  The description of unstable motions in the Restricted Planar Circular 3-Body
Problem, modeling the dynamics of a Sun-Planet-Asteriod system, is one of the
fundamental problems in Celestial Mechanics. The goal of this paper is to
analyze homoclinic and instability phenomena at coorbital motions, that is when
the negligible mass Asteroid is at 1:1 mean motion resonance with the Planet
(i.e. nearly equal periods) and performs close to circular motions. Several
bodies in our Solar system belong to such regimes. In this paper, we obtain the
following results. First, we prove that, for a sequence of ratios between the
masses of the Planet and the Sun going to 0, there exist a 2-round homoclinic
orbit to the Lagrange point L3, i.e. homoclinic orbits that approach the
critical point twice. Second, we construct chaotic motions (hyperbolic sets
with symbolic dynamics) as a consequence of the existence of transverse
homoclinic orbits to Lyapunov periodic orbits associated to L3. Finally, we
prove that the RPC3BP possesses Newhouse domains by proving that the energy
level unfolds generically a quadratic homoclinic tangency to a periodic orbit.
