 98254 N. Chernov
 Decay of correlations and dispersing billiards
(113K, LATeX)
Apr 2, 98

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Abstract. Dispersing billiards (or Sinai billiards)
are classical models of dynamical systems that exhibit
strong chaotic behavior but are highly nonlinear and
contain singularities. It was a long standing conjecture
that, due to singularities, the rate of the decay of
correlations in dispersing billiards (or the rate of
mixing, or the speed of relaxation to equilibrium)
is subexponential, i.e. slower than that in Anosov
and Axiom~A systems. Recently, L.S.~Young disproved
this conjecture  she established an exponential decay
of correlations for a periodic Lorentz gas with finite
horizon. We prove the same result for all the major
classes of planar dispersing billiards, including
Lorentz gases without horizon and tables with corner
points. We also design and prove a general theorem on
the exponential decay of correlations for smooth hyperbolic
systems with singularities, which is particularly convenient
for physical models like billiards.
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