Phase portraits of the two-body problem with Manev potential (Q2716263)

The well-known Manev two-body problem is described by the potential \(V(r)=a/r+ b/r^2\), where \(r\) is the distance between the bodies, and \(a\), \(b\) are arbitrary constants. The authors describe the global flow of Manev system for varying \(a\) and \(b\), and examine the foliation of phase space by invariant sets. The Liouville-Arnold theory of integrable Hamiltonian systems is applied to the Manev system to calculate critical points and critical values for special maps. Hill regions are classified according to different values of \(a\) and \(b\). This is followed by a study of energy levels and topological invariants.