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
External document linkhttps://www.ceremade.dauphine.fr/~fejoz/articles.php
Book titleVariational Methods. In Imaging and Geometric Control
Book authorJ.-B. Caillau, M. Bergounioux, G. Peyré, C. Schnörr, T. Haberkorn
Series titleRadon Series on Computational and Applied Mathematics, 18
Number of pages526
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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 / Keywordsthree-body problem; symmetries; degeneracies; KAM theorem
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