Thumbnail - No thumbnail

Introduction to KAM theory, with a view to celestial mechanics

Féjoz, Jacques (2016), Introduction to KAM theory, with a view to celestial mechanics, in J.-B. Caillau, M. Bergounioux, G. Peyré, C. Schnörr, T. Haberkorn, Variational Methods. In Imaging and Geometric Control, De Gruyter, p. 387-433. 10.1515/9783110430394-013

Type
Chapitre d'ouvrage
External document link
https://www.ceremade.dauphine.fr/~fejoz/articles.php
Date
2016
Book title
Variational Methods. In Imaging and Geometric Control
Book author
J.-B. Caillau, M. Bergounioux, G. Peyré, C. Schnörr, T. Haberkorn
Publisher
De Gruyter
Series title
Radon Series on Computational and Applied Mathematics, 18
ISBN
978-3-11-043039-4
Number of pages
526
Pages
387-433
Publication identifier
Metadata
Show full item record
Author(s)
Féjoz, Jacques
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Institut de Mécanique Céleste et de Calcul des Ephémérides [IMCCE]
Abstract (EN)
The theory of Kolmogorov, Arnold, and Moser (KAM) consists of a set of results regarding the persistence of quasiperiodic solutions, primarily in Hamiltonian systems.We bring forward a “twisted conjugacy” normal form, due to Herman, which contains all the (not so) hard analysis. We focus on the real analytic setting. A variety of KAM results follow, includingmost classical statements as well asmore general ones. This strategy makes it simple to deal with various kinds of degeneracies and symmetries. As an example of application, we prove the existence of quasiperiodic motions in the spatial lunar three-body problem.
Subjects / Keywords
three-body problem; symmetries; degeneracies; KAM theorem