Geodesic flows and billiards in the presence of magnetic fields

本项目的目的是研究紧致黎曼流形上磁测地线流和磁台球的定性行为。特别是，哈密顿动力系统的变分方法和现代辛几何的工具将被应用于研究光滑紧致区域和多边形中的磁场动力学。该项目的其他方面涉及磁测地线流的刚性问题，以及辛能力在闭合磁轨迹研究中的应用。

The aim of this project is to investigate the qualitative behaviour of magnetic geodesic flows and magnetic billiards on compact Riemannian manifolds. In particular, variational methods from Hamiltonian dynamical systems and tools from modern symplectic geometry will be applied to study the dynamics of magnetic fields in smooth compact domains and polygons. Other strands of this project are concerned with rigidity questions for magnetic geodesic flows and the application of symplectic capacities to the study of closed magnetic trajectories.