Archive for Rational Mechanics and Analysis

, Volume 221, Issue 1, pp 335–362 | Cite as

Secular Instability in the Three-Body Problem

  • J. FéjozEmail author
  • M. Guardia


Consider the three-body problem, in the regime where one body revolves far away around the other two, in space, the masses of the bodies being arbitrary but fixed; in this regime, there are no resonances in mean motions. The so-called secular dynamics governs the slow evolution of the Keplerian ellipses. We show that it contains a horseshoe and all the chaotic dynamics which goes along with it, corresponding to motions along which the eccentricity of the inner ellipse undergoes large, random excursions. The proof goes through the surprisingly explicit computation of the homoclinic solution of the first order secular system, its complex singularities and the Melnikov potential.


Invariant Manifold Homoclinic Orbit Heteroclinic Orbit Homoclinic Solution Unstable Orbit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© European Union 2016

Authors and Affiliations

  1. 1.PSL Research University (Université Paris-Dauphine/CEREMADE & Observatoire de Paris /IMCCE)ParisFrance
  2. 2.Universitat Politècnica de Catalunya (Departament de Matemàtiques)BarcelonaSpain

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