Entropy and the localization of eigenfunctions

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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.

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APA

Anantharaman, N. (2008). Entropy and the localization of eigenfunctions. Annals of Mathematics, 168(2), 435–475. https://doi.org/10.4007/annals.2008.168.435

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