  We present a computer assisted proof of existence of a family of Lyapunov
orbits which stretches from L2 up to half the distance to the smaller primary
in the Jupiter-Sun planar restricted circular 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.
