  In dynamical systems of few degrees of freedom, periodic solutions consist
the backbone of the phase space and the determination and computation of their
stability is crucial for understanding the global dynamics. In this paper we
study the classical three body problem in three dimensions and use its dynamics
to assess the long-term evolution of extrasolar systems. We compute periodic
orbits, which correspond to exact resonant motion, and determine their linear
stability. By computing maps of dynamical stability we show that stable
periodic orbits are surrounded in phase space with regular motion even in
systems with more than two degrees of freedom, while chaos is apparent close to
unstable ones. Therefore, families of stable periodic orbits, indeed, consist
backbones of the stability domains in phase space.
