Liouville classification of integrable geodesic flows on a torus of revolution in a potential field

Abstract

A Liouville classification of integrable Hamiltonian systems being geodesic flows on a twodimensional torus of revolution in an invariant potential field is obtained in the case of linear integral. This classification is obtained using the Fomenko–Zieschang invariant (so called marked molecules) of the systems under consideration. All types of bifurcation curves are described. A classification of singularities of the system solutions is also obtained.