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}
}