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- W4226063742 abstract "Periodic solutions of the planar $N$-body problem determine braids through the trajectory of $N$ bodies. Braid types can be used to classify periodic solutions. According to the Nielsen-Thurston classification of surface automorphisms, braids fall into three types: periodic, reducible and pseudo-Anosov. To a braid of pseudo-Anosov type, there is an associated stretch factor greater than 1, and this is a conjugacy invariant of braids. In 2006, the third author discovered a family of multiple choreographic solutions of the planar $2n$-body problem. We prove that braids obtained from the solutions in the family are of pseudo-Anosov type, and their stretch factors are expressed in metallic ratios. New numerical periodic solutions of the planar $2n$-body problem are also provided." @default.
- W4226063742 created "2022-05-05" @default.
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- W4226063742 date "2022-04-04" @default.
- W4226063742 modified "2023-10-16" @default.
- W4226063742 title "Braids, metallic ratios and periodic solutions of the $2n$-body problem" @default.
- W4226063742 doi "https://doi.org/10.48550/arxiv.2204.01420" @default.
- W4226063742 hasPublicationYear "2022" @default.
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