Abstract
We deal with the spatial three-body problem in the various regimes where the Hamiltonian is split as the sum of two Keplerian systems plus a small perturbation. This is a region of the phase space \(T^{{\ast}}\mathbb{R}^{6}\) where the perturbation is small [3], the so called perturbing region \(\mathcal{P}_{\varepsilon,n}\). In particular, we prove the existence of quasi-periodic motions where the inner particles describe bounded near-rectilinear trajectories whereas the outer particle follows an orbit lying near the invariable plane. These motions fill in five-dimensional invariant tori. Moreover, the inner particles move in orbits either near an axis perpendicular to the invariable plane or near the invariable plane.
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Palacián, J.F., Sayas, F., Yanguas, P. (2015). Quasi-Periodic Almost-Collision Motions in the Spatial Three-Body Problem. In: Corbera, M., Cors, J., Llibre, J., Korobeinikov, A. (eds) Extended Abstracts Spring 2014. Trends in Mathematics(), vol 4. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-22129-8_9
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DOI: https://doi.org/10.1007/978-3-319-22129-8_9
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-22128-1
Online ISBN: 978-3-319-22129-8
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