- 00-375 Alberto Berretti, Corrado Falcolini, Guido Gentile
- The shape of analyticity domains of Lindstedt series: the standard map
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.