Quasi-periodic solutions for completely resonant non-linear wave equations in 1D and 2D | Zendy

Michela Procesi | Zendy

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Quasi-periodic solutions for completely resonant non-linear wave equations in 1D and 2D

Author(s) -

Michela Procesi

Publication year - 2005

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2005.13.541

Subject(s) - uncountable set , mathematics , cantor set , mathematical analysis , omega , invariant subspace , measure (data warehouse) , class (philosophy) , periodic boundary conditions , wave equation , subspace topology , physics , boundary value problem , pure mathematics , countable set , linear subspace , quantum mechanics , database , artificial intelligence , computer science

We provide quasi-periodic solutions with two frequencies for a class of completely resonant non-linear wave equations in one and two spatial dimensions and with periodic boundary conditions.This is the first existence result for quasi-periodic solutions inthe completely resonant case. The main idea is to work in an appropriate invariant subspace, in order to simplify the bifurcation equation. The frequencies, close to that of the linear system, belong to an uncountable Cantor set of measure zero where no small divisor problem arises

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