Isomorphisms of geodesic flows on quadrics

    2009, Volume 14, Numbers 4-5, pp.  455-465

    Author(s): Borisov A. V., Mamaev I. S.

    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.
    Keywords: quadric, geodesic flows, integrability, compactification, regularization, isomorphism
    Citation: Borisov A. V., Mamaev I. S., Isomorphisms of geodesic flows on quadrics, Regular and Chaotic Dynamics, 2009, Volume 14, Numbers 4-5, pp. 455-465

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