Problèmes de petits diviseurs dans les équations aux dérivées partielles / Walter Craig

Auteur principal : Craig, Walter, 1953-2019, AuteurType de document : MonographieCollection : Panoramas et synthèses, 9Langue : français.Pays: France.Éditeur : Paris : Société Mathématique de France, 2000Description : 1 vol. (120 p.) : fig. ; 24 cmISBN: 9782856290958.ISSN: 1272-3835.Bibliographie : Bibliogr. p. [117]-120.Sujet MSC : 35B10, Qualitative properties of solutions to partial differential equations, Periodic solutions to PDEs
37K55, Dynamical system aspects of infinite-dimensional Hamiltonian and Lagrangian systems, Perturbations, KAM
En-ligne : Sommaire
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Bibliogr. p. [117]-120

This volume surveys the recent adaptations of KAM theory to the search for time-periodic solutions of (mostly 1D) nonlinear wave and Schrödinger equations on bounded domains. After some introductory material (first two chapters), and an exposition of the circle of ideas around the Lyapunov center theorem (Chapter 3), the author gives a clear and detailed outline of the proof of the results of Craig and Wayne on the existence of Cantor sets of periodic solutions (Chapters 4-7). The last chapter sketches some further recent results. This work is a convenient introduction to the applications of KAM theory to PDE with discrete spectrum. (Zentralblatt)

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