  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 $C^\infty$ 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 $\tau=1$ (e. g. with ratio of the two independent
frequencies equal to the golden mean).
