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 $C^\io$ 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 $\t=1$ (\eg with ratio of the two independent frequencies equal to the golden mean).
Borel summability and Lindstedt series / O., Costin; Gallavotti, Giovanni; A., Giuliani; G., Gentile. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - STAMPA. - 269:(2006), pp. 175-193. [10.1007/s00220-006-0079-0]
Borel summability and Lindstedt series
GALLAVOTTI, Giovanni;
2006
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 $C^\io$ 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 $\t=1$ (\eg 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.
