English

Chaotic dynamics for the two body problem on a sphere

Dynamical Systems 2025-11-25 v1

Abstract

We prove the existence of chaotic trajectories for the two body problem on a sphere. The trajectories we construct encounter near-collisions and are similar to the second species solutions of Poincar\'e of the classical 3 body problem. The construction uses a general result on Lagrangian systems with Newtonian singularities of the potential which is based on the method of anti-integrable limit of Serge Aubry.

Keywords

Cite

@article{arxiv.2511.19178,
  title  = {Chaotic dynamics for the two body problem on a sphere},
  author = {Sergey Bolotin},
  journal= {arXiv preprint arXiv:2511.19178},
  year   = {2025}
}
R2 v1 2026-07-01T07:52:15.897Z