Superexponential stability of KAM tori
Abstract
We study the dynamics in the neighborhood of an invariant torus of a nearly integrable system. We provide an upper bound to the diffusion speed, which turns out to be of superexponentially small size exp[-exp(1/σ)], σ being the distance from the invariant torus. We also discuss the connection of this result with the existence of many invariant tori close to the considered one.
- Publication:
-
Journal of Statistical Physics
- Pub Date:
- March 1995
- DOI:
- 10.1007/BF02180145
- Bibcode:
- 1995JSP....78.1607M
- Keywords:
-
- Classical perturbation theory;
- Hamiltonian dynamical systems;
- KAM theory;
- exponential stability;
- Arnold stability