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arXiv · 2307.03837

Compactification of the energy surfaces for n bodies

Andreas Knauf·Richard Montgomery
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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.

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Andreas Knauf, Richard Montgomery. 2023-07-07. Compactification of the energy surfaces for n bodies. https://arxiv.org/abs/2307.03837

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