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This article is cited in 47 scientific papers (total in 48 papers)
Geodesical equivalence and the Liouville integration of the geodesic flows
V. S. Matveeva, P. Ĭ. Topalovb a Max-Planck-Institute f. Mathematik,
Gottfried-Claren-Strasse 26, 53225 Bonn
b Institute of Mathematics and Informatics, BAS,
Acad. G.Bonchev Str., bl. 8,
Sofia, 1113,
Bulgaria
Abstract:
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.
Received: 02.02.1998
Citation:
V. S. Matveev, P. Ĭ. Topalov, “Geodesical equivalence and the Liouville integration of the geodesic flows”, Regul. Chaotic Dyn., 3:2 (1998), 30–45
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https://www.mathnet.ru/eng/rcd937 https://www.mathnet.ru/eng/rcd/v3/i2/p30
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