98-254 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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