Abstract:Stable Hamiltonian structures generalize contact forms and define a volume-preserving vector field known as the Reeb vector field. These structures appear along a stable regular energy level set of a Hamiltonian system, where the Reeb field is just a reparametrization of the Hamiltonian vector field. We study two aspects of Reeb vector fields defined by stable Hamiltonian structures in 3-manifolds: on one hand, we classify all the examples with finitely many periodic orbits under a non-degeneracy condition; on… Show more
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