On the dynamics of minimal homeomorphisms of $\mathbb{T}^2$ which are   not pseudo-rotations
  We prove that any minimal $2$-torus homeomorphism which is isotopic to the identity and whose rotation set is not just a point exhibits uniformly bounded rotational deviations on the perpendicular direction to the rotation set. As a consequence of this, we show that any such homeomorphism is topologically mixing and we prove Franks-Misiurewicz conjecture under the assumption of minimality. 
Alejandro Kocsard
math.DS