Séminaire de Géométrie, Groupes et Dynamique

Pierre Dehornoy: "Broken books and Reeb dynamics"

Europe/Paris
435 (UMPA)

435

UMPA

Description
Given a vector field in a 3-manifold, an open book decomposition is a topological decomposition of the manifold that allows to study the dynamics of the vector field through a first-return map on a surface. 
Unfortunately, open book decompositions rarely exist. 
In the context of contact geometry, it is known by Giroux Correspondance that every contact structure admits a contact form which admits an open book decomposition. 
However nothing is known for a given contact form or, equivalently, for a given Reeb vector field. 
In a recent work with Colin and Rechtman, we propose a weaker version that we call broken book decomposition. We prove that generic Reeb flows admit broken book decompositions, and use them to prove dynamical properties, in particular concerning the number of periodic orbits and the entropy of such flows.