  The elliptic isosceles restricted three body problem (REI3BP) models the
motion of a massless body under the influence of the Newtonian gravitational
force caused by two other bodies called the primaries. The primaries of masses
$m_{1}=m_{2}$ move along a degenerate Keplerian elliptic collision orbit (on a
line) under their gravitational attraction, whereas the third, massless
particle, moves on the plane perpendicular to their line of motion and passing
through the center of mass of the primaries. By symmetry, the component of the
angular momentum $G$ of the massless particle along the direction of the line
of the primaries is conserved.
  We show the existence of symbolic dynamics in the REI3BP for large $G$ by
building a Smale horseshoe on a certain subset of the phase space. As a
consequence we deduce that the REI3BP possesses oscillatory motions, namely
orbits which leave every bounded region but return infinitely often to some
fixed bounded region. The proof relies on the existence of transversal
homoclinic connections associated to an invariant manifold at infinity. Since
the distance between the stable and unstable manifolds of infinity is
exponentially small, Melnikov theory does not apply.
