Phys. Rev. Lett. 70, 3675–3679 (1993)Braids in classical dynamicsReceived 19 October 1992; published in the issue dated 14 June 1993 Point masses moving in 2+1 dimensions draw out braids in space-time. If they move under the influence of some pairwise potential, what braid types are possible? By starting with fictional paths of the desired topology and ‘‘relaxing’’ them by minimizing the action, we explore the braid types of potentials of the form V∝rα from α≤-2, where all braid types occur, to α=2, where the system is integrable. We also discuss issues of symmetry and stability. We propose this kind of topological classification as a tool for extending the ‘‘symbolic dynamics’’ approach to many-body dynamics. © 1993 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.70.3675
DOI:
10.1103/PhysRevLett.70.3675
PACS:
03.20.+i, 02.40.-k
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