三体问题的Saari同形猜想
Saari's Homographic Conjecture of the Three-Body Problem
摘要：
Saari的单应性猜想推广了DonaldSaari在1970年提出的一个经典命题，即具有常数构形测度的牛顿$n$ -体问题的解是单应性的.换句话说，如果相互距离满足一定的关系，粒子系统的配置可能会改变大小和位置，但不会改变形状。我们证明了这一猜想的大型集的初始条件在三体问题的齐次潜力，包括牛顿的。我们的一些结果是正确的$n\ge 3$。
英文摘要：
Saari's homographic conjecture, which extends a classical statement proposed by Donald Saari in 1970, claims that solutions of the Newtonian $n$-body problem with constant configurational measure are homographic. In other words, if the mutual distances satisfy a certain relationship, the configuration of the particle system may change size and position but not shape. We prove this conjecture for large sets of initial conditions in three-body problems given by homogeneous potentials, including the Newtonian one. Some of our results are true for $n\ge 3$.
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