  We examine the long-term time-dependence of Gaussian wave packets in a
circular infinite well (billiard) system and find that there are approximate
revivals. For the special case of purely $m=0$ states (central wave packets
with no momentum) the revival time is $T_{rev}^{(m=0)} = 8\mu R^2/\hbar \pi$,
where $\mu$ is the mass of the particle, and the revivals are almost exact. For
all other wave packets, we find that $T_{rev}^{(m \neq 0)} = (\pi^2/2)
T_{rev}^{(m=0)} \approx 5T_{rev}^{(m=0)}$ and the nature of the revivals
becomes increasingly approximate as the average angular momentum or number of
$m \neq 0$ states is/are increased. The dependence of the revival structure on
the initial position, energy, and angular momentum of the wave packet and the
connection to the energy spectrum is discussed in detail. The results are also
compared to two other highly symmetrical 2D infinite well geometries with exact
revivals, namely the square and equilateral triangle billiards. We also show
explicitly how the classical periodicity for closed orbits in a circular
billiard arises from the energy eigenvalue spectrum, using a WKB analysis.
