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).
Costin, O., Gallavotti, G., Gentile, G., Giuliani, A. (2007). Borel summability and Lindstedt series. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 269, 175-193 [10.1007/s00220-006-0079-0].
Borel summability and Lindstedt series
GENTILE, Guido;GIULIANI, ALESSANDRO
2007-01-01
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).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
