 99377 Alberto Berretti and Guido Gentile
 Scaling Properties for the Radius of
Convergence of Lindstedt Series: Generalized Standard Maps
(520K, Postscript)
Oct 8, 99

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Abstract. For a class of symplectic twodimensional maps
which generalize the standard map by allowing more general
nonlinear terms, the radius of convergence of the Lindstedt
series describing the homotopically nontrivial invariant curves
is proved to satisfy a scaling law as the complexified rotation number
tends to a rational value nontangentially 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.
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