New results and unsolved problems in Liouville classification of integrable Hamiltonian systems

Abstract:
We consider Liouville classification of integrable Hamiltonian systems with two degrees of freedom in terms of the Fomenko-Zieschang invariant. The invariants are calculated for integrable cases of Steklov and Sokolov from rigid body dynamics by the loop molecule method. We also discuss the typical problems that arise in this method.