Generic properties of 3-dimensional Reeb flows: Birkhoff sections and entropy - Institut de Mathématiques de Marseille 2014- Access content directly
Preprints, Working Papers, ... Year : 2023

Generic properties of 3-dimensional Reeb flows: Birkhoff sections and entropy

Abstract

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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Dates and versions

hal-04552422 , version 1 (19-04-2024)

Identifiers

  • HAL Id : hal-04552422 , version 1

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Vincent Colin, Pierre Dehornoy, Umberto Hryniewicz, Ana Rechtman. Generic properties of 3-dimensional Reeb flows: Birkhoff sections and entropy. 2024. ⟨hal-04552422⟩
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