  We study the dynamics of planetary systems with two planets moving in the
same plane, when frictional forces act on the two planets, in addition to the
gravitational forces. The model of the general three-body problem is used.
Different laws of friction are considered. The topology of the phase space is
essential in understanding the evolution of the system. The topology is
determined by the families of stable and unstable periodic orbits, both
symmetric and non symmetric. It is along the stable families, or close to them,
that the planets migrate when dissipative forces act. At the critical points
where the stability along the family changes, there is a bifurcation of a new
family of stable periodic orbits and the migration process changes route and
follows the new stable family up to large eccentricities or to a chaotic
region. We consider both resonant and non resonant planetary systems. The 2/1,
3/1 and 3/2 resonances are studied. The migration to larger or smaller
eccentricities depends on the particular law of friction. Also, in some cases
the semimajor axes increase and in other cases they are stabilized. For
particular laws of friction and for special values of the parameters of the
frictional forces, it is possible to have partially stationary solutions, where
the eccentricities and the semimajor axes are fixed.
