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

de Oliveira, Carolina

doi:10.1090/tran/9119

$3-2-1$ foliations for Reeb flows on the tight 3-sphere
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by Carolina Lemos de Oliveira

Trans. Amer. Math. Soc.

DOI: https://doi.org/10.1090/tran/9119

Published electronically: April 9, 2024

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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 $\mathbb {R}^4$ admitting $3-2-1$ foliations when restricted to suitable energy levels.

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