TITLE:
Invariant manifolds near L1 and L2 in the Quasi-bicircular Problem

AUTHORS:
Jose J. Rosales^(1), Angel Jorba^(1) and Marc Jorba-Cusco^(2)
(1) Departament de Matematiques i Informatica
    Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain
(2) Universidad Internacional de la Rioja (UNIR),
    Av. de la Paz, 137, 26006 Logro\~{n}o, Spain

E-mails: rosales@maia.ub.es, angel@maia.ub.es, marc.jorba@unir.net

ABSTRACT:
The Quasi-Bicircular Problem (QBCP) is a periodic time dependent
perturbation of the Earth-Moon Restricted Three-Body Problem (RTBP)
that accounts for the effect of the Sun. It is based on using a
periodic solution of the Earth-Moon-Sun three-body problem to write
the equations of motion of the infinitesimal particle.  The paper
focuses on the dynamics near the L1 and L2 points of the Earth-Moon
system in the QBCP. By means of a periodic time dependent reduction to
the center manifold, we show the existence of two families of
quasi-periodic Lyapunov orbits around L1 (resp. L2) with two basic
frequencies. The first of these two families is contained in the
Earth-Moon plane and undergoes an out-of plane (quasi-periodic)
pitchfork bifurcation giving rise to a family of quasi-periodic Halo
orbits. This analysis is complemented with the continuation of
families of 2D tori. In particular, the planar and vertical Lyapunov
families are continued, and their stability analyzed. Finally,
examples of invariant manifolds associated to invariant 2D tori around
the L2 that pass close to the Earth are shown. This phenomena is not
observed in the RTBP, and opens the room to direct transfers from the
Earth to the Earth-Moon L2 region.