  We study some dynamical properties of a Lorentz gas. We have considered both
the static and time dependent boundary. For the static case we have shown that
the system has a chaotic component characterized with a positive Lyapunov
Exponent. For the time-dependent perturbation we describe the model using a
four-dimensional nonlinear map. The behaviour of the average velocity is
considered in two situations (i) non-dissipative and (ii) dissipative. Our
results show that the unlimited energy growth is observed for the
non-dissipative case. However, when dissipation, via damping coefficients, is
introduced the senary changes and the unlimited engergy growth is suppressed.
The behaviour of the average velocity is described using scaling approach.
