FM 2000-6      mp_arc@math.utexas.edu \# 99-377
                chao-dyn@xyz.lanl.gov  \# NO

Authors: Alberto Berretti, Guido Gentile

Title: Scaling Properties for the Radius of Convergence
    of Lindstedt Series: Generalized Standard maps

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 describibg the homotopically
    non-trivial invariant curves is proved to satisfy
    a scaling law as the cpmplexified 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.

Keywords: Generalized standard maps, perturbation theory,
resonances, invariant tori, scaling properties, genericity

Addresses:
A.B.: Matematica, Universita' di Roma 2,
        Viale della Ricerca Scientifica, 00133, Roma, Italia.
G.G.: Matematica, Universita' di Roma 3,
        Largo S. Leonardo Murialdo, 1, 00146, Roma, Italia

e-mail: berretti@mat.uniroma2.it
        gentile@matrm3.mat.uniroma3.it