A simple proof of the invariant tori theorem
Résumé
We first reduce the proof of Kolmogorov's theorem on the persistence of quasiperiodic invariant tori in Hamiltonian systems, to Herman's normal form, a well-posed inversion problem. The latter problem is then adressed with a simple inverse function theorem in the analytic category, whose own proof relies on the Newton algorithm and on interpolation inequalities.
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