Alberto Berretti and Guido Gentile
Scaling Properties for the Radius of Convergence 
of a Lindstedt Series: the Standard Map
(514K, Postscript)

ABSTRACT.  By using a version of the tree expansion for the Lindstedt series, we 
prove that its radius of convergence for the standard map 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 $\eps$, 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.