Document Type

Article

Publication Date

12-2008

Department

Mathematics

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 ≥ 3.

Comments

This article was originally published in Transactions of the American Mathematical Society, 360(12): 6447-6473. (c) 2008 American Mathematical Society

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