On Rational Integrals of Geodesic Flows

    2014, Vol. 10, No. 4, pp.  439-445

    Author(s): Kozlov V. V.

    This paper is concerned with the problem of first integrals of the equations of geodesics on twodimensional 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, Rus. J. Nonlin. Dyn., 2014, Vol. 10, No. 4, pp.  439-445

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