English

Periodic Solutions with Alternating Singularities in the Collinear Four-body Problem

Dynamical Systems 2008-11-20 v1

Abstract

This paper shows the existence of a periodic orbit with singularity in the symmetric collinear four body problem. In each period of the orbit, there is a binary collision (BC) between the inner two bodies and a simultaneous binary collision (SBC) of the two clusters on both sides of the origin. The system is regularized and the existence is proven by using the implicit function theorem and a continuity argument on differential equations of the regularized Hamiltonian.

Keywords

Cite

@article{arxiv.0811.3199,
  title  = {Periodic Solutions with Alternating Singularities in the Collinear Four-body Problem},
  author = {Ouyang Tiancheng and Duokui Yan},
  journal= {arXiv preprint arXiv:0811.3199},
  year   = {2008}
}

Comments

submitted, manuscripta mathematica

R2 v1 2026-06-21T11:43:25.879Z