Abstract: Reeb vector fields (or flows) of contact structures form an important family of volume preserving vector fields. On a closed 3-manifold, these vector fields always have at least two periodic orbits. The aim of the talk is to introduce broken book decompositions associated to a Reeb flow and deduce from their existence results on the number of periodic orbits: any non-degenerate Reeb vector field has either two or infinitely many periodic orbits. These are results obtained in collaboration with V. Colin and P. Dehornoy. As motivation, I will review other results on the existence of periodic orbits for non-singular vector fields and the known examples without periodic orbits. Finally, I will present other applications of broken book decompositions.
Dienstag, den 7. Februar 2023 um 13:30 Uhr, in INF205, SR B Dienstag, den 7. Februar 2023 at 13:30, in INF205, SR B
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. B. Pozzetti, Prof. P. Albers