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arXiv · 2002.06985

A simple proof for a $C^\infty$ Nekhoroshev theorem

Dario Bambusi·Beatrice Langella
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Abstract

We prove a $C^\infty$ version of the Nekhoroshev's estimate on the stability times of the actions in close to integrable Hamiltonian systems. The proof we give is a variant of the original Nekhoroshev's proof and it consists in first conjugating, globally in the phase space, and up to a small remainder, the system to a normal form. Then we perform the geometric part of the proof in the normalized variables. As a result, we obtain a proof which is simpler than the usual ones.

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Dario Bambusi, Beatrice Langella. 2020-02-17. A simple proof for a $C^\infty$ Nekhoroshev theorem. https://arxiv.org/abs/2002.06985

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