A study of braids arising from simple choreographies of the planar Newtonian N-body problem
Year: 2025
Type: preprint
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. 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.
Source: arXiv (Cornell University)
Authors: Kajihara, Yuika, Kin, Eiko, Shibayama, Mitsuru
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979303550
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