The modern theory of Dynamical Systems is in major part an offspring of celestial mechanics. Poincare proved non-integrability of the three body problem when he discovered the homoclinic picture. Alexeev explained the existence of the oscillatory motions (a planet approaches infinity but always returns to a bounded domain) in Sitnikov model (one of the restricted versions of the three body problem) using methods of hyperbolic dynamics.
We show that the structures related to the most recent results in the smooth dynamical systems (area preserving Henon family and homoclinic bifurcations, persistent tangencies, splitting of separatrices) also appear in the three body problem. In particular, we prove that in many cases the set of oscillatory motions has a full Hausdorff dimension.