- 06-14 O. Costin, G. Gallavotti, G. Gentile, A. Giuliani
- Borel summability and Lindstedt series
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Jan 15, 06
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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 $\tau=1$ (e. g. with ratio of the two independent frequencies equal to the golden mean).