Genus zero transverse foliations for weakly convex Reeb flows on the tight 3-sphere
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Naiara V. de Paulo, Umberto Hryniewicz, Seongchan Kim, Pedro A. S. Salomão
2022
Abstract
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. 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.
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