Emmanuel Trélat
Date et heure
Conférence - Physique mathématique

Shnirelman proved in 1974 the following theorem: "Let $(X,g)$ be a closed Riemannian manifold with ergodic geodesic flow, and let $(\phi_n,\lambda_n)$ be a spectral decomposition of the Laplacian. Then there exists a density-one sequence $(n_j)$ of integers such that the sequence of probability measures $|\phi_{n_j}|^2 dx_g $ (with $dx_g$ the Riemannian measure) converges weakly to the measure $dx_g$." In this talk I will give a version of that theorem for sub-Riemannian Laplacians on a 3D contact manifold, and I will discuss possible extensions to other SR geometries. This is a joint work with Yves Colin de Verdière (Grenoble) and Luc Hillairet (Orléans).