Entropy and the localization of eigenfunctions

• Autores: Nalini Anantharaman
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 168, Nº 2, 2008, págs. 435-475
• Idioma: inglés
• DOI: 10.4007/annals.2008.168.435
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• Resumen

  • 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.