English

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

Dynamical Systems 2020-02-11 v4

Abstract

We prove that any minimal 22-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.

Keywords

Cite

@article{arxiv.1611.03784,
  title  = {On the dynamics of minimal homeomorphisms of $\mathbb{T}^2$ which are not pseudo-rotations},
  author = {Alejandro Kocsard},
  journal= {arXiv preprint arXiv:1611.03784},
  year   = {2020}
}

Comments

37 pages, 5 figures. To appear in Ann. Sci. \'Ecole Norm. Sup