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Existence and stability of quasi-periodic solutions for derivative wave equations

TitleExistence and stability of quasi-periodic solutions for derivative wave equations
Publication TypeJournal Article
Year of Publication2013
AuthorsBerti, M, Biasco, L, Procesi, M
JournalAtti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni
Volume24
Pagination199-214
ISSN11206330
KeywordsConstant coefficients; Dynamical systems; Existence and stability; Infinite dimensional; KAM for PDEs; Linearized equations; Lyapunov exponent; Lyapunov methods; Quasi-periodic solution; Small divisors; Wave equations
Abstract

In this note we present the new KAM result in [3] which proves the existence of Cantor families of small amplitude, analytic, quasi-periodic solutions of derivative wave equations, with zero Lyapunov exponents and whose linearized equation is reducible to constant coefficients. In turn, this result is derived by an abstract KAM theorem for infinite dimensional reversible dynamical systems*.

DOI10.4171/RLM/652

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