  The long-term stability of the evolution of two-planet systems is considered
by using the general three body problem (GTBP). Our study is focused on the
stability of systems with adjacent orbits when at least one of them is highly
eccentric. In these cases, in order for close encounters, which destabilize the
planetary systems, to be avoided, phase protection mechanisms should be
considered. Additionally, since the GTBP is a non-integrable system, chaos may
also cause the destabilization of the system after a long time interval. By
computing dynamical maps, based on Fast Lyapunov Indicator, we reveal regions
in phase space with stable orbits even for very high eccentricities (e>0.5).
Such regions are present in mean motion resonances (MMR). We can determine the
position of the exact MMR through the computation of families of periodic
orbits in a rotating frame. Elliptic periodic orbits are associated with the
presence of apsidal corotation resonances (ACR). When such solutions are
stable, they are associated with neighbouring domains of initial conditions
that provide long-term stability. We apply our methodology so that the
evolution of planetary systems of highly eccentric orbits is assigned to the
existence of such stable domains. Particularly, we study the orbital evolution
of the extrasolar systems HD 82943, HD 3651, HD 7449, HD 89744 and HD 102272
and discuss the consistency between the orbital elements provided by the
observations and the dynamical stability.
