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

Author:

de Oliveira Carolina

Abstract

We study the existence of 3 2 1 3-2-1 foliations adapted to Reeb flows on the tight 3 3 -sphere. These foliations admit precisely three binding orbits whose Conley-Zehnder indices are 3 3 , 2 2 , and 1 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 3-2-1 foliations with prescribed binding orbits. We also exhibit a concrete Hamiltonian on R 4 \mathbb {R}^4 admitting 3 2 1 3-2-1 foliations when restricted to suitable energy levels.

Funder

Fundação de Amparo à Pesquisa do Estado de São Paulo

Publisher

American Mathematical Society (AMS)

Reference34 articles.

1. Entrelacements et équations de Pfaff;Bennequin, Daniel,1983

2. Compactness results in symplectic field theory;Bourgeois, F.;Geom. Topol.,2003

3. Periodic approximations of irrational pseudo-rotations using pseudoholomorphic curves;Bramham, Barney;Ann. of Math. (2),2015

4. On the existence of supporting broken book decompositions for contact forms in dimension 3;Colin, Vincent;Invent. Math.,2023

5. C. L. de Oliveira, 3-2-1 foliations for Reeb flows on 𝑆³, Ph.D. Thesis, Universidade de São Paulo, 2020.

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