标题： 萨里关于平面三体问题在牛顿势和强力势下的普遍质量同构猜想 显示英文标题

标题： Saari's homographic conjecture for general masses in planar three-body problem under Newton potential and a strong force potential

摘要： Saari's homographic conjecture claims that, in the N-body problem under the homogeneous potential, $U=\alpha^{-1}\sum m_i m_j/r_{ij}^\alpha$ for $\alpha\ne 0$, a motion having constant configurational measure $\mu=I^{\alpha/2}U$ is homographic, where $I$ represents the moment of inertia defined by $I=\sum m_i m_j r_{ij}^2/\sum m_k$, $m_i$ the mass, and $r_{ij}$ the distance between particles. 我们证明了在平面三体问题中，对于一般的质量$m_k>0$，在牛顿势（$\alpha=1$）和强力势（$\alpha=2$）下该猜想。 显示英文摘要

摘要： Saari's homographic conjecture claims that, in the N-body problem under the homogeneous potential, $U=\alpha^{-1}\sum m_i m_j/r_{ij}^\alpha$ for $\alpha\ne 0$, a motion having constant configurational measure $\mu=I^{\alpha/2}U$ is homographic, where $I$ represents the moment of inertia defined by $I=\sum m_i m_j r_{ij}^2/\sum m_k$, $m_i$ the mass, and $r_{ij}$ the distance between particles. We prove this conjecture for general masses $m_k>0$ in the planar three-body problem under Newton potential ($\alpha=1$) and a strong force potential ($\alpha=2$).