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

Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

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.

Files: 98-350.src( desc , 98-350.ps )