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

