Stochastic perturbations preserve statistical features in chaotic billiards but induce non-uniform boundary stationary measures in integrable ones, linking small perturbations to Evans stochastic billiard.
Tabachnikov,Geometry and billiards, (AMS, Provi- dence, 2005)
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Stochastically perturbed billiards: fingerprints of chaos and universality classes
Stochastic perturbations preserve statistical features in chaotic billiards but induce non-uniform boundary stationary measures in integrable ones, linking small perturbations to Evans stochastic billiard.