jacobi’s geodesic problem and some integrable cases from rigid body dynamics (the cases of Clebsch and Brun). A relationship between these isomorphisms is indicated. The problem of compactification for geodesic flows on noncompact surfaces is stated. This problem is hypothesized to be intimately connected with the property of integrability.

MSC:

37K25 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry
53C22 Geodesics in global differential geometry
70E40 Integrable cases of motion in rigid body dynamics
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