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Jacques Smulevici

Null coordinates for quasi-periodic 1d wave operators and applications
Monday, 14 October, 2024 - 13:30
Résumé : 
Given a quasi-periodic wave operator $\psi_{tt}-\psi_{xx}+\mathcal{B}^{xx}(\omega t,x)\partial_{xx}$, where $\mathcal{B}^{xx}:\mathbb{T}^{\nu+1} \rightarrow \mathbb{R}$ is parity preserving, reversible and small enough and where $\omega$ is diophantine, we explain how to construct \emph{null coordinates} respecting the quasi-periodicity. In these coordinates, the principal symbol of the wave operator then has constant coefficients. 
 
As an application, we give a novel proof of \emph{reducibility}, a typical element for the construction of quasi-periodic solutions to non-linear pdes, obtained very recently in a work of Berti, Feola, Procesi and Terracina on the quasi-periodically forced linear Klein-Gordon. 
 
Our main motivation for this problem comes from the possible applications to the construction of small non-linear time-periodic pertubations of the Anti-de-Sitter spacetime. This is a joint work with Athanasios Chatzikaleas. 

 

Institution de l'orateur : 
SU
Thème de recherche : 
Physique mathématique
Salle : 
IRMA Salle 1
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