GdT EDP et Théorie Spectrale

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.