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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.01867 |
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Table of Contents:
- 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. When the braid is of pseudo-Anosov type, it has an associated stretch factor greater than 1, which reflects the complexity of the corresponding 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.