Topology of the Liouville foliation on a 2-sphere in the Dullin-Matveev integrable case

The paper is concerned with the study of the topology of the Liouville foliations of the Dullin-Matveev integrable case. The critical point set of the Hamiltonian is found, the types of isoenergy surfaces are calculated, the non-degeneracy conditions are verified, the types of non-degenerate points of the Poisson action are determined, the moment map is investigated and the bifurcation diagram is constructed. A test for the Bott property is verified by numerical simulation. The indices of critical circles, the bifurcation types and the rough molecules are found. The rough Liouville classification of this integrable case is virtually accomplished as a result. Bibliography: 24 titles