The meromorphic non-integrability of the three-body problem

2000/09/25 by Alexei Tsygvintsev, Tsygvintsev, Alexei · 1 citation
Mathematics · Physics and Astronomy · #37K10 #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Waves and Solitons #math.DS #msc:37K10

paper · pdf · doi:10.48550/arxiv.math/0009218

17 pages, submitted to Crelle's Journal

arxiv created 2000/09/25 · openalex publication_date 2000/09/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the planar three-body problem and prove the absence of a complete set of complex meromorphic first integrals in a neighborhood of the Lagrangian solution. We use the Ziglin's method and study the monodromy group of the corresponding normal variational equations.

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• Smooth integrability of diffeomorphisms

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