TITLE:
Numerical continuation of families of homoclinic connections of
periodic orbits in the RTBP


AUTHORS:
Esther Barrabes, Josep M. Mondelo, Merce Olle
E-mails: barrabes@ima.udg.edu, jmm@mat.uab.cat, merce.olle@upc.edu


ABSTRACT:
The goal of this paper is the numerical computation and continuation
of families of  homoclinic connections of the Lyapunov
families of periodic orbits (p.o.) associated with the
collinear equilibrium points,  $L_1$, $L_2$ and $L_3$,
of the planar circular Restricted Three--Body Problem (RTBP).
We describe the method used
that allows to follow individual families of homoclinic
connections by numerical continuation of a system of (nonlinear)
equations that has as unknowns the initial condition of the
 p.o., the linear approximation of its stable and unstable
manifolds, and a point in a given Poincaré section in which the
unstable and stable manifolds match.
For the $L_3$ case, some comments are made on the geometry of
the manifold tubes and the possibility of obtaining trajectories
with prescribed itineraries.