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arXiv · 1405.0654

Reeb orbits trapped by Denjoy minimal sets

Takahiro Arai·Takashi Inaba·Yosuke Kano
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Abstract

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.

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Takahiro Arai, Takashi Inaba, Yosuke Kano. 2014-05-04. Reeb orbits trapped by Denjoy minimal sets. https://arxiv.org/abs/1405.0654

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