Structure of the centre manifold of the \(L_1,L_2\) collinear libration points in the restricted three-body problem

  • Giuseppe PucaccoEmail author
Original Article
Part of the following topical collections:
  1. 50 years of Celestial Mechanics and Dynamical Astronomy


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.


Collinear 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.

Compliance with ethical standards

Conflict of interest

The author declares that he has no conflict of interest.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Dipartimento di Fisica and INFN – Sezione di Roma IIUniversità di Roma “Tor Vergata”RomeItaly

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