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| A choreography is a periodic solution of the N-body problem where the N bodies follow each other at regular intervals around a single closed path. Since Chenciner and Montgomery's (re)discovery of the figure-8 choreography in 2000, there has been considerable interest in finding new ones. The approach is usually to use variational methods on the appropriate loop space and the proofs have been a combination of symmetry arguments and analysis. In this talk I will describe a complete classification of all the possible symmetry groups arising in this problem. It is joint work with my PhD student Katrina Steckles. |
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