In this project we will investigate to what extent certain dynamical phenomena that are well understood for geodesic flows on surfaces have a symplectic counterpart in the larger class of Reeb flows in dimension three. For this purpose we intend to combine methods from symplectic topology, such as holomorphic curve theory, with methods from dynamical systems, such as smooth ergodic theory. We are especially interested in integrable behaviour of such systems in the case of vanishing topological entropy, conditions forcing positive topological entropy, and associated dynamical phenomena such as exponential growth rate und uniform distribution of periodic orbits.
DFG Programme
CRC/Transregios
