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

TL;DR

This paper provides a comprehensive analysis of the center manifold structure at the collinear libration points in the circular restricted three-body problem using Hamiltonian normal forms and symmetry reduction techniques.

Contribution

It introduces a global phase-space analysis of the center manifold at L1 and L2 points using resonant Hamiltonian normal forms and symmetry reduction, applicable for any mass parameter.

Findings

Characterization of the phase-space structure near L1 and L2.

Construction of a detuned Birkhoff-Gustavson normal form.

Analysis of bifurcation sequences of orbit families.

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.