A simple proof of the invariant torus theorem
Dynamical Systems
2010-07-26 v1
Abstract
We give a simple proof of Kolmogorov's theorem on the persistence of a quasiperiodic invariant torus in Hamiltonian systems. The theorem is first reduced to a well-posed inversion problem (Herman's normal form) by switching the frequency obstruction from one side of the conjugacy to another. Then the proof consists in applying a simple, well suited, inverse function theorem in the analytic category, which itself relies on the Newton algorithm and on interpolation inequalities. A comparison with other proofs is included in appendix.
Cite
@article{arxiv.1005.5604,
title = {A simple proof of the invariant torus theorem},
author = {Jacques Féjoz},
journal= {arXiv preprint arXiv:1005.5604},
year = {2010}
}