2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125300Resonant 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 $τ=1$ (e. g. with ratio of the two independent frequencies equal to the golden mean).17 pages, 1 figureMathematical Physics37J40; 37C55; 70K43; 70H08text