Geodesical equivalence and the Liouville integration of the geodesic flows
1998, Volume 3, Number 2, pp. 30-45
Author(s): Matveev V. S., Topalov P. I.
Author(s): Matveev V. S., Topalov P. I.
We suggest a simple approach for obtaining integrals of Hamiltonian systems if there is known a trajectorian map of two Hamiltonian systems. An explicite formila is given. As an example, it is proved that if on a manifold are given two Riemannian metrics which are geodesically equivalent then there is a big family of integrals. Our theorem is a generalization of the well-known Painleve–Liouville theorems.
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