Let $\varphi$ be any flow on $T^n$ obtained as the suspension of a diffeomorphism of $T^{ n-1}$ and let $\mathcal A$ be any compact invariant set of $\varphi$. 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 generalizes the construction of Geiges, R\"ottgen and Zehmisch.
Categories: math.SG math.DS