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Borel summability and Lindstedt series

O. Costin·G. Gallavotti·G. Gentile·A. Giuliani
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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 $C^\infty$ 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).

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O. Costin, G. Gallavotti, G. Gentile, A. Giuliani. 2006-01-15. Borel summability and Lindstedt series. https://doi.org/10.1007/s00220-006-0079-0

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