Sinai Billiards under Small External Forces

Consider a particle moving freely on the torus and colliding elastically with some xed convex bodies. This model is called a periodic Lorentz gas, or a Sinai billiard. It is a Hamiltonian system with a smooth invariant measure, whose ergodic and statistical properties have been well investigated. Now let the particle be subjected to a small external force. This new system is not likely to have a smooth invariant measure. Then a Sinai-Ruelle-Bowen (SRB) measure describes the evolution of typical phase trajectories. We nd general suucient conditions on the external force under which the SRB measure for the collision map exists, is unique, and enjoys good ergodic and statistical properties, including Bernoulliness and an exponential decay of correlations.