Structure of the center manifold of the L1 and L2 collinear libration points in the restricted three-body problem

Abstract

We present a global analysis of the center 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.

arXiv commentPaper included in the Topical Collection for the 50th birthday of CM&DA, 19 pages, 7 figures

References in corpus (8)

• Quantitative predictions with detuned normal forms
• Halo orbits around the collinear points of the restricted three-body problem
• An energy-momentum map for the time-reversal symmetric 1:1 resonance with Z_2 X Z_2 symmetry
• A Hopf variables view on the libration points dynamics
• The 1:+2 / 1:-2 resonance
• Qualitative and analytical results of the bifurcation thresholds to halo orbits
• Validated numerics for period-tupling and touch-and-go bifurcations of symmetric periodic orbits in reversible systems
• Bifurcation sequences in the symmetric 1:1 Hamiltonian resonance

Cited by in corpus (4)

• On the analytical construction of halo orbits and halo tubes in the elliptic restricted three-body problem
• Transits close to the Lagrangian solutions $L_1,L_2$ in the Elliptic Restricted Three-body Problem
• The dynamics around the collinear points of the elliptic three-body problem: A normal form approach
• Bifurcation of frozen orbits in a gravity field with zonal harmonics