Hyperbolic scattering in the planar n-body problem

For the planar $n$-body problem with homogeneous strong force potentials, given an arbitrary pair of normalized collision-free configurations $(a, b)$, we prove that for any positive energy $h$, there are infinitely many $h$-energy scattering orbits between $a$ and $b$.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-11-02
DOI
https://doi.org/10.48550/arxiv.2611.02781
Primary Topic
Advanced Differential Equations and Dynamical Systems
Type
preprint
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preprint

Hyperbolic scattering in the planar n-body problem

Guowei Yu, Junhao Lie
arXiv (Cornell University)
Advanced Differential Equations and Dynamical Systems
preprint

Hyperbolic scattering in the planar n-body problem

Guowei Yu, Junhao Lie
preprint en

Abstract

For the planar $n$-body problem with homogeneous strong force potentials, given an arbitrary pair of normalized collision-free configurations $(a, b)$, we prove that for any positive energy $h$, there are infinitely many $h$-energy scattering orbits between $a$ and $b$.

arXiv (Cornell University)
Advanced Differential Equations and Dynamical Systems
DOIOpen Access PDFOpenAlex
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Hyperbolic scattering in the planar n-body problem — Guowei Yu, Junhao Lie · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS