Simple choreographies of the planar Newtonian N-body Problem

2015/09/16 by Guowei Yu, Yu, Guowei
Engineering · Physics and Astronomy · #37N05 #70F07 #Astro and Planetary Science #Dynamical Systems (math.DS) #FOS: Mathematics #Spacecraft Dynamics and Control #Stellar, planetary, and galactic studies

paper · pdf · doi:10.48550/arxiv.1509.04999

openalex publication_date 2015/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the N-body problem, a simple choreography is a periodic solution, where all masses chase each other on a single loop. In this paper we prove that for the planar Newtonian N-body problem with equal masses, N ≥ 3, there are at least 2^N-3 + 2^[(N-3)/2] different main simple choreographies. This confirms a conjecture given by Chenciner and etc. in \citeCGMS02.

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