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

Toshiaki Fujiwara, Hiroshi Fukuda, Hiroshi Ozaki +1

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 configurat…