Fractional Lindstedt series
Gallavotti, Giovanni ; Gentile, Guido ; Giuliani, Alessandro
arXiv, 0509056 / Harvested from arXiv
Text on arXiv
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, i.e. they are not analytic functions of the perturbation parameter. 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 the perturbation parameter, 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.
Publié le : 2005-09-26
Classification:  Mathematical Physics,  Mathematics - Dynamical Systems,  37J40, 37C55, 70K43, 70H08 
@article{0509056,
     author = {Gallavotti, Giovanni and Gentile, Guido and Giuliani, Alessandro},
     title = {Fractional Lindstedt series},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0509056}
}

Gallavotti, Giovanni; Gentile, Guido; Giuliani, Alessandro. Fractional Lindstedt series. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0509056/