I don't think they did it that way, rathe, they are using the computer to help them predict repeating lissajous patterns (for want of a better term) on their transformed sphere-space.
That then relates back to a specific repeating orbit in 3-space.
This is rather interesting, in that it is quite similar (methinks) to the knot classification problem.
But looking at the lissajous figures, it doesn't really seem to me that there are fourteen new classes, unless the lagrange solutions -- which are all a single class -- were counted as five.
But it's no less impressive, what they have done. They have started to transform from physicists to mathematicians.
Source: http://rss.slashdot.org/~r/Slashdot/slashdotScience/~3/eMfwSxciDq0/story01.htm
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