2009/09/28 by Florin Diacu, Toshiaki Fujiwara, Ernesto Perez-Chavela +1 · 2 citations
Physics and Astronomy · Mathematics · #math-ph #math.MP
paper · pdf · doi:10.1090/s0002-9947-08-04517-0
published as Trans. Amer. Math. Soc. 360 (2008), 6447-6473
arxiv created 2009/09/28 · arxiv updated 2009/12/01
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≥ 3.