N. Chernov
Sinai billiards under small external forces
(119K, LATeX)

ABSTRACT.  Consider a particle moving freely on the torus and 
colliding elastically with some fixed 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 find general sufficient 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.