FM 06-3; mp_arc 06-14 ; math-ph/0601032

Author: Ovidiu Costin, Giovanni Gallavotti, Guido Gentile, Alessandro Giuliani

Title Borel summability and Lindstedt series:

Abstract: Resonant motions of integrable systems subject to perturbations may continue to exist and to cover surfaces with parametric equations admitting a formal power expansion in the strength of the perturbation. Such series may be, sometimes, summed via suitable sum rules defining $C^\io$ functions of the perturbation strength: here we find sufficient conditions for the Borel summability of their sums in the case of two-dimensional rotation vectors with Diophantine exponent $\t=1$ (\eg with ratio of the two independent frequencies equal to the golden mean)

Key words:  Resonances, KAM theory, Divergent Series, Lindstedt Series, Borel Summability
Ovidiu Costin
Department of Mathematics
Ohio State University

Giovanni Gallavotti
Dipartimento di Fisica, INFN
Universita' di Roma "La Sapienza"
P.le A. Moro 2
I 00185 Roma, Italia

Guido Gentile
Dipartimento di Matematica
Universita` di Roma 3
Largo S. Leonardo Murialdo

Alessandro Giuliani
Mathematics Department
Princeton University
Princeton, NJ 08540