Priscilla Souza Silva (Universitat de Barcelona): Domains of Effective Stability near L5 in the R3BP

It is well known that Effective Stability Domains can occur in
non-integrable dynamical systems with N>2 degrees of freedom even when
N-dimensional invariant tori are not able to confine trajectories in
the 2N phase-space and Arnold diffusion effects are expected.

We are interested in the global shape of the practical stability domains
around each triangular equilibrium point of the spatial Restricted
Three-body Problem for small values of the mass parameter. Particularly,
we want to identify the invariant dynamical structures which account for
the long-term confinement of trajectories and are at the boundary of
these stability regions.

We present a detailed numerical inspection of the escape processes,
identifying two different scenarios:
(i) In the first case, the stable and unstable hyperbolic manifolds of
the central manifold of L3 play a role in the confinement of trajectories
(similarly to what happens for the planar version of the R3BP);
(ii) In the second case, the confinement of trajectories is due to the
invariant manifolds of a bi-parametric family of unstable T2 tori
associated to a family of periodic orbits that bifurcate from
the vertical Lyapunov orbits in the central manifold of L5.