We show that a dynamically convex Reeb flow on the standard tight lens space (L(p, 1), ξ std ), p > 1, admits a p-unknotted closed Reeb orbit P which is the binding of a rational open book decomposition with disk-like pages. Each page is a rational global surface of section for the Reeb flow and the Conley-Zehnder index of the p-th iterate of P is 3. We also check dynamical convexity in the Hénon-Heiles system for low positive energies. In this case the rational open book decomposition follows from the fact that the sphere-like component of the energy surface admits a Z 3 -symmetric periodic orbit and the flow descends to a Reeb flow on the standard tight (L(3, 2), ξ std ).

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SCHNEIDER, A. Global surfaces of section for dynamically convex Reeb flows on L(p, 1) and 3 − 2 2 foliation in the Hénon-Heiles Hamiltonian. Tese (Doutorado)

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