Abstract.
We point out a deep connection between KAM theorem and Nekhoroshev's theorem. Precisely, we reformulated the construction by Arnold of the set of invariant tori using Nekhoroshev's theorem as a basic tool. We prove in this way the existence of a hierarchic structure of nested domains characterized by a diffusion speed exponentially decreasing at each step. The set of KAM tori appears as the domain characterized by vanishing diffusion speed.
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Received: November 1, 1995; revised: May 15, 1996
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Giorgilli, A., Morbidelli, A. Invariant KAM tori and global stability for Hamiltonian systems. Z. angew. Math. Phys. 48, 102–134 (1997). https://doi.org/10.1007/PL00001462
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DOI: https://doi.org/10.1007/PL00001462