Abstract
On montre la convergence d'une modification des séries de Zeipel aux fréquences fixées d'avance qui tiennent compte de perturbations à courte période dans les seconds membres des équations différentielles de la méchanique céleste. À l'aide de ces séries on établit l'existence des solutions quasipériodiques résonantes n'exigeant ancunes paramètres complémentaires.
Abstract
The convergence of a modification of the Zeipel's series of fixed frequences taking into account the short period perturbations of the right hand membres of the differential equations of celestial mechanics has been shown. By means of these series the existence of quasi-periodic solutions depending on the degenerate spectre of frequences without any complementary parametres has been established.
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Merman, G.A. Sur les petits diviseurs. Celestial Mechanics 27, 225–265 (1982). https://doi.org/10.1007/BF01228503
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DOI: https://doi.org/10.1007/BF01228503