Journal of Statistical Physics

, Volume 78, Issue 5, pp 1607–1617

Superexponential stability of KAM tori

  • Alessandro Morbidelli
  • Antonio Giorgilli
Short Communications

DOI: 10.1007/BF02180145

Cite this article as:
Morbidelli, A. & Giorgilli, A. J Stat Phys (1995) 78: 1607. doi:10.1007/BF02180145


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.

Key Words

Classical perturbation theoryHamiltonian dynamical systemsKAM theoryexponential stabilityArnold stability

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • Alessandro Morbidelli
    • 1
  • Antonio Giorgilli
    • 2
  1. 1.Observatoire de la Côte d'AzurCNRSNice Cedex 4France
  2. 2.Dipartimento di Matematica dell'Università di Milano and Gruppo Nazionale di Fisica Matematica del CNRMilanItaly