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.
Invariant KAM tori and global stability for Hamiltonian systems / A. Giorgilli, A. Morbidelli. - In: ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK. - ISSN 0044-2275. - 1:48(1997 Jan), pp. 102-134. [10.1007/PL00001462]
Invariant KAM tori and global stability for Hamiltonian systems
A. GiorgilliPrimo
;
1997
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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