The parametric equations of the surfaces on which highly resonant quasi-periodic motions develop (lower-dimensional tori) cannot be analytically continued, in general, in the perturbation parameter $\e$, i.e. they are not analytic functions of $\e$. However rather generally quasi-periodic motions whose frequencies satisfy only one rational relation (``resonances of order $1$'') admit formal perturbation expansions in terms of a fractional power of $\e$ depending on the degeneration of the resonance. We find conditions for this to happen, and in such a case we prove that the formal expansion is convergent after suitable resummation
Fractional Lindstedt series / Gallavotti, Giovanni; Gentile, G; Giuliani, A.. - In: JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 0022-2488. - STAMPA. - 47:(2006), pp. 012702-1-012702-33. [10.1063/1.2157052]
Fractional Lindstedt series
GALLAVOTTI, Giovanni;
2006
Abstract
The parametric equations of the surfaces on which highly resonant quasi-periodic motions develop (lower-dimensional tori) cannot be analytically continued, in general, in the perturbation parameter $\e$, i.e. they are not analytic functions of $\e$. However rather generally quasi-periodic motions whose frequencies satisfy only one rational relation (``resonances of order $1$'') admit formal perturbation expansions in terms of a fractional power of $\e$ depending on the degeneration of the resonance. We find conditions for this to happen, and in such a case we prove that the formal expansion is convergent after suitable resummationI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
