We use Lerman’s contact cut construction to find a sufficient condition for Hamiltonian diffeomorphisms of compact surfaces to embed into a closed $3$ -manifold as Poincaré return maps on a global surface of section for a Reeb flow. In particular, we show that the irrational pseudorotations of the $2$ -disc constructed by Fayad and Katok embed into the Reeb flow of a dynamically convex contact form on the $3$ -sphere.

中文翻译：

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- 圆盘和 Reeb 的伪旋转在 - 球面上流动

我们使用 Lerman 的接触切割构造来找到紧致曲面的哈密顿微分同胚嵌入到封闭的充分条件$3$-manifold 作为 Poincaré 在 Reeb 流的全局截面表面上返回映射。特别是，我们证明了$2$- 由 Fayad 和 Katok 构建的圆盘嵌入到 Reeb 流中的动态凸接触形式$3$-领域。