 04227 Michela Procesi
 Quasiperiodic solutions for completely resonant nonlinear wave equations in 1D and 2D
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Jul 23, 04

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Abstract. We provide quasiperiodic solutions with two frequencies $\omega\in \mathbb{R}^2$, for a class of completely resonant nonlinear wave equations in one and two spatial dimensions and with periodic boundary conditions.
This is the first existence result for quasiperiodic solutions in the 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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