标题： 拉普拉斯算子在Anosov流形上的本征函数的半离域化 显示英文标题

标题： Half-delocalization of eigenfunctions for the Laplacian on an Anosov manifold

摘要： 我们研究紧致黎曼流形上拉普拉斯算子的高能本征函数，该流形具有Anosov测地流。 与一组本征函数相关的半经典测度的局部化由该测度的Kolmogorov-Sinai熵来表征。 我们证明该熵必然有一个下界，当流形具有常负曲率时，该下界等于最大熵的一半。 从这个意义上说，高能本征函数至少是半扩散的。 显示英文摘要

摘要： We study the high-energy eigenfunctions of the Laplacian on a compact Riemannian manifold with Anosov geodesic flow. The localization of a semiclassical measure associated with a sequence of eigenfunctions is characterized by the Kolmogorov-Sinai entropy of this measure. We show that this entropy is necessarily bounded from below by a constant which, in the case of constant negative curvature, equals half the maximal entropy. In this sense, high-energy eigenfunctions are at least half-delocalized.