Borel summability and Lindstedt series

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).

arXiv comment17 pages, 1 figure

References in corpus (1)

• Hyperbolic low-dimensional invariant tori and summations of divergent series

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