A simple proof of the invariant torus theorem

Jacques Féjoz

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arXiv · 1005.5604

A simple proof of the invariant torus theorem

Jacques Féjoz

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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.

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Jacques Féjoz. 2010-05-31. A simple proof of the invariant torus theorem. https://arxiv.org/abs/1005.5604

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