Maciej Capinski (Institute of Mathematics, AGH University of Science and Technology, Krakow):Computer Assisted Proof for Fibers of Invariant Manifolds in the Planar Restricted Circular Three Body Problem

We first present a computer assisted proof for detection of
the family of Lyapounov orbits around the equilibrium point L1 in the
Planar Restricted Circular Three Body Problem. The method provides very
tight estimates and can be applied over a broad range of energies of
the orbits. We then present a method for detection of fibers of
stable/unstable manifolds associated with the family of orbits. The
method is based on a combination of a parameterization method together
with cone conditions and topological arguments. We also discuss
propagation of the fibers along the flow to prove transversal
intersections of the manifolds.