98-350 Alberto Berretti and Guido Gentile
Scaling Properties for the Radius of Convergence of a Lindstedt Series: the Standard Map (514K, Postscript) May 18, 98
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Abstract. By using a version of the tree expansion for the Lindstedt series, we prove that its radius of convergence for the standard map satisfies a scaling property as the (complex) rotation number tends to any rational (resonant) value, non-tangentially to the real axis. By suitably rescaling the perturbative parameter \$\eps\$, the function conjugating the dynamic on the (KAM) invariant curve with given rotation number to a linear rotation has a well defined limit, which can be explicitly computed.

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