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arXiv · 2511.19178

Chaotic dynamics for the two body problem on a sphere

Sergey Bolotin
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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.

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Sergey Bolotin. 2025-11-24. Chaotic dynamics for the two body problem on a sphere. https://doi.org/10.1063/5.0285476

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