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arXiv · 2104.10295

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

Carolina Lemos de Oliveira
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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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Carolina Lemos de Oliveira. 2021-04-21. $3-2-1$ foliations for Reeb flows on the tight 3-sphere. https://arxiv.org/abs/2104.10295

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