Journal of Statistical Physics
, Volume 71, Issue 3, pp 569606
First online:
Exponential stability of states close to resonance in infinitedimensional Hamiltonian systems
 Dario BambusiAffiliated withDipartimento di Matematica dell'Università
 , Antonio GiorgilliAffiliated withDipartimento di Matematica dell'Università
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We develop canonical perturbation theory for a physically interesting class of infinitedimensional 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 FPUlike 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 Title
 Exponential stability of states close to resonance in infinitedimensional Hamiltonian systems
 Journal

Journal of Statistical Physics
Volume 71, Issue 34 , pp 569606
 Cover Date
 199305
 DOI
 10.1007/BF01058438
 Print ISSN
 00224715
 Online ISSN
 15729613
 Publisher
 Kluwer Academic PublishersPlenum Publishers
 Additional Links
 Topics
 Keywords

 Hamiltonian systems
 infinite dimensional systems
 Nekhoroshev theory
 perturbation theory
 Industry Sectors
 Authors

 Dario Bambusi ^{(1)}
 Antonio Giorgilli ^{(1)}
 Author Affiliations

 1. Dipartimento di Matematica dell'Università, 20133, Milano, Italy