On Rational Integrals of Geodesic Flows

    2014, Volume 19, Number 6, pp.  601-606

    Author(s): Kozlov V. V.

    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.
    Keywords: conformal coordinates, rational integral, irreducible integrals, Cauchy–Kovalevskaya theorem
    Citation: Kozlov V. V., On Rational Integrals of Geodesic Flows, Regular and Chaotic Dynamics, 2014, Volume 19, Number 6, pp. 601-606

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