Nena-Maria Röttgen: Compact invariant sets do not imply periodic orbits - examples of geodesic, Reeb and Hamiltonian flows

Examples of non vanishing vector fields on closed manifolds without periodic orbits are mainly constructed by using Wilson plugs. I will introduce the definition of a plug and explain how it can be used to find examples of such vector fields. For Reeb flows plugs can not exist but I will present examples of semi contact plugs in dimension five and higher, compare their dynamics with the 3-dimensional situation, show similar results for the geodesic flow and discuss relations to the Weinstein conjecture.Finally I will apply the semi contact plug construction to build Hamiltonian plugs.