TITLE: On Birkhoff's conjecture about convex billiards AUTHORS: Amadeu Delshams and Rafael Ramirez-Ros Dept. de Matematica Aplicada I (ETSEIB), Universitat Politecnica de Catalunya, Diagonal 647, 08028 Barcelona (Spain). E-mails: amadeu@ma1.upc.es, rafael@tere.upc.es ABSTRACT: Birkhoff conjectured that the elliptic billiard was the only integrable convex billiard. Here we prove a local version of this conjecture: ANY non-trivial symmetric entire perturbation of an elliptic billiard is non-integrable. BOOK: M. Sofonea and J.-N. Corvellec, editors, Proceedings of the 2nd Catalan Days on Applied Mathematics, Presses univ. de Perpignan, Perpignan, France, 1995, pp. 85-94.