  The AMD-stability criterion allows to discriminate between a-priori stable
planetary systems and systems for which the stability is not granted and needs
further investigations. AMD-stability is based on the conservation of the
Angular Momentum Deficit (AMD) in the averaged system at all orders of
averaging. While the AMD criterion is rigorous, the conservation of the AMD is
only granted in absence of mean-motion resonances (MMR). Here we extend the
AMD-stability criterion to take into account mean-motion resonances, and more
specifically the overlap of first order MMR. If the MMR islands overlap, the
system will experience generalized chaos leading to instability. The
Hamiltonian of two massive planets on coplanar quasi-circular orbits can be
reduced to an integrable one degree of freedom problem for period ratios close
to a first order MMR. We use the reduced Hamiltonian to derive a new overlap
criterion for first order MMR. This stability criterion unifies the previous
criteria proposed in the literature and admits the criteria obtained for
initially circular and eccentric orbits as limit cases. We then improve the
definition of AMD-stability to take into account the short term chaos generated
by MMR overlap. We analyze the outcome of this improved definition of
AMD-stability on selected multi-planet systems from the Extrasolar Planets
Encyclopeadia.
