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Stable Hamiltonian structures generalize contact forms and define avolume-preserving vector field known as the Reeb vector field. We study twoaspects of Reeb vector fields defined by stable Hamiltonian structures on3-manifolds: on one hand, we classify all the examples with finitely manyperiodic orbits under a non-degeneracy condition; on the other, we givesufficient conditions for the existence of a supporting broken bookdecomposition and for the existence of a Birkhoff section.

Periodic orbits and Birkhoff sections of stable Hamiltonian structures