Regular and Chaotic Dynamics

, Volume 19, Issue 6, pp 601–606 | Cite as

On rational integrals of geodesic flows

  • Valery V. Kozlov


This paper is concerned with the problem of first integrals of the equations of geodesics on two-dimensional surfaces that are rational in the velocities (or momenta). The existence of nontrivial rational integrals with given values of the degrees of the numerator and the denominator is proved using the Cauchy-Kovalevskaya theorem.


conformal coordinates rational integral irreducible integrals Cauchy-Kovalevskaya theorem 

MSC2010 numbers

34A34 58E10 


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Copyright information

© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia

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