论文标题
混乱的粒子运动围绕均匀的圆环
Chaotic particle motion around a homogeneous circular ring
论文作者
论文摘要
我们考虑通过放置在$ n $维欧几里得空间中的同质圆环产生的重力场中的测试粒子运动。我们观察到，在$ n = 6、7，\ ldots，10 $中没有稳定的固定轨道，但存在于$ n = 3、4、5 $中，并澄清它们出现的区域。在$ n = 3 $中，我们表明汉密尔顿 - 雅各比方程的变量的分离并未发生，尽管我们没有发现稳定绑定轨道的混乱迹象。由于该系统可集成在$ n = 4 $中，因此不会出现混乱。在$ n = 5 $中，我们找到了一些混乱的稳定界限。因此，该系统至少在$ n = 5 $中是不可集成的，并表明相应的黑色环空间中的时间型地测量系统是不可整合的。
We consider test particle motion in a gravitational field generated by a homogeneous circular ring placed in $n$-dimensional Euclidean space. We observe that there exist no stable stationary orbits in $n=6, 7, \ldots, 10$ but exist in $n=3, 4, 5$ and clarify the regions in which they appear. In $n=3$, we show that the separation of variables of the Hamilton-Jacobi equation does not occur though we find no signs of chaos for stable bound orbits. Since the system is integrable in $n=4$, no chaos appears. In $n=5$, we find some chaotic stable bound orbits. Therefore, this system is nonintegrable at least in $n=5$ and suggests that the timelike geodesic system in the corresponding black ring spacetimes is nonintegrable.
