The invariant manifold structures of the collinear libration points for the restricted three-body problem provide the framework for understanding transport phenomena from a geometrical point of view. In particular, the stable and unstable invariant manifold tubes associated with libration point orbits are the phase space conduits transporting material… (More)
This paper is devoted to clarify the algorithmic definition of the weak stability boundary in the framework of the planar Restricted Three Body Problem. The role of the invariant hyperbolic manifolds associated to the central manifolds of the libration points L 1 and L 2 , as boundary of the weak stability region, is shown.
To Henri Poincaré on the 150th anniversary of his birth. Abstract. The title of this paper is inspired by the work of Poincaré [1890, 1892], who introduced many key dynamical systems methods during his research on celestial mechanics and especially the three body problem. Since then, many researchers have contributed to his legacy by developing and applying… (More)