Invariant KAM tori and global stability for Hamiltonian systems
by Antonio Giorgilli and Alessandro Morbidelli
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.
ZAMP 48, 102-134 (1997)
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