00-375 Alberto Berretti, Corrado Falcolini, Guido Gentile

The shape of analyticity domains of Lindstedt series: the standard map (405K, Postscript) Sep 21, 00

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Abstract. The analyticity domains of the Lindstedt series for the standard map are studied numerically using Pade' approximants to model their natural boundaries. We show that if the rotation number is a Diophantine number close to a rational value p/q, then the radius of convergence of the Lindstedt series becomes smaller than the critical threshold for the corresponding KAM curve, and the natural boundary on the plane of the complexified perturbative parameter acquires a flower-like shape with 2q petals. We conjecture that the natural boundary has typically a fractal shape, which only in particular cases degenerates to an apparently regular curve.

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