A semi-theoretical method to detect classical monodromy

An integrable Hamiltonian system presents monodromy if the action-angle variables cannot be defined globally. We consider a classical system with azimuthal symmetry and explore the topology structure of its phase space. Based on the behavior of closed orbits around singular points or regions of the energy-momentum plane, a semi-theoretical method is derived to detect classical monodromy. The validity of the monodromy test is numerically illustrated for several systems with azimuthal symmetry.