Geodesic
Isomorphisms of geodesic flows on quadrics
Russian journal of nonlinear dynamics, Tome 5 (2009) no. 2, pp. 145-158.

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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.
Mots-clés : quadric, compactification, isomorphism.
Keywords: geodesic flows, integrability, regularization 
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     author = {A. V. Borisov and I. S. Mamaev},
     title = {Isomorphisms of geodesic flows on quadrics},
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A. V. Borisov; I. S. Mamaev. Isomorphisms of geodesic flows on quadrics. Russian journal of nonlinear dynamics, Tome 5 (2009) no. 2, pp. 145-158. http://geodesic.mathdoc.fr/item/ND_2009_5_2_a0/