On the dynamics of minimal homeomorphisms of $\mathbb{T}^2$ which are not pseudo-rotations

Alejandro Kocsard

Published 2016-11-11Version 1

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 either semi-conjugate to an irrational circle rotation, or is topologically mixing.