Saari's Homographic Conjecture of the Three-Body Problem

Details Saari's Homographic Conjecture of the Three-Body Problem Saari's Homographic Conjecture of the Three-Body Problem

2009-09-28

arxiv.org/abs/0909.4991v1

Trans. Amer. Math. Soc. 360 (2008), 6447-6473

Physics

Mathematical Physics

Scientific paper

10.1090/S0002-9947-08-04517-0

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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