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.