TITLE: Unbounded growth of energy in periodic perturbations of geodesic flows of the torus AUTHORS: Amadeu Delshams(1), Rafael de la Llave(2), Tere M. Seara(1) (1) Departament de Matem\`atica Aplicada I, Universitat Polit\`ecnica de Catalunya, Diagonal 647, 08028 Barcelona, Spain E-mails: amadeu@ma1.upc.es, tere@ma1.upc.es (2) Department of Mathematics, University of Texas at Austin, Austin, TX, 78712, USA E-mail: llave@math.utexas.edu ABSTRACT: We summarize the main ideas of a paper by the authors. We establish, using geometric methods, a result that had been established by J. Mather using variational methods. Namely, that for generic metrics and potentials---in particular for arbitrarily small potentials and for metrics arbitrarily close to integrable---, one can find orbits whose energy grows to infinity. KEYWORDS: geodesic flow, a priori chaotic systems, Melnikov method, normal hyperbolicity. 1991 MSC numbers: 58F17, 34C37