论文标题
将拓扑熵的Reeb轨道
Reeb orbits that force topological entropy
论文作者
论文摘要
我们开发了一个拓扑熵的强迫理论，用于REEB流量$ 3 $。如果$（y，ξ）$在封闭的联系人中的横向链接$ l $ $ 3 $ - manifold $（y，ξ）$被迫使拓扑熵，那么topogical Entropy the Reeb流动带有消失的拓扑熵，并且每一个reeb上的$（y，ξ）$在$（y，ξ）上实现了一组定期的REEB ORBITS，具有阳性式拓扑构造。我们的主要结果在横向链接$ L $上建立了拓扑条件，这意味着$ l $ tose tose tose拓扑熵。这些条件是根据两个浮子理论不变性的：在Momin引入的横向链接的补充中的圆柱接触同源性，以及在横向链接补充的脱带Legendrian接触同源性。然后，我们使用这些结果表明，在每个封闭的触点上，$ 3 $ - manifold都接受了带有消失的拓扑熵的Reeb流动，存在横向结，强制拓扑熵。
We develop a forcing theory of topological entropy for Reeb flows in dimension $3$. A transverse link $L$ in a closed contact $3$-manifold $(Y,ξ)$ is said to force topological entropy if $(Y,ξ)$ admits a Reeb flow with vanishing topological entropy, and every Reeb flow on $(Y,ξ)$ realizing $L$ as a set of periodic Reeb orbits has positive topological entropy. Our main results establish topological conditions on a transverse link $L$ which imply that $L$ forces topological entropy. These conditions are formulated in terms of two Floer theoretical invariants: the cylindrical contact homology on the complement of transverse links introduced by Momin, and the strip Legendrian contact homology on the complement of transverse links. We then use these results to show that on every closed contact $3$-manifold that admits a Reeb flow with vanishing topological entropy, there exists transverse knots that force topological entropy.
