Topological analysis of the two-centre problem on the two-dimensional sphere

The two-centre problem on the two-dimensional sphere (with the standard metric of constant positive curvature) is investigated from the topological point of view. The Fomenko–Zieschang invariants are constructed, which completely describe the topology of the Liouville foliations on isoenergy surfaces of this system. Various types of motion in the configuration space (regular motions and limit motions corresponding to bifurcations of Liouville tori) are described. The connection between Fomenko–Zieschang invariants (marked molecules) and various types of motion is considered.