Geodesic
On rational integrals of geodesic flows
Russian journal of nonlinear dynamics, Tome 10 (2014) no. 4, pp. 439-445

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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. 
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     author = {Valery V. Kozlov},
     title = {On rational integrals of geodesic flows},
     journal = {Russian journal of nonlinear dynamics},
     pages = {439--445},
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     number = {4},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2014_10_4_a3/}
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Valery V. Kozlov. On rational integrals of geodesic flows. Russian journal of nonlinear dynamics, Tome 10 (2014) no. 4, pp. 439-445. http://geodesic.mathdoc.fr/item/ND_2014_10_4_a3/