  The restricted planar elliptic three body problem (RPETBP) describes the
motion of a massless particle (a comet) under the gravitational field of two
massive bodies (the primaries, say the Sun and Jupiter) revolving around their
center of mass on elliptic orbits with some positive eccentricity. The aim of
this paper is to show the existence of orbits whose angular momentum performs
arbitrary excursions in a large region. In particular, there exist diffusive
orbits, that is, with a large variation of angular momentum.
  The leading idea of the proof consists in analysing parabolic motions of the
comet. By a well-known result of McGehee, the union of future (resp. past)
parabolic orbits is an analytic manifold. In a properly chosen coordinate
system these manifolds are stable (resp. unstable) manifolds of a manifold at
infinity $P_\infty$, which we call manifold at parabolic infinity.
  On this manifold, it is possible to define two scattering maps, which contain
the map structure of the homoclinic trajectories to it, i.e. orbits parabolic
both in the future and the past. Since the inner dynamics inside $P_\infty$ is
trivial, two different scattering maps are used. The combination of these two
scattering maps permits the design of the desired diffusive pseudo-orbits.
Using shadowing techniques and these pseudo orbits we show the existence of
true trajectories of the RPETBP whose angular momentum varies in any
predetermined fashion.
