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 -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