Celestial mechanics

, Volume 37, Issue 1, pp 1–25 | Cite as

A proof of Nekhoroshev's theorem for the stability times in nearly integrable Hamiltonian systems

  • Giancarlo Benettin
  • Luigi Galgani
  • Antonio Giorgilli


In the present paper we give a proof of Nekhoroshev's theorem, which is concerned with an exponential estimate for the stability times in nearly integrable Hamiltonian systems. At variance with the already published proof, which refers to the case of an unperturbed Hamiltonian having the generic property of steepness, we consider here the particular case of a convex unperturbed Hamiltonian. The corresponding simplification in the proof might be convenient for an introduction to the subject.


Hamiltonian System Generic Property Stability Time Exponential Estimate Integrable Hamiltonian System 
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Copyright information

© D. Reidel Publishing Company 1985

Authors and Affiliations

  • Giancarlo Benettin
    • 1
  • Luigi Galgani
    • 2
  • Antonio Giorgilli
    • 3
  1. 1.Dipartimento di Fisica dell'Università, PadovaGruppo Nazionale di Struttura della Materia del C.N.R-Unità di PadovaPadovaItalia
  2. 2.Dipartimento di Matematica dell'UniversitàMilanoItalia
  3. 3.Dipartimento di Fisica dell'UniversitàMilanoItalia

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