Geodesic flows and billiards in the presence of magnetic fields

存在磁场时的测地线流和台球

• 批准号: 42369092
• 负责人: Professor Dr. Karl Friedrich Siburg
• 金额: --
• 依托单位: Lehrstuhl IX: Analysis, Mathematische Physik und Dynamische Systeme
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2007
• 资助国家: 德国
• 起止时间: 2006-12-31 至 2009-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/42369092?language=en
• 关键词: Geodesic; flows; billiards; presence; magnetic

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.

这个项目的目的是研究紧致黎曼流形上的磁测地线流和磁台球的定性行为。特别是，变分方法从哈密顿动力系统和工具，从现代辛几何将被应用到研究磁场的动态光滑紧凑的域和多边形。这个项目的其他股关注的刚性问题的磁测地流和应用辛能力的研究封闭的磁轨迹。