论文标题
可整合的Bertrand磁性测量流
Superintegrable Bertrand magnetic geodesic flows
论文作者
论文摘要
旋转对称的自然机械系统中的可整合系统的描述（即具有封闭轨迹的系统）回到Bertrand和Darboux。我们描述了旋转对称的磁性测量流中的所有可整合（在慢速运动的域）系统中。我们表明，当革命的二维流形上，所有足够缓慢的运动是周期性的，并且仅当公制具有恒定的标态曲率并且磁场是均匀的，即与面积形式成正比。
The problem of description of superintegrable systems (i.e., systems with closed trajectories in a certain domain) in the class of rotationally symmetric natural mechanical systems goes back to Bertrand and Darboux. We describe all superintegrable (in a domain of slow motions) systems in the class of rotationally symmetric magnetic geodesic flows. We show that all sufficiently slow motions in a central magnetic field on a two-dimensional manifold of revolution are periodic if and only if the metric has a constant scalar curvature and the magnetic field is homogeneous, i.e. proportional to the area form.
