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Fractional Lindstedt series

Giovanni Gallavotti·Guido Gentile·Alessandro Giuliani
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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, 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.

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Giovanni Gallavotti, Guido Gentile, Alessandro Giuliani. 2005-09-26. Fractional Lindstedt series. https://doi.org/10.1063/1.2157052

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