Rotation sets with nonempty interior and transitivity in the universal   covering
  Let $f$ be a transitive homeomorphism of the two-dimensional torus in the homotopy class of the identity. We show that a lift of $f$ to the universal covering is transitive if and only if the rotation set of the lift contains the origin in its interior. 
Nancy Guelman, Andres Koropecki and Fabio Armando Tal
math.DS