论文标题
$ 2N $问题的辫子，金属比和定期解决方案
Braids, metallic ratios and periodic solutions of the $2n$-body problem
论文作者
论文摘要
Planar $ n $ body问题的定期解决方案通过$ N $车体的轨迹确定了辫子。辫子类型可用于对周期性解决方案进行分类。根据尼尔森·瑟斯顿（Nielsen-Thurston）的表面自身形态分类，辫子分为三种类型：周期性，还原和伪anosov。对于伪anosov类型的辫子，有一个大于1的相关伸展因子，这是辫子的共轭。 2006年，第三作者发现了一个由平面$ 2N $体育问题的多个编舞解决方案的家庭。我们证明，从家族中的溶液中获得的辫子是伪anosov类型的，其拉伸因子以金属比表示。还提供了新的数值定期解决方案$ 2N $ - 体育问题。
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.
