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)

G-zipped file;
Zip compressed file;