| Abstract: |
| One of the open problems in the N-body problem is the following: for any given pure braid, does there exist a periodic solution that realizes it? As a more fundamental question, one may ask whether, for any given braid, there exists a Hamiltonian system that realizes it in the first place. In 1986, Moser showed that for a given area-preserving map, there exists a Hamiltonian system that realizes it as a Poincar\`{e} map. Using his technique, we prove that for any braid, there exists a Hamiltonian system whose orbits realize the given braid. In particular, when the braid is pseudo-Anosov, the corresponding Poincar\`{e} map is also pseudo-Anosov. |
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