Normal form invariants around spin-orbit periodic orbits

We consider a model of spin-orbit interaction, describing the motion of an oblate satellite rotating about an internal spin-axis and orbiting about a central planet. The resulting second order differential equation depends up on the parameters provided by the equatorial oblateness of the satellite an d its orbital eccentricity. Normal form transformations around the main spi n-orbit resonances are carried out explicitly. As an outcome, one can compu te some invariants; the fact that these quantities are not identically zero is a necessary condition to prove the existence of nearby periodic orbits (Birkhoff fixed point theorem). Moreover, the nonvanishing of the invariant s provides also the stability of the spin-orbit resonances, since it guaran tees the existence of invariant curves surrounding the periodic orbit.