Finiteness of relative equilibria of the four-body problem

Marshall Hampton; Richard Moeckel

doi:10.1007/s00222-005-0461-0

Finiteness of relative equilibria of the four-body problem

Marshall Hampton, Richard Moeckel

Research output: Contribution to journal › Article › peer-review

163 Scopus citations

Abstract

We show that the number of relative equilibria of the Newtonian four-body problem is finite, up to symmetry. In fact, we show that this number is always between 32 and 8472. The proof is based on symbolic and exact integer computations which are carried out by computer.

Original language	English (US)
Pages (from-to)	289-312
Number of pages	24
Journal	Inventiones Mathematicae
Volume	163
Issue number	2
DOIs	https://doi.org/10.1007/s00222-005-0461-0
State	Published - Feb 2006

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Finiteness of relative equilibria of the four-body problem

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