 00126 N. Chernov
 Sinai billiards under small external forces
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Mar 23, 00

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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 SinaiRuelleBowen (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.
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