Topological entropy and geodesic flows on surfaces (B01)

• Subject Area: Mathematics
• Term: since 2017
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 281071066

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
• Subproject of: TRR 191: Symplectic Structures in Geometry, Algebra and Dynamics
• Applicant Institution: Universität zu Köln
• Co-Applicant Institution: Ruhr-Universität Bochum
• Project Heads: Professor Dr. Barney Bramham; Professor Dr. Umberto Hryniewicz; Professor Dr. Gerhard Knieper