Liouville classification of integrable Hamiltonian systems on surfaces of revolution

The algorithm of calculation of the Fomenko–Zieschang invariants for the Hamiltonian systems on 2-dimensional surfaces of revolution is described in this paper in the case of potential $V(r)=\cos r$. One typical example of the investigated system was studied in this article. Classical examples of the systems which are equivalent in the sense of Liouville to the studied system were founded. It is shown that the studied system is equivalent to geodesic flow on corresponding surface.