  Particle motion in a smoothly oscillating non-integrable billiard is known to
result in unbounded energy growth. Though the asymptotic energy growth rate of
an ensemble of particles in an oscillating chaotic billiard is known to be
quadratic, there are no estimates available for smoothly oscillating
pseudo-integrable billiards. The energy growth rate in such systems is so slow
that it is very hard to predict the asymptotic rates from finite time
computations. In this paper, a method is proposed to estimate the asymptotic
energy growth rate in a system by using short-time data. The idea is applied to
the case of an oscillating pseudo-integrable system, and it is shown that the
asymptotic energy growth rate in such systems could be exponential.
