06-14 O. Costin, G. Gallavotti, G. Gentile, A. Giuliani

Borel summability and Lindstedt series (85K, Plain TeX with 1 ps figure) Jan 15, 06

Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

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).

Files: 06-14.src( 06-14.keywords , cggg17.tex , fig1.ps )