Abstract. The goal of this paper is the numerical computation and continuation of homoclinic connections of the Lyapunov families of periodic orbits (p.o.) associated with the collinear equilibrium points, L₁, L₂ and L₃, of the planar circular restricted three-body problem (RTBP). We describe the method used that allows us 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 L₃ case, some comments are made on the geometry of the manifold tubes and the possibility of obtaining trajectories with prescribed itineraries.

Mathematics Subject Classification: 70F07, 70F15, 70H12, 70H33, 70K44

Print publication: Issue 12 (December 2009)
Received 26 January 2009, in final form 6 October 2009
Published 30 October 2009