Moser's theorem for lower dimensional tori

AbstractMoser's Cℓ-version of Kolmogorov's theorem on the persistence of maximal quasi-periodic solutions for nearly-integrable Hamiltonian system is extended to the persistence of non-maximal quasi-periodic solutions corresponding to lower-dimensional elliptic tori of any dimension n between one and the number of degrees of freedom. The theorem is proved for Hamiltonian functions of class Cℓ for any ℓ>6n+5 and the quasi-periodic solutions are proved to be of class Cp for any p with 2<p<p* for a suitable p*=p*(n,ℓ)>2 (which tends to infinity when ℓ→∞)