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arXiv · 0909.4991

Saari's Homographic Conjecture of the Three-Body Problem

Florin Diacu·Toshiaki Fujiwara·Ernesto Perez-Chavela·Manuele Santoprete
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Abstract

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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Florin Diacu, Toshiaki Fujiwara, Ernesto Perez-Chavela, Manuele Santoprete. 2009-09-28. Saari's Homographic Conjecture of the Three-Body Problem. https://doi.org/10.1090/s0002-9947-08-04517-0

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