  In 1991 Llibre and MacKay proved that if $f$ is a 2-torus homeomorphism
isotopic to identity and the rotation set of $f$ has a non empty interior then
$f$ has positive topological entropy. Here, we give a converselike theorem. We
show that the interior of the rotation set of a 2-torus $C^{1+ \alpha}$
diffeomorphism isotopic to identity of positive topological entropy is not
empty, under the additional hypotheses that $f$ is topologically transitive and
irreducible. We also give examples that show that these hypotheses are
necessary.
