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

Author(s)

de Paulo, Naiara V. ; Hryniewicz, Umberto ; Kim, Seongchan ; Salomao, Pedro A. S.

• Document type: Journal article
• Source: ADVANCES IN MATHEMATICS; v. 457, p. 55-pg., 2024-09-06.

Abstract

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, we 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. 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. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC license (http:// creativecommons .org /licenses /by -nc /4 .0/). (AU)

• FAPESP's process: 16/25053-8 - Dynamics and geometry in low dimensions
• Grantee: André Salles de Carvalho
• Support Opportunities: Research Projects - Thematic Grants