论文标题
零侧叶零横向叶子，用于紧密$ 3 $ -sphere上的弱凸reb
Genus zero transverse foliations for weakly convex Reeb flows on the tight $3$-sphere
论文作者
论文摘要
如果每个Reeb轨道的Conley-Zehnder索引至少为$ 2 $，则紧密的$ 3 $ -sphere $（S^3，ξ_0）$的联系表被称为弱凸。在本文中，我们在$（s^3，ξ_0）上研究了弱凸触点表格的Reeb流，并承认规定有限的索引套件 - $ 2 $ reeb orbits，它们都是双曲线且相互无链接的。我们提出条件，使这些指数 - $ 2 $轨道是零横向叶片属的绑定轨道，其额外的装订轨道具有索引$ 3 $。此外，我们在现实分析的情况下表明，如果指数稳定/不稳定的歧管的分支 - $ 2 $旋转是相互不合理的，则REEB流的拓扑熵为正。
A contact form on the tight $3$-sphere $(S^3,ξ_0)$ is called weakly convex if the Conley-Zehnder index of every Reeb orbit is at least $2$. In this article, we study Reeb flows of weakly convex contact forms on $(S^3,ξ_0)$ admitting a prescribed finite set of index-$2$ Reeb orbits, which are all hyperbolic and mutually unlinked. We present conditions so that these index-$2$ orbits are binding orbits of a genus zero transverse foliation whose additional binding orbits have index $3$. In addition, we show in the real-analytic case that the topological entropy of the Reeb flow is positive if the branches of the stable/unstable manifolds of the index-$2$ orbits are mutually non-coincident.
