The diamagnetic Kepler problem

It has turned out that the analysis ofclassical periodic orbits is the key to understanding the modulations in thequantal spectra of hydrogen Rydberg atoms in magnetic fields. Inspired by this quantum chaological connection, we analyse some fundamental periodic orbits of the diamagnetic Kepler problem, abandoning the condition of vanishing azimuthal angular momentuml _z used in the literature so far. We report the bifurcation and confluence schemes of the orbits in their dependence onl _z and discuss the structural changes in terms of catastrophe theory.