论文标题
$ 3 $维的通用属性Reeb流量：Birkhoff部分和熵
Generic properties of $3$-dimensional Reeb flows: Birkhoff sections and entropy
论文作者
论文摘要
在本文中，我们使用破碎的书籍分解来研究关闭$ 3 $ manifolds的Reeb流。我们表明，如果可以通过周期性轨道近似地近似liouville的态度，那么相关的REEB流程有一个Birkhoff部分。鉴于IRIE的等分定理，这表明这意味着其REEB流的一组联系表包含Birkhoff部分，其中包含$ C^\ Infty $ - 多面体学中的开放和密集的集合。我们还表明，在$ c^\ infty $ topology中，REEB流动的呈正拓扑熵的一组接触形式是开放且密集的。
In this paper we use broken book decompositions to study Reeb flows on closed $3$-manifolds. We show that if the Liouville measure of a nondegenerate contact form can be approximated by periodic orbits, then there is a Birkhoff section for the associated Reeb flow. In view of Irie's equidistribution theorem, this is shown to imply that the set of contact forms whose Reeb flows have a Birkhoff section contains an open and dense set in the $C^\infty$-topology. We also show that the set of contact forms whose Reeb flows have positive topological entropy is open and dense in the $C^\infty$-topology.
