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.
A $C^\infty$ Nekhoroshev theorem / Bambusi, Dario; Langella, Beatrice. - In: MATHEMATICS IN ENGINEERING. - ISSN 2640-3501. - 3:2(2021), pp. 1-17. [10.3934/mine.2021019]
A $C^\infty$ Nekhoroshev theorem
Langella, Beatrice
2021-01-01
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.| File | Dimensione | Formato | |
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