Alberto Berretti and Guido Gentile
Scaling Properties for the Radius of 
Convergence of Lindstedt Series: Generalized Standard Maps
(520K, Postscript)

ABSTRACT.   For a class of symplectic two-dimensional maps 
 which generalize the standard map by allowing more general 
 nonlinear terms, the radius of convergence of the Lindstedt 
 series describing the homotopically non-trivial invariant curves 
 is proved to satisfy a scaling law as the complexified rotation number 
 tends to a rational value non-tangentially to the real axis, thus 
 generalizing previous results of the authors. The function 
 conjugating the dynamics to rotations possesses a limit 
 which is explicitly computed and related to hyperelliptic 
 functions in the case of nonlinear terms which are 
 trigonometric polynomials.