Entropy and the localization of eigenfunctions

• 成果类型: Article
• 署名作者: Anantharaman, Nalini
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2008.168.435
• 发表日期: 2008
• 页码: 435-475
• 关键词: hyperbolic surfaces; ergodicity; LIMITS; MAPS

摘要

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.