Scaling properties for the radius of convergence of a Lindstedt series: The standard map

By using a version of the tree expansion for the standard map, we prove tha t the radius of convergence of the corresponding Lindstedt series satisfies a scaling property as the (complex) rotation number tends to any rational (resonant) value, non-tangentially to the real axis. By suitably rescaling the perturbative parameter epsilon, the function conjugating the dynamic on the (KAM) invariant curve with given rotation number to a linear rotation has a well defined limit, which can be explicitly computed. (C) Elsevier, P aris.