The geometrical and dynamical properties of area preserving maps in the neighborhood of
an elliptic fixed point are analyzed in the framework of resonant normal forms. The
interpolating flow is not obtained from a map tangent to the identity, but from the normal form
of the given map and a time independent interpolating Hamiltonian H is introduced. On this
Hamiltonian the local stability properties of the fixed point and the geometric structure of the
orbits are transparent. Numerical agreement between the level lines of H and the orbits of …