Simple choreographies of the planar Newtonian $N$-body Problem

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, $N\ge 3$, 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 \cite{CGMS02}.

31pages, 6 figures. Refinements in notations and proofs

References in corpus (3)

• Unchained polygons and the N-body problem
• Variational proof of the existence of the super-eight orbit in the four-body problem
• Shape Space Figure-$8$ Solution of Three Body Problem with Two Equal Masses

Cited by in corpus (1)

• Shape Space Figure-$8$ Solution of Three Body Problem with Two Equal Masses