Abstract: 
\def\T{{\sym T}}\def\Z{{\sym Z}}Let $F$ be a homeomorphism of $\T^2=\R^2/\Z^2$
isotopic to the identity and $f$ a lift to the universal covering space $\R^2$. We suppose that
$\kappa\in H^1(\T^2,\R)$ is a cohomology class which is positive on the rotation set of $f$. We prove
the existence of a smooth Lyapunov function of $f$ whose derivative lifts a 
non-vanishing smooth
closed form on $\T^2$ whose cohomology class is
$\kappa$.

1. Laboratoire Analyse,
   Géométrie et Applications
   C.N.R.S.-U.M.R 7539
   Institut Galilée
   Université Paris 13
   Avenue J.-B. Clément
   93430 Villetaneuse, France