Abstract. 
We consider a bounded domain on the plane containing N rotating disks
pinned down at their centers. The system is coupled to heat baths that
absorb and emit particles through several openings on the boundary of
the domain. The particles do not interact with each other, have
specular collisions with the boundary of the domain, and exchange
energy with the disks.

For certain classes of such systems, we show that if there exists an
invariant measure with support away from the states with "trapped
trajectories", then it is both absolutely continuous and ergodic. The
key properties of the system that lead to absolute continuity and
ergodicity are randomness of the injection process and ability to
control angular velocities of the disks through appropriate particle
injections.