TITLE:
A geometric approach  to the existence of orbits with
unbounded energy in  generic periodic perturbations
by a potential of generic geodesic flows of  ${\bf T}^{2}$

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 give a proof based in geometric perturbation theory of a result
proved by J.N. Mather using variational methods.
Namely, the existence of orbits with unbounded energy in
perturbations of a generic geodesic flow in ${\bf T}^{2}$
by a generic periodic potential.

KEYWORDS:
geodesic flow, a priori chaotic systems, Melnikov method,
normal hyperbolicity.

1991 MSC numbers:
58F17, 34C37

