Averaging in difference equations driven by dynamical systems

Yuri Kifer*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

The averaging setup arises in the study of perturbations of parametric families of dynamical systems when parameters start changing slowly in time. Usually, averaging methods are applied to systems of differential equations which combine slow and fast motions. This paper deals with difference equations case which leads to wider class of models and examples. The averaging principle is justified here under a general condition which is verified when unperturbed transformations either preserve smooth measures or they are hyperbolic. The convergence speed in the averaging principle is estimated for some cases, as well.

Original languageEnglish
Pages (from-to)103-123
Number of pages21
JournalAsterisque
Issue number287
StatePublished - 2003

Keywords

  • Averaging
  • Difference equations
  • Dynamical systems

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