Completely integrable Hamiltonian systems,
algebraic separation of variables, bifurcation diagram, bifurcations of
Liouville tori.
Main publications:
M. P. Kharlamov, P. E. Ryabov, “Bifurcations of the first integrals in the Kowalevski–Yehia case”, Regular and Chaotic Dynamics, 2:2 (1997), 25–40
P. E. Ryabov, “Bifurcations of First Integrals in the Sokolov Case”, Theoret. and Math. Phys., 134:2 (2003), 181–197
P. E. Ryabov, “Explicit integration and the topology of the D. N. Goryachev case”, Doklady Mathematics, 84:1 (2011), 502–505
M. P. Kharlamov, P. E. Ryabov, “Net Diagrams for the Fomenko Invariant in the Integrable System with
Three Degrees of Freedom”, Doklady Mathematics, 86:3 (2012), 839–842
P. E. Ryabov, “Phase topology of one irreducible integrable problem in the dynamics
of a rigid body”, Theoret. and Math. Phys., 176:2 (2013), 1000–1015
ISTINA
