  We present results from a study of the fine structure of oscillon dynamics in
the 3+1 spherically symmetric Klein-Gordon model with a symmetric double-well
potential. We show that in addition to the previously understood longevity of
oscillons, there exists a resonant (and critical) behavior which exhibits a
time-scaling law. The mode structure of the critical solutions is examined, and
we also show that the upper-bound to oscillon formation (in $r_0$ space) is
either non-existent or higher than previously believed. Our results are
generated using a novel technique for implementing non-reflecting boundary
conditions in the finite difference solution of wave equations. The method uses
a coordinate transformation which blue-shifts and ``freezes'' outgoing
radiation. The frozen radiation is then annihilated via dissipation explicitly
added to the finite-difference scheme, with very little reflection into the
interior of the computational domain.
