Bertrand systems on spaces of constant sectional curvature. The action-angle analysis (Q5938518)

Bertrand systems, i.e. isotropic potential systems for which all bounded orbits are closed, on three-dimensional spaces of constant curvature are discussed, with special stress on the analysis in terms of action-angle variables and the corresponding problems of quasiclassical analysis and quantization. It is proved that from the action-angle point of view, these models are described by formulae additively combining the corresponding expressions in Euclidean space with expressions from free geodetic motion.