Abstract
In nature one often encounters systems that differ from integrable ones by small perturbations. Thus, for example, the problem of the motion of planets around the Sun can be regarded as a perturbation of the integrable problem of the motion of noninteracting point masses around a fixed center of attraction. Methods for studying such systems have been developed, which form what is known as perturbation theory. These methods are usually simple and effective. They often enable us to describe the perturbed motion almost as completely as the unperturbed motion. Some of them were already proposed and applied by Lagrange and Laplace in their investigations of secular perturbations of planets. The justification of various methods in perturbation theory is rather difficult. Justification questions have been approached only relatively recently, and some of them are still far from being completely solved.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1988 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Arnold, V.I. (1988). Perturbation Theory for Integrable Systems. In: Arnold, V.I. (eds) Dynamical Systems III. Encyclopaedia of Mathematical Sciences, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02535-2_5
Download citation
DOI: https://doi.org/10.1007/978-3-662-02535-2_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-02537-6
Online ISBN: 978-3-662-02535-2
eBook Packages: Springer Book Archive