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

Abstract

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.

37 pages, 5 figures. To appear in Ann. Sci. École Norm. Sup

References in corpus (2)

• Forcing theory for transverse trajectories of surface homeomorphisms
• Rotational deviations and invariant pseudo-foliations for periodic point free torus homeomorphisms

Cited by in corpus (2)

• Rotational deviations and invariant pseudo-foliations for periodic point free torus homeomorphisms
• Inexistence of sublinear diffusion for a class of torus homeomorphisms