Regular and Chaotic Dynamics

, Volume 14, Issue 4–5, pp 455–465 | Cite as

Isomorphisms of geodesic flows on quadrics

Articles

Abstract

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.

Key words

quadric geodesic flows integrability compactification regularization isomorphism 

MSC2000 numbers

53C22 37Kxx 

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Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  1. 1.Institute of Computer ScienceUdmurt State UniversityIzhevskRussia

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