Generic properties of 3-dimensional Reeb flows: Birkhoff sections and entropy
Résumé
In this paper we use broken book decompositions to study Reeb
flows on closed 3-manifolds. We show that if the Liouville measure of a nonde-
generate contact form can be approximated by periodic orbits, then there is a
Birkhoff section for the associated Reeb flow. In view of Irie’s equidistribution
theorem, this is shown to imply that the set of contact forms whose Reeb flows
have a Birkhoff section contains an open and dense set in the C∞-topology.
We also show that the set of contact forms whose Reeb flows have positive
topological entropy is open and dense in the C∞-topology.
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