Statistics of visits to zero angle corners of billiards

Abstract

Consider a Sinai billiard table Q (bounded region of the plane, with a finite number of dispersing boundaries âQ;) such that two circular pieces of the boundary are tangent at C . Consider the dynarnical systE'm T describing the free motion of a point mass in Q, with elastic refiections on the boundary (angle of incidence with the normal to the curve equal to the angle of reflection). \V e prove tha.t the sequence of successive entrance times in a certain small neighbourhooà of the comer C converges in law, when suitable normalizeà, to a Poisson point process.