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

Guowei Yu

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arXiv · 1509.04999

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

Guowei Yu

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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}.

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Guowei Yu. 2016-08-30. Simple choreographies of the planar Newtonian $N$-body Problem. https://arxiv.org/abs/1509.04999

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