RUS  ENG
Full version
JOURNALS // Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports]

Sib. Èlektron. Mat. Izv., 2022, Volume 19, Issue 2, Pages 1088–1093 (Mi semr1560)

Non-polynomial integrals of multidimensional geodesic flows and Lie algebras
S. V. Agapov

References

1. G.D. Birkhoff, Dynamical Systems, Colloquium Publications, 9, American Mathematical Society, New York, 1927  crossref  mathscinet  zmath
2. V.V. Kozlov, Symmetries, topology and resonances in Hamiltonian mechanics, Springer-Verlag, Berlin, 1996  mathscinet  zmath
3. V.V. Ten, “Local integrals of geodesic flows”, Regul. Chaotic Dyn., 2:2 (1997), 87–89  mathnet  mathscinet  zmath
4. G. Abdikalikova, A.E. Mironov, “On exact solutions of a system of quasi-linear equations describing integrable geodesic flows on a surface”, Sib. Èlektron. Mat. Izv., 16 (2019), 949–954  crossref  mathscinet  zmath
5. V.N. Kolokol'tsov, “Geodesic flows on two-dimensional manifolds with an additional first integral that is polynomial in the velocities”, Math. USSR, Izv., 21 (1983), 291–306  mathnet  crossref  zmath
6. G. Darboux, Lessons on the general theory of surfaces and the geometric applications of infinitesimal calculus, Gauthier-Villars & Fils, Paris, 1889  mathscinet  zmath
7. G. Heilbronn, Intégration des équations différentielles ordinaires par la méthode de Drach, Gauthier-Villars, Paris, 1956  mathscinet  zmath
8. J. Hietarinta, “New integrable Hamiltonians with transcendental invariants”, Phys. Rev. Lett., 52:1057 (1984)  mathscinet
9. C.D. Collinson, “A note on the integrability conditions for the existence of rational first integrals of the geodesic equations in a Riemannian space”, Gen. Relativ. Gravitation, 18:2 (1986), 207–214  crossref  mathscinet  zmath  adsnasa
10. A.M. Perelomov, Integrable systems of classical mechanics and Lie algebras, Birkhäuser, Basel etc, 1990  mathscinet  zmath
11. C.D. Collinson, P.J. O'Donnell, “A class of empty spacetimes admitting a rational first integral of the geodesic equation”, Gen. Relativ. Gravitation, 24:4 (1992), 451–455  crossref  mathscinet  zmath  adsnasa
12. A.J. Maciejewski, M. Przybylska, “Darboux polynomials and first integrals of natural polynomial Hamiltonian systems”, Phys. Lett., A, 326:3-4 (2004), 219–226  crossref  mathscinet  zmath  adsnasa
13. V.V. Kozlov, “On rational integrals of geodesic flows”, Regul. Chaotic Dyn., 19:6 (2014), 601–606  mathnet  crossref  mathscinet  zmath  adsnasa
14. A. Aoki, T. Houri, K. Tomoda, “Rational first integrals of geodesic equations and generalised hidden symmetries”, Classical Quantum Gravity, 33:19 (2016), 195003  crossref  mathscinet  zmath  adsnasa
15. S. Agapov, V. Shubin, “Rational integrals of 2-dimensional geodesic flows: new examples”, J. Geom. Phys., 170 (2021), 104389  crossref  mathscinet  zmath
16. A. Galajinsky, “Some metrics admitting nonpolynomial first integrals of the geodesic equation”, Phys. Lett., B, 820 (2021), 136483  crossref  mathscinet  zmath
17. J. Patera, R.T. Sharp, P. Winternitz, H. Zassenhaus, “Invariants of real low dimension Lie algebras”, J. Math. Phys., 17 (1976), 986–994  crossref  mathscinet  zmath  adsnasa


© Steklov Math. Inst. of RAS, 2026