2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/221318We introduce the concepts of rotation numbers and rotation vectors for billiard maps. Our approach is based on the birkhoff ergodic theorem. We anticipate that it will be useful, in particular, for the purpose of establishing the non-ergodicity of billiard in certain domains.Dynamical Systems37E45; 37A10text