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.