Celestial Mechanics and Dynamical Astronomy

, Volume 55, Issue 2, pp 131–159 | Cite as

Quantitative perturbation theory by successive elimination of harmonics

  • Alessandro Morbidelli
  • Antonio Giorgilli
Article

Abstract

We revisit some results of perturbation theories by a method of successive elimination of harmonics inspired by some ideas of Delaunay. On the one hand, we give a connection between the KAM theorem and the Nekhoroshev theorem. On the other hand, we support in a quantitative fashion a semi-numerical method of analysis of a perturbed system recently introduced by one of the authors.

Key words

Perturbation methods KAM theorem Nekhoroshev theorem action-angle variables 

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Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Alessandro Morbidelli
    • 1
  • Antonio Giorgilli
    • 2
  1. 1.Département de Mathématique FUNDPNamurBelgium
  2. 2.Dipartimento di Matematica dell'Universitá di MilanoMilanoItaly

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