Nekhoroshev and KAM Theorems Revisited via a Unified Approach

  • Amadeu Delshams
  • Pere Gutiérrez
Part of the NATO ASI Series book series (NSSB, volume 331)


We consider an n-degrees of freedom nearly-integrable Hamiltonian system. The system is put in normal form and estimates are obtained for the size of the remainder. The transformation to normal form is constructed by means of an iterative process. This normal form provides the analytic part required for both proofs of KAM and Nekhoroshev theorems.

Assuming non-degeneracy conditions on the unperturbed Hamiltonian, the geometric part can be fulfilled. Our estimates rely on bounds of the associated vectorfields, and provide, in Nekhoroshev theorem, the “optimal” stability exponent: l/2n for quasiconvex Hamiltonians.


Normal Form Hamiltonian System Invariant Torus Integrable Hamiltonian System Diophantine Condition 
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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Amadeu Delshams
    • 1
  • Pere Gutiérrez
    • 2
  1. 1.Dep. de Matemàtica Aplicada IUniv. Pol. de CatalunyaBarcelonaSpain
  2. 2.Dep. de Matemàtica Aplicada IIUniv. Pol. de CatalunyaBarcelonaSpain

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