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Journal Articles Annales de l'Institut Fourier Year : 2007

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

Abstract

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.
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Dates and versions

hal-00104963 , version 1 (09-10-2006)
hal-00104963 , version 2 (27-02-2007)

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Cite

Nalini Anantharaman, Stéphane Nonnenmacher. Half-delocalization of eigenfunctions for the Laplacian on an Anosov manifold. Annales de l'Institut Fourier, 2007, 57 (7), pp.2465-2523. ⟨hal-00104963v2⟩
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