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

2022/06/26 by Naiara V. de Paulo, Umberto L. Hryniewicz, de Paulo, Naiara V. +5
Computer Science · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Symplectic Geometry (math.SG) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2206.12856

openalex publication_date 2022/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A contact form on the tight 3-sphere (S30) 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 (S30) 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.

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