3-2-1 foliations for Reeb flows on the tight 3-sphere

2021/04/21 by Carolina Lemos de Oliveira, de Oliveira, Carolina Lemos
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2104.10295

openalex publication_date 2021/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the existence of 3-2-1 foliations adapted to Reeb flows on the tight 3-sphere. These foliations admit precisely three binding orbits whose Conley-Zehnder indices are 3, 2, and 1, respectively. All regular leaves are disks and annuli asymptotic to the binding orbits. Our main results provide sufficient conditions for the existence of 3-2-1 foliations with prescribed binding orbits. We also exhibit a concrete Hamiltonian on ℝ⁴ admitting 3-2-1 foliations when restricted to suitable energy levels.

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