Skip to content

Borel summability and Lindstedt series

O. Costin, G. Gallavotti, G. Gentile, A. Giuliani

math-pharXiv:math-ph/0601032

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∞ 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 τ=1 (e. g. with ratio of the two independent frequencies equal to the golden mean).

Create a lesson