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

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.