NORMAL-FORM FOR LIBRATIONAL CURVES OF THE STANDARD MAP

We present a method for constructing analytic expansions approximating librational invariant curves in the case of the so-called generalized standard map. After some preliminary changes of variables, we apply a direct Birkhoff normal form to a fixed order. The resulting system de scribes homotopically trivial invariant curves close to a periodic orb it. We investigate the stability of the librational curves applying a numerical method developed by J. Greene.