Periodic orbit theory revisited in the anisotropic Kepler problem

o (φ) from both quantum subsectors show peaks at the actions of the periodic orbits with correct peak heights and widths corresponding to their Lyapunov expo- nents. The formulation takes care of the cut-off of the energy levels, and the agreement between the D(φ)s of the quantum mechanical (QM) and POT sides is observed to be independent of the choice of cut-off. The systematics appearing in the densities of the periodic orbits is explained in terms of features of the periodic orbits. It is shown that, from quantum energy levels, one can extract information on AKP periodic orbits, even the Lyapunov exponents—the success of inverse quantum chaology in AKP.