论文标题
关于支持损坏的书籍分解的联系形式3
On the existence of supporting broken book decompositions for contact forms in dimension 3
论文作者
论文摘要
我们证明，在维度3中，每种非等级接触表格都是由破损的书籍分解携带的。作为一种应用，我们会发现，如果M是一个不可约定的面向的3个manifold，它不是图形的歧管，例如双曲线歧管，则M上的每个非等级Reeb vector场都具有正拓扑熵。此外，我们在封闭的3个manifold上获得，每个非排效Reeb矢量场都有两个或无限的周期轨道，并且只有在球体或镜头空间上才有两个周期轨道。
We prove that in dimension 3 every nondegenerate contact form is carried by a broken book decomposition. As an application we get that if M is a closed irreducible oriented 3-manifold that is not a graph manifold, for example a hyperbolic manifold, then every nondegenerate Reeb vector field on M has positive topological entropy. Moreover, we obtain that on a closed 3-manifold, every nondegenerate Reeb vector field has either two or infinitely many periodic orbits, and two periodic orbits are possible only on the sphere or on a lens space.
