Reeb orbits trapped by Denjoy minimal sets

Abstract

Let φ be any flow on T ⁿ obtained as the suspension of a smooth diffeomorphism of ${T^{n-1}}$, and let ${\mathcal {A}}$ be any compact invariant set of φ. We realize ${(\mathcal{A}, \varphi|_{\mathcal{A}})}$ up to reparametrization as an invariant set of the Reeb flow of a contact form on ${\mathbb{R}^{2n+1}}$ equal to the standard contact form outside a compact set and defining the standard contact structure on all of ${\mathbb{R}^{2n+1}}$. This uses the method from Geiges, Röttgen, and Zehmisch.