Work

Periodic orbits and Birkhoff sections of stable Hamiltonian structures

Year: 2025

Type: article

Abstract: Stable Hamiltonian structures generalize contact forms and define a volume-preserving vector field known as the Reeb vector field. We study two aspects of Reeb vector fields defined by stable Hamiltonian structures on 3 -manifolds: on the one hand, we classify all the examples with finitely many periodic orbits under a non-degeneracy condition; on the other, we give sufficient conditions for the existence of a supporting broken book decomposition and for the existence of a Birkhoff section.

Source: Journal de l’École polytechnique — Mathématiques

DOI: 10.5802/jep.289

Authors: Robert Cardona, Ana Rechtman