Rohil Prasad, UC Berkeley

Abstract: In this talk, I'll report on a recent joint preprint (arXiv:2401.14445) with Dan Cristofaro-Gardiner. We explore the topological dynamics of Reeb flows beyond periodic orbits and find the following rather general phenomenon. For any Reeb flow for a torsion contact structure on a closed 3-manifold Y, there exists an infinite family of proper compact invariant subsets whose union is dense in Y. Such a statement is false if the invariant subsets are required to be periodic orbits. Stronger results can also be proved that parallel theorems of Le Calvez-Yoccoz, Franks, and Salazar for homeomorphisms of the 2-sphere. In fact, we can also extend their results to Hamiltonian diffeomorphisms of closed surfaces of any genus.