2014/09/30 by Roberto Markarian, Leonardo T. Rolla, Vladas Sidoravicius +2 · 1 citation
Mathematics · #math.DS #math.PR #msc:37E40 #msc:60J05
paper · pdf · doi:10.1088/0951-7715/28/12/4425
published as Nonlinearity, v. 28, p. 4425-4434, 2015
arxiv created 2018/06/13 · arxiv updated 2018/06/15
We consider a strictly convex billiard table with C2 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 perturbations the resulting Markov chain is uniformly ergodic, although this is not true in general.