99-377 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 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.

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