AlignedTwo aligned rings \(C_{nv}(2R)\)There is not much to say for these aligned rings: they are only stable if \(n<7\) and if the rings are sufficiently far apart. They necessarily have vorticities of opposite signs. In the diagram, the horizontal axis is θ0, the vertical is θ1 . Lyapounov stable points in red elliptic ones in blue (none of the latter if n is even)
For \(n=4\) one has,  If n is odd, there are very thin slivers of elliptic points around the curved edge of the Lyapounov stable regions, but too narrow to see at this scale. |