Stochastic perturbations of convex billiards

R Markarian, L T Rolla, V Sidoravicius, F A Tal, M E Vares
2015 Nonlinearity  
We consider a strictly convex billiard table with $C^2$ boundary, with the dynamics subjected to random perturbations. Each time the billiard ball hits the boundary its reflection angle has a random perturbation. The perturbation distribution corresponds to the physical situation where either the scale of the surface irregularities is smaller than but comparable to the diameter of the reflected object, or the billiard ball is not perfectly rigid. We prove that for a large class of such
more » ... ss of such perturbations the resulting Markov chain is uniformly ergodic, although this is not true in general.
doi:10.1088/0951-7715/28/12/4425 fatcat:fexaas4advgk5c6wsitg5uzfly