ar X iv : m at h - ph / 0 60 10 32 v 1 1 5 Ja n 20 06 Borel summability and Lindstedt series

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).