2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63091This paper addresses the question of genericity of existence of elliptic islands for the billiard map associated to strictly convex closed curves. More precisely, we study 2-periodic orbits of billiards associated to C5 closed and strictly convex curves and show that the existence of elliptic islands is a dense property on the subset of those billiards having an elliptic 2-periodic point. Our main tools are normal perturbations, the Birkhoff Normal Form for elliptic fixed points and Moser's Twist Theorem.12 pages, 6 figuresDynamical Systems37C05, 37E40, 70K42text