Julian Lazaro Aguirre

Foliations and minimality for twist maps

In this paper we consider area-preserving twist maps $f:\mathbf{T}^2\to\mathbf{T}^2$ with vertical rotation sets reduced to a single irrational number $\alpha$. Our first result states that under these hypotheses, there exists a $f$-invariant foliation $\mathcal{F}_G=\{\operatorname{Graph}(\phi_t)\}_{t\in\mathbf{T}^1}$...