Three bodies and Lagrange points
The figure-eight solution is periodic. A small change in the start does not stay small. In the frame that rotates with two primaries, L4 and L5 can hold a test mass. L1, L2, and L3 do not.
The figure-eight solution is periodic. A small change in the start does not stay small. In the frame that rotates with two primaries, L4 and L5 can hold a test mass. L1, L2, and L3 do not.