  We investigate the classical and quantum dynamics of an electron confined to
a circular quantum dot in the presence of homogeneous $B_{dc}+B_{ac}$ magnetic
fields. The classical motion shows a transition to chaotic behavior depending
on the ratio $\epsilon=B_{ac}/B_{dc}$ of field magnitudes and the cyclotron
frequency ${\tilde\omega_c}$ in units of the drive frequency. We determine a
phase boundary between regular and chaotic classical behavior in the $\epsilon$
vs ${\tilde\omega_c}$ plane. In the quantum regime we evaluate the quasi-energy
spectrum of the time-evolution operator. We show that the nearest neighbor
quasi-energy eigenvalues show a transition from level clustering to level
repulsion as one moves from the regular to chaotic regime in the
$(\epsilon,{\tilde\omega_c})$ plane. The $\Delta_3$ statistic confirms this
transition. In the chaotic regime, the eigenfunction statistics coincides with
the Porter-Thomas prediction. Finally, we explicitly establish the phase space
correspondence between the classical and quantum solutions via the Husimi phase
space distributions of the model. Possible experimentally feasible conditions
to see these effects are discussed.
