  We study nonlinear dynamics of the kicked particle whose motion is confined
by square billiard. The kick source is considered as localized at the center of
square with central symmetric spatial distribution. It is found that ensemble
averaged energy of the particle diffusively grows as a function of time. This
growth is much more extensive than that of kicked rotor energy. It is shown
that momentum transfer distribution in kicked billiard is considerably
different than that for kicked free particle. Time-dependence of the ensemble
averaged energy for different localizations of the kick source is also
explored. It is found that changing of localization doesn't lead to crucial
changes in the time-dependence of the energy. Also, escape and transport of
particles are studied by considering kicked open billiard with one and three
holes, respectively. It is found that for the open billiard with one hole the
number of (non-interacting) billiard particles decreases according to
exponential law.
