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

Guowei Yu

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

Dynamical Systems 2016-08-31 v3

Authors: Guowei Yu

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}.

Keywords

N-body problem simple choreography periodic solution Newtonian problem equal masses

Cite

@article{arxiv.1509.04999,
  title  = {Simple choreographies of the planar Newtonian $N$-body Problem},
  author = {Guowei Yu},
  journal= {arXiv preprint arXiv:1509.04999},
  year   = {2016}
}

Comments

31pages, 6 figures. Refinements in notations and proofs

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