Certain classical models, such as dispersing billiards, 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 such models is subexponential. Recently, L.-S. Young disproved this conjecture - she established an exponential decay of correlations for a periodic Lorentz gas with finite horizon. We extend this result to all the major classes of dispersing billiards. We also discuss many-particle interacting systems with exponential decay of correlations.
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