Cors, Josep MariaPalacián Subiela, Jesús FranciscoYanguas Sayas, Patricia2019-03-052019-03-0520191536-0040 (Electronic)10.1137/18M1190859https://academica-e.unavarra.es/handle/2454/32505Within the framework of the planar three-body problem we establish the existence of quasi-periodic motions and KAM 4-tori related to the co-orbital motion of two small moons about a large planet where the moons move in nearly circular orbits with almost equal radii. The approach is based on a combination of normal form and symplectic reduction theories and the application of a KAM theorem for high-order degenerate systems. To accomplish our results we need to expand the Hamiltonian of the three-body problem as a perturbation of two uncoupled Kepler problems. This approximation is valid in the region of phase space where co-orbital solutions occur.20 papplication/pdfeng© 2019, Society for Industrial and Applied Mathematics. Unauthorized reproduction of this article is prohibited.Three-body problemSymplectic scalingCo-orbital regime1:1 mean-motion resonanceNormalization and reductionKAM theory for multiscale systemsQuasi-periodic motion and invariant 4-toriArtículo / ArtikuluaAcceso abierto / Sarbide irekiainfo:eu-repo/semantics/openAccess