English

Compactification of the energy surfaces for n bodies

Dynamical Systems 2023-07-11 v1

Abstract

For n bodies moving in Euclidean d-space under the influence of a homogeneous pair interaction we compactify every center-of-mass energy surface, obtaining a 2d(n -1)-1 - dimensional manifold with corners in the sense of Melrose. After a time change, the flow on this manifold is globally defined and non-trivial on the boundary.

Keywords

Cite

@article{arxiv.2307.03837,
  title  = {Compactification of the energy surfaces for n bodies},
  author = {Andreas Knauf and Richard Montgomery},
  journal= {arXiv preprint arXiv:2307.03837},
  year   = {2023}
}

Comments

44 pages, 10 figures, submitted to Alain Chenciner's 80th birthday conference proceedings to be published in Regular and Chaotic Dynamics