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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, Partial differential equations -- Qualitative properties of solutions, Periodic solutions
37K55, Dynamical systems and ergodic theory -- Infinite-dimensional Hamiltonian systems, Perturbations, KAM for infinite-dimensional systems
En-ligne : Sommaire
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Séries Panor 9 (Browse shelf) Available 00439-01

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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