  We propose a model of Sinai billiards with moving scatterers, in which the
locations and shapes of the scatterers may change by small amounts between
collisions. Our main result is the exponential loss of memory of initial data
at uniform rates, and our proof consists of a coupling argument for
non-stationary compositions of maps similar to classical billiard maps. This
can be seen as a prototypical result on the statistical properties of
time-dependent dynamical systems.
