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).
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Communicated by A. Kupiainen
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Costin, O., Gallavotti, G., Gentile, G. et al. Borel Summability and Lindstedt Series. Commun. Math. Phys. 269, 175–193 (2007). https://doi.org/10.1007/s00220-006-0079-0
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DOI: https://doi.org/10.1007/s00220-006-0079-0