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On the stability of the Lagrangian homographic solutions in a curved three-body problem on $\mathbb{S}^2$

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  • The problem of three bodies with equal masses in $\mathbb{S}^2$ is known to have Lagrangian homographic orbits. We study the linear stability and also a "practical'' (or effective) stability of these orbits on the unit sphere.
    Mathematics Subject Classification: Primary: 70F07, 70H12; Secondary: 34D08, 37J25.


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  • [1]

    C. Batut, K. Belabas, D. Bernardi, H. Cohen and M. OlivierUsers' guide to PARI/GP, (freely available from http://pari.math.u-bordeaux.fr/).


    F. Diacu and E. Pérez-Chavela, Homographic solutions of the curved 3-body problem, Journal of Differential Equations, 250 (2011), 340-366.doi: 10.1016/j.jde.2010.08.011.


    A. Giorgilli, A. Delshams, E. Fontich, L. Galgani and C. Simó, Effective stability for a Hamiltonian system near an elliptic equilibrium point, with an application to the restricted three body problem, Journal of Differential Equations, 77 (1989), 167-198.doi: 10.1016/0022-0396(89)90161-7.


    T. Kapela and C. SimóRigorous KAM results around arbitrary periodic orbits for Hamiltonian systems, Preprint, arXiv:1105.3235.


    R. Martínez, A. Samà and C. Simó, "Stability of Homographic Solutions of the Planar Three-Body Problem with Homogeneous Potentials," Proceedings EQUADIFF (2003), 1005–1010. World Scientific, 2005.


    R. Martínez, A. Samà and C. Simó, Stability diagram for 4D linear periodic systems with applications to homographic solutions, Journal of Differential Equations, 226 (2006), 619-651.doi: 10.1016/j.jde.2006.01.014.


    R. Martínez, A. Samà and C. Simó, Analysis of the stability of a family of singular-limit linear periodic systems in $R^4.$ applications, Journal of Differential Equations, 226 (2006), 652-686.doi: 10.1016/j.jde.2005.09.012.


    C. Siegel and J. Moser, "Lectures on Celestial Mechanics," Springer, 1971.


    C. Simó, On the analytical and numerical approximation of invariant manifolds, Modern methods in celestial mechanics, (eds, D. Benest and C. Froeschlé), 285-330, Editions Frontières, Paris, 1990. (Also available at {http://www.maia.ub.es/dsg/2004/}).


    E. T. Whittaker, "A Treatise on the Analytical Dynamics of Particles and Rigid Bodies," Cambridge Univ. Press, fourth edition, reprinted, 1970.

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