Year: 2026
Type: preprint
Abstract: 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 $α$. Our first result states that under these hypotheses, there exists a unique $f$-invariant foliation $\mathcal{F}_G=\{\operatorname{Graph}(ϕ_t)\}_{t\in\mathbf{T}^1}$, where each function $ϕ_t:\mathbf{T}^1\to\mathbf{T}^1$ is $K$-Lipschitz for some constant $K=K(f)$. Moreover, we also prove that if $\mathcal{F}_G$ is a Lipschitz foliation, then $f$ is minimal.
Source: arXiv (Cornell University)
Institution: Universidade de São Paulo
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214181590