Borel summability and Lindstedt series

Details Borel summability and Lindstedt series Borel summability and Lindstedt series

2006-01-15

arxiv.org/abs/math-ph/0601032v1

Communications in Mathematical Physics, 269, 175-193, 2006

Physics

Mathematical Physics

17 pages, 1 figure

Scientific paper

10.1007/s00220-006-0079-0

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).

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