Literature cited
V. V. Kozlov, “Topological obstructions to integrability of natural mechanical systems,” Dokl. Akad. Nauk SSSR,249, No. 6, 1299–1302 (1979).
D. V. Anosov, “Geodesic flows on closed Riemannian manifolds of negative curvature,” Tr. Mat. Inst. Akad. Nauk (MIAN),90, (1967).
V. V. Kozlov, “Groups of symmetries of dynamical systems,” PMM,52, No. 4, 531–541 (1988).
A. N. Kolmogorov, “Dynamical systems with integral invariant on the torus,” Dokl. Akad. Nauk SSSR,93, 763–766 (1953).
G. Birkoff, Dynamical Systems [Russian translation], Gostekhizdat, Moscow-Léningrad (1941).
V. N. Kolokol'tsov, “Geodesic flows on two-dimensional manifolds with supplementary first integral polynomial in the velocities,” Izv. Akad. Nauk SSSR, Ser. Mat.,46, No. 5, 994–1010 (1982).
S. V. Bolotin, “Nonintegrability of the problem of n centers for n > 2,” Vestn., Moscow State University, Ser. 1, Mat. Mekhan., No. 3, 65–68 (1984).
I. A. Taimanov, “Topological properties of integrable geodesic flows,” Mat. Zametki,44, No. 2, 283–284 (1988).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 48, No. 5, pp. 62–67, November, 1990.
Rights and permissions
About this article
Cite this article
Kozlov, V.V. Groups of symmetries of geodesic flows on closed surfaces. Mathematical Notes of the Academy of Sciences of the USSR 48, 1119–1122 (1990). https://doi.org/10.1007/BF01236297
Issue Date:
DOI: https://doi.org/10.1007/BF01236297