Journal of Statistical Physics

, Volume 71, Issue 3, pp 569–606

Exponential stability of states close to resonance in infinite-dimensional Hamiltonian systems

  • Dario Bambusi
  • Antonio Giorgilli

DOI: 10.1007/BF01058438

Cite this article as:
Bambusi, D. & Giorgilli, A. J Stat Phys (1993) 71: 569. doi:10.1007/BF01058438


We develop canonical perturbation theory for a physically interesting class of infinite-dimensional systems. We prove stability up to exponentially large times for dynamical situations characterized by a finite number of frequencies. An application to two model problems is also made. For an arbitrarily large FPU-like system with alternate light and heavy masses we prove that the exchange of energy between the optical and the acoustical modes is frozen up to exponentially large times, provided the total energy is small enough. For an infinite chain of weakly coupled rotators we prove exponential stability for two kinds of initial data: (a) states with a finite number of excited rotators, and (b) states with the left part of the chain uniformly excited and the right part at rest.

Key words

Hamiltonian systems infinite dimensional systems Nekhoroshev theory perturbation theory 

Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • Dario Bambusi
    • 1
  • Antonio Giorgilli
    • 1
  1. 1.Dipartimento di Matematica dell'UniversitàMilanoItaly

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