  Classical stationary points of an analytic Hamiltonian induce singularities
of the density of quantum energy levels and their flow with a control parameter
in the system's infinite-size limit. We show that for a system with $f$ degrees
of freedom, a non-degenerate stationary point with index $r$ causes a
discontinuity (for $r$ even) or divergence ($r$ odd) of the $(f-1)$ th
derivative of both density and flow of the spectrum. An increase of flatness
for a degenerate stationary point shifts the singularity to lower derivatives.
The findings are verified in an $f=3$ toy model.
