Broken book decompositions for generic Reeb vector elds
Ana Rechtman (Univ. Grenoble Alpes, França)

An important class of non-singular volume preserving vector elds are Reeb vector elds. In dimension 3 these have been the subject of study in the last few decades, in particular around the problem of the existence of periodic orbits. We now know that every Reeb vector has at least two periodic orbits (a result proved by Cristofaro-Gardiner and Hutchings in 2016). In this talk I will explain that a non-degenerate Reeb vector elds admits a systems of transverse surfaces with boundary that form a broken book decomposition of the ambient 3-manifold. A broken book decomposition is a generalization of an open book decomposition. Broken book decompositions have proved to very useful for studying dynamical aspects of a Reeb vector eld, in particular it allows to prove that a non-degenerate Reeb vector eld has either two or innitely many periodic orbits, and to give results on the topological entropy of the ow.

This is a joint work with V. Colin and P. Dehornoy.