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On rational integrals of geodesic flows. (English) Zbl 1343.37047
Summary: 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.

MSC:
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37C10 Dynamics induced by flows and semiflows
37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
35A10 Cauchy-Kovalevskaya theorems
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References:
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