Sinai billiards under small external forces

Consider a particle moving freely on the torus and colliding elastically wi th some fixed convex bodies. This model is called a periodic Lorentz gas, o r a Sinai billiard. It is a Hamiltonian system with a smooth invariant meas ure, whose ergodic and statistical properties have been well investigated. Now let the particle be subjected to a small external force. This new syste m is not likely to have a smooth invariant measure. Then a Sinai-Ruelle-Bow en (SRB) measure describes the evolution of typical phase trajectories. We find general sufficient conditions on the external force under which the SR B measure for the collision map exists, is unique, and enjoys good ergodic and statistical properties, including Bernoulliness and an exponential deca y of correlations.