Generic properties of 3-dimensional Reeb flows: Birkhoff sections and entropy
Résumé
In this paper we use broken book decompositions to study Reebflows 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 aBirkhoff section for the associated Reeb flow. In view of Irie’s equidistributiontheorem, this is shown to imply that the set of contact forms whose Reeb flowshave 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 positivetopological entropy is open and dense in the C∞-topology.
| Origine | Fichiers produits par l'(les) auteur(s) |
|---|