Structure of the centre manifold of the \(L_1\), \(L_2\) collinear libration points in the restricted three-body problem. (English) Zbl 1451.70021
Summary: 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.
MSC:
| 70F07 | Three-body problems |
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