Symplectic methods for generalized billiards (B08)

• Subject Area: Mathematics
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 281071066

The main goal of this project is to explore the reach of methods from symplectic dynamics, especially holomorphic curve theory, to study billiard dynamics on two-dimensional tables with an emphasis on non-convex tables. We will construct transverse foliations for Reeb flows approximating the billiards dynamics and draw dynamical conclusions via a limiting procedure. We expect new qualitative and quantitative existence results for periodic orbits, as well as new ways to detect topological entropy and hyperbolicity in these systems.

• DFG Programme: CRC/Transregios
• Subproject of: TRR 191: Symplectic Structures in Geometry, Algebra and Dynamics
• Applicant Institution: Universität zu Köln
• Project Heads: Professor Dr. Peter Albers; Professor Dr. Barney Bramham; Professor Dr. Umberto Hryniewicz