Entropy and the localization of eigenfunctions

Abstract

We study the large eigenvalue limit for the eigenfunctions of the Laplacian, on a compact manifold of negative curvature — in fact, we only assume that the geodesic flow has the Anosov property. In the semi-classical limit, we prove that the Wigner measures associated to eigenfunctions have positive metric entropy. In particular, they cannot concentrate entirely on closed geodesics.

Authors

Nalini Anantharaman

Centre de Mathématiques Laurent Schwartz
Ecole Polytechnique
91128 Palaiseau
France