Liouville classification of integrable Hamiltonian systems on surfaces of revolution

An algorithm for calculation of Fomenko-Zieschang invariants for Hamiltonian systems on 2-dimensional surfaces of revolution is described in the case of the potential V (r) = cos r. One typical example of such system is considered. Classic examples of systems equivalent to this system in the sense of Liouville are obtained. It is shown that a system studied on a surface of revolution is Liouville equivalent to a geodesic flow on this surface. © 2015, Allerton Press, Inc.