integrable Hamiltonian systems, magnetic geodesic flows
Main publications:
S. V. Agapov, M. Bialy, A. E. Mironov, “Integrable magnetic geodesic flows on 2-torus: new examples via quasi-linear system of pdes”, Commun. Math. Phys., 351:3 (2017), 993–1007
S. Agapov, A. Valyuzhenich, “Polynomial integrals of magnetic geodesic flows on the 2-torus on several energy levels”, Disc. Cont. Dyn. Syst. - A, 39:11 (2019), 6565-6583
S. Agapov, V. Shubin, “Rational integrals of 2-dimensional geodesic flows: new examples”, Journal of Geometry and Physics, 170 (2021), 104389
S. Agapov, A. Potashnikov, V. Shubin, “Integrable magnetic geodesic flows on 2-surfaces”, Nonlinearity, 36:4 (2023), 2128-2147
S. Agapov, “Local high-degree polynomial integrals of geodesic flows and the generalized hodograph method”, Journal of Geometry and Physics, 217 (2025), 105629
S. V. Agapov, D. V. Solov'ev, “Rational integrals of natural systems in a magnetic field”, Siberian Math. J., 66:3 (2025), 609–617
2.
S. Agapov, “Local high-degree polynomial integrals of geodesic flows and the generalized hodograph method”, Journal of Geometry and Physics, 217 (2025), 105629 , 16 pp.
2024
3.
S. V. Agapov, A. E. Mironov, “Finite-Gap Potentials and Integrable Geodesic Equations on a 2-Surface”, Proc. Steklov Inst. Math., 327 (2024), 1–11
4.
S. Agapov, V. Shubin, “New examples of non-polynomial integrals of two-dimensional geodesic flows”, J. Phys. A: Math. Theor., 57 (2024), 015204 , 17 pp.
S. V. Agapov, M. V. Demina, “Integrable geodesic flows and metrisable second-order ordinary differential equations”, Journal of Geometry and Physics, 199 (2024), 105168 , 14 pp.
S. Basalaev, S. Agapov, “Dynamics in the Kepler problem on the Heisenberg group”, Analysis and Mathematical Physics, 14 (2024), 58 , 15 pp.
2023
7.
S. V. Agapov, “High-degree polynomial integrals of a natural system on the two-dimensional torus”, Siberian Math. J., 64:2 (2023), 261–268
2024
8.
S. V. Agapov, Zh. Sh. Fakhriddinov, “On some properties of semi-Hamiltonian systems arising in the problem of integrable geodesic flows on the two-dimensional torus”, Siberian Math. J., 64:5 (2024), 1063–1075
9.
S. V. Agapov, M. M. Tursunov, “On the rational integrals of two-dimensional natural systems”, Siberian Math. J., 64:4 (2024), 787–795
2023
10.
S. Agapov, A. Potashnikov, V. Shubin, “Integrable magnetic geodesic flows on 2-surfaces”, Nonlinearity, 36:4 (2023), 2128–2147
S. V. Agapov, “Letter to the Editor”, Sib. Èlektron. Mat. Izv., 20:1 (2023), 47
2022
12.
S. V. Agapov, “Non-polynomial integrals of multidimensional geodesic flows and Lie algebras”, Sib. Èlektron. Mat. Izv., 19:2 (2022), 1088–1093
2021
13.
S. V. Agapov, A. A. Valyuzhenich, V. V. Shubin, “Some remarks on high degree polynomial integrals of the magnetic geodesic flow on the two-dimensional torus”, Siberian Math. J., 62:4 (2021), 581–585
14.
S. Agapov, V. Shubin, “Rational integrals of 2-dimensional geodesic flows: new examples”, Journal of Geometry and Physics, 170 (2021), 104389
S. V. Agapov, Siberian Math. J., 61:4 (2020), 563–574
16.
S. V. Agapov, Siberian Math. J., 61:2 (2020), 199–207
2019
17.
Agapov, S., Valyuzhenich, A., “Polynomial integrals of magnetic geodesic flows on the 2-torus on several energy levels”, Discrete and Continuous Dynamical Systems- Series A, 39:11 (2019), 6565-6583
S. V. Agapov, M. R. Borchashvili, “On a certain sub-Riemannian geodesic flow on the Heisenberg group”, Siberian Math. J., 58:6 (2017), 943–951
19.
S. V. Agapov, M. Bialy, A. E. Mironov, “Integrable magnetic geodesic flows on 2-torus: new examples via quasi-linear system of PDEs”, Commun. Math. Phys., 351:3 (2017), 993-1007
S. V. Agapov, “On the sub-Riemannian geodesic flow for the Goursat distribution”, Siberian Math. J., 57:1 (2016), 1–6
2015
21.
S. V. Agapov, “On the integrable magnetic geodesic flow on a 2-torus”, Sib. Èlektron. Mat. Izv., 12 (2015), 868–873
2013
22.
S. V. Agapov, D. N. Alexandrov, “Fourth-Degree Polynomial Integrals of a Natural Mechanical System on a Two-Dimensional Torus”, Math. Notes, 93:5 (2013), 780–783
2025
