Computer Assisted Existence Proofs of Lyapunov Orbits at L₂ and Transversal Intersections of Invariant Manifolds in the Jupiter--Sun PCR3BP

We present a computer assisted proof of existence of a family of Lyapunov orbits which stretches from L₂ (the collinear libration point between the primaries) up to half the distance to the smaller primary in the Jupiter--Sun planar circular restricted three body problem. We then focus on a small family of Lyapunov orbits with energies close to comet Oterma and show that their associated invariant manifolds intersect transversally. Our computer assisted proof provides explicit bounds on the location and on the angle of intersection.