The Non-collision Sigularities of the 5 body Problem

  • Zhihong Xia
Conference paper
Part of the Mathematical Sciences Research Institute Publications book series (MSRI, volume 22)


This paper is a survey on the author’s work on the non-collision singularities in the Newtonian n-body problem. The non-collision singularity in the n-body system corresponds to the solution which blow up to infinity in finite time. The question whether there exists such solution was first raised by Painleve in the last century and since then, it has been open. Here, we show that such solutions do exist in a 5-body problem. The method we use is based on careful analysis of near collisions orbits and McGehee’s technique of blowing up collision singularities.


Angular Momentum Body Problem Binary Collision Central Configuration Triple Collision 
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Copyright information

© Springer-Verlag New York, Inc. 1991

Authors and Affiliations

  • Zhihong Xia
    • 1
  1. 1.Department of MathematicsHarvard UniversityCambridgeUSA

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