| Abstract: |
| We study periodic solutions of the planar Newtonian N-body problem with equal masses.Each periodic solution traces out a braid with N strands in 3-dimensional space. According to the Nielsen-Thurston classification of surface automorphisms, braids can be classified into three types: periodic, reducible, and pseudo-Anosov. When a braid is of pseudo-Anosov type, it has an associated stretch factor greater than 1, which reflects the complexity of the periodic solution. For each $N \ge 3$, Guowei Yu established the existence of a family of simple choreographies to the planar Newtonian N-body problem.We prove that braids arising from Yu`s periodic solutions are of pseudo-Anosov types, except in the special case where all particles move along a circle. We also identify the simple choreographies whose braid types have the largest and smallest stretch factors, respectively. |
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