论文标题
2步尼尔曼叶元上的磁轨迹
Magnetic trajectories on 2-step nilmanifolds
论文作者
论文摘要
这项工作的目的是研究Nilmanifolds上的磁轨迹。编写了磁方程，并在配备有左右变体度量的2步nilpotent Lie组上找到了一个不变的Lorentz力的家族的相应溶液。在Heisenberg Lie组中计算了一些示例，$ n = 3,5 $，显示与精确表格的情况有所不同。与椭圆形积分相关的有趣磁轨迹出现在$ H_3 $中。治疗了每个能级或紧凑型商的封闭或周期性磁轨迹存在的问题。
The aim of this work is the study of magnetic trajectories on nilmanifolds. The magnetic equation is written and the corresponding solutions are found for a family of invariant Lorentz forces on a 2-step nilpotent Lie group equipped with a left-invariant metric. Some examples are computed in the Heisenberg Lie groups $H_n$ for $n=3,5$, showing differences with the case of exact forms. Interesting magnetic trajectories related to elliptic integrals appear in $H_3$. The question of existence of closed or periodic magnetic trajectories for every energy level on Lie groups or on compact quotients is treated.
