From the Lagrange Triangle to the Figure Eight Choreography: Proof of Marchal's Conjecture

2024/06/25 by Calleja, Renato, García-Azpeitia, Carlos, Hénot, Olivier +2 · 4 citations
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2406.17564

Abstract

For the three body problem with equal masses, we prove that the most symmetric continuation class of Lagrange's equilateral triangle solution, also referred to as the P₁₂ family of Marchal, contains the remarkable figure eight choreography discovered by Moore in 1993, and proven to exist by Chenciner and Montgomery in 2000. This settles a conjecture of Marchal which dates back to the 1999 conference on Celestial Mechanics in Evanston Illinois, celebrating Donald Saari's 60th birthday.

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