Abstract.
We provide the direct proof of the Nekhoroshev theorem on the stability of nearly integrable analytic symplectic maps. Specifically, we prove the stability of the actions for a number of iterations which grows exponentially with an inverse power of the norm of the perturbation by conjugating the generating function of the map to suitable normal forms with exponentially small remainder.
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Communicated by Eduard Zehnder
submitted 16/06/03, accepted 31/03/04
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Guzzo, M. A Direct Proof of the Nekhoroshev Theorem for Nearly Integrable Symplectic Maps. Ann. Henri Poincaré 5, 1013–1039 (2004). https://doi.org/10.1007/s00023-004-0188-2
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DOI: https://doi.org/10.1007/s00023-004-0188-2