报告题目：Closed magnetic geodesics with prescribed energy levels

报告摘要：A magnetic system is a Riemannian manifold equipped with a closed 2-form (called magnetic form). The Lorentz force, which is closely associated with this system, acts on the tangent bundle of the manifold through a specific endomorphism. With in this framework, the motion dynamics of a charged particle moving on the Riemannian manifold under the influence of a magnetic field can be accurately described by a second-order differential equation. A solution of the second-order differential equation is called a magnetic geodesic. A closed magnetic geodesic is a periodic magnetic geodesic and one of the most relevant interests in the theory is the study of existence, multiplicity and free homotopy class of closed magnetic geodesic in a given energy level. In this talk, I will use Morse theory to study the multiplicity of closed magnetic geodesics on a non-compact manifold.

报告人简介：龚文敏，北京师范大学数学科学学院副教授，研究兴趣为辛几何与哈密顿动力系统交叉前沿问题，如退化哈密顿周期解和拉格朗日相交的Arnol'd猜想，闭磁测地线存在性与多解性问题，辛映射类群的分类问题以及Hofer几何等。相关论文发表于 Israel Journal of Mathematics, Nonlinearity, J. Geom. Phys.等杂志上。

报告时间：2025年4月25日16：00-17:00

报告地点：同析4号楼322室