Secular instability in the spatial three-body problem

Abstract

International audience

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.