Genus zero transverse foliations for weakly convex Reeb flows on the tight 3-sphere (Q6633098)

A contact form on the tight \(3\)-sphere \((S^3, \xi_0)\) is called weakly convex if the Conley-Zehnder index of every Reeb orbit is at least \(2\). In this article, the authors study Reeb flows of weakly convex contact forms on \((S^3, \xi_0)\) admitting a prescribed finite set of index-\(2\) Reeb orbits, which are all hyperbolic and mutually unlinked. They provide 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, they 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.