  The classical dynamics of a particle that is driven by a rapidly oscillating
potential (with frequency $\omega$) is studied. The motion is separated into a
slow part and a fast part that oscillates around the slow part. The motion of
the slow part is found to be described by a time-independent equation that is
derived as an expansion in orders of $\omega^{-1}$ (in this paper terms to the
order $\omega^{-3}$ are calculated explicitly). This time-independent equation
is used to calculate the attracting fixed points and their basins of
attraction. The results are found to be in excellent agreement with numerical
solutions of the original time-dependent problem.
