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

DOI10.1090/TRAN/9119arXiv2104.10295OpenAlexW3156018177WikidataQ129749734 ScholiaQ129749734MaRDI QIDQ6365782

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Publication date: 20 April 2021

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

Full work available at URL: https://doi.org/10.1090/tran/9119

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