False singularities in partial sums over closed orbits

The contribution to the spectral density from all the repetitions of a single classical closed orbit can have singularities that are not eigenenergies of the system. Only by summing over all different topologies of orbits do these false singularities get replaced by delta peaks at the true eigenenergies. The authors illustrate this with an example where the expansion and sum over repetitions are exact rather than asymptotic.