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Groupe de Travail EDP et Théorie Spectrale

Local behaviour of high-energy eigenfunctions of integrable billiards

Alba García

( (Madrid) )

Salle de Conférences

le 22 novembre 2024 à 09:30

In this talk, we consider a bounded domain in the Euclidean plane and examine the Laplacian eigenvalue problem supplemented with specific boundary conditions. A famous conjecture by Berry proposes that in chaotic systems, eigenfunctions resemble random monochromatic waves; however, this behavior is generally not expected in integrable systems. In this talk, we explore the behavior of high-energy eigenfunctions and their connection to Berry’s random wave model. We do so by studying a related property called Inverse Localization, which describes how eigenfunctions can approximate monochromatic waves in small regions of the domain.