Symbolic dynamics in the restricted elliptic isosceles three body problem

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