Reeb orbits that force topological entropy

Abstract We develop a forcing theory of topological entropy for Reeb flows in dimension three. A transverse link L closed contact $3$ -manifold $(Y,\xi )$ is said to force if admits flow with vanishing entropy, and every on realizing as set periodic orbits has positive entropy. Our main results establish conditions , which imply that forces These are formulated terms two Floer theoretical invariants: the cylindrical homology complement links introduced by Momin [A. Momin. J. Mod. Dyn. 5 (2011), 409–472], strip Legendrian links, Alves [M. R. Alves. PhD Thesis Université Libre de Bruxelles, 2014] further developed here. then use these show there exist knots