Alessandra Cellettiy
Mathematics Departement - University of Roma, Italy
Birkhoff periodic orbits associated to spin-orbit resonances in
Celestial Mechanics and in particular to the Moon-Earth and Mercury-Sun
systems are considered. A general method (based on a quantitative version
of the Implicit Function Theorem) for the construction of such orbits with
particular attention to "effective estimates" on the size of the
perturbative parameters is presented and tested on the above
mentioned systems. Lyapunov stability of the periodic orbits is
investigated numerically and by constructing KAM librational invariant
surfaces trapping the periodic orbits.