Structure of the centre manifold of the \(L_1,L_2\) collinear libration points in the restricted three-body problem
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We present a global analysis of the centre manifold of the collinear points in the circular restricted three-body problem. The phase-space structure is provided by a family of resonant 2-DOF Hamiltonian normal forms. The near 1:1 commensurability leads to the construction of a detuned Birkhoff–Gustavson normal form. The bifurcation sequences of the main orbit families are investigated by a geometric theory based on the reduction of the symmetries of the normal form, invariant under spatial mirror symmetries and time reversion. This global picture applies to any values of the mass parameter.
KeywordsCollinear points Lyapunov and halo orbits Normal forms
We acknowledge useful discussions with A. Celletti, C. Efthymiopoulos, H. Hanßmann, A. Giorgilli, M. Guzzo, A. Marchesiello and D. Wilkzak. The work is partially supported by INFN, Sezione di Roma Tor Vergata and GNFM-INdAM. The author acknowledges the grant Stardust-R Marie Curie Initial Training Network.
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The author declares that he has no conflict of interest.
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