  The quantum density of states of the H\'enon-Heiles potential displays a
pronounced beating pattern. This has been explained by the interference of
three isolated classical periodic orbits with nearby actions and periods. A
singular magnetic flux line, passing through the origin, drastically alters the
beats even though the classical Lagrangean equations of motion remain
unchanged. Some of the changes can be easily understood in terms of the
Aharonov-Bohm effect. However, we find that the standard periodic orbit theory
does not reproduce the diffraction-like quantum effects on those classical
orbits which intersect the singular flux line, and argue that corrections of
relative order $\hbar$ are necessary to describe these effects. We also discuss
the changes in the distribution of nearest-neighbour spacings in the eigenvalue
spectrum, brought about by the flux line. pacs{PACS numbers: 05.45.+b,
02.50.+s,03.65.-w,03.65.Ge }
