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Secular instability in the spatial three-body problem

Féjoz, Jacques; Guardia, Marcel (2016), Secular instability in the spatial three-body problem, Archive for Rational Mechanics and Analysis, 221, 1, p. 335–362. 10.1007/s00205-015-0962-y

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Type
Article accepté pour publication ou publié
Date
2016
Journal name
Archive for Rational Mechanics and Analysis
Volume
221
Number
1
Publisher
Springer
Pages
335–362
Publication identifier
10.1007/s00205-015-0962-y
Metadata
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Author(s)
Féjoz, Jacques
Guardia, Marcel
Abstract (EN)
Consider the spatial three-body problem, in the regime where one bodyrevolves far away around the other two, in space, the masses of the bodies being arbi-trary but fixed; in this regime, there are no resonances in mean motions. The so-calledsecular dynamics governs the slow evolution of the Keplerian ellipses. We show thatit contains a horseshoe and all the chaotic dynamics which goes along with it, corre-sponding to motions along which the eccentricity of the inner ellipse undergoes large,random excursions. The proof goes through the surprisingly explicit computation of thehomoclinic solution of the first order secular system, its complex singularities and theMelnikov potential.
Subjects / Keywords
systèmes dynamiques; three-body problem

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