A proof of the invariant torus theorem of Kolmogorov

Jacques Fejoz (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

A variant of Kolmogorov's initial proof is given, in terms of a group of symplectic transformations and of an elementary fixed point theorem.

Mots clés: Composition operators; Système hamiltonien; Tore invariant; KAM theory; Normal form; Quasi-periodic motions; Stability; Nash-moser theorem; Perturbation theory; Inverse function theorem; Interpolation inequalities; Analytic norms

Domaines: Systèmes dynamiques [math.DS]; Physique [physics]; Astrophysique [astro-ph]

Jacques Fejoz. A proof of the invariant torus theorem of Kolmogorov. Regular and Chaotic Dynamics, 2012, 17 (1), pp.1-5. ⟨10.1134/S1560354712010017⟩. ⟨hal-00659140⟩