Abstract
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.
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Kozlov, V.V. On rational integrals of geodesic flows. Regul. Chaot. Dyn. 19, 601–606 (2014). https://doi.org/10.1134/S156035471406001X
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DOI: https://doi.org/10.1134/S156035471406001X