Reeb orbits trapped by Denjoy minimal sets

Let $φ$ 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 $φ$. We realize $(\mathcal A, φ|_{\mathcal A})$ 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, Röttgen and Zehmisch.

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