Averaging of time--periodic systems without a small parameter

Abstract : In this article, we present a new approach to averaging in non-Hamiltonian systems with periodic forcing. The results here do not depend on the existence of a small parameter. In fact, we show that our averaging method fits into an appropriate nonlinear equivalence problem, and that this problem can be solved formally by using the Lie transform framework to linearize it. According to this approach, we derive formal coordinate transformations associated with both first-order and higher-order averaging, which result in more manageable formulae than the classical ones. Using these transformations, it is possible to correct the solution of an averaged system by recovering the oscillatory components of the original non-averaged system. In this framework, the inverse transformations are also defined explicitly by formal series; they allow the estimation of appropriate initial data for each higher-order averaged system, respecting the equivalence relation. Finally, we show how these methods can be used for identifying and computing periodic solutions for a very large class of nonlinear systems with time-periodic forcing. We test the validity of our approach by analyzing both the first-order and the second-order averaged system for a problem in atmospheric chemistry.
Type de document :
Article dans une revue
Discrete and Continuous Dynamical Systems - Series A, American Institute of Mathematical Sciences, 2006, 14 (4), pp.753-782
Liste complète des métadonnées

Littérature citée [35 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-00162628
Contributeur : Mickael Chekroun <>
Soumis le : lundi 16 juillet 2007 - 09:15:43
Dernière modification le : mardi 24 avril 2018 - 17:20:15
Document(s) archivé(s) le : lundi 27 juin 2011 - 16:42:09

Fichiers

HAL_Averaging.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-00162628, version 1

Collections

Citation

Mickael Chekroun, Michael Ghil, Jean Roux, Ferenc Varadi. Averaging of time--periodic systems without a small parameter. Discrete and Continuous Dynamical Systems - Series A, American Institute of Mathematical Sciences, 2006, 14 (4), pp.753-782. 〈hal-00162628〉

Partager

Métriques

Consultations de la notice

350

Téléchargements de fichiers

86