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Pré-Publication, Document De Travail Année : 2006

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

Résumé

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 et versions

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

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Nalini Anantharaman, Stéphane Nonnenmacher. Half-delocalization of eigenfunctions for the Laplacian on an Anosov manifold. 2006. ⟨hal-00104963v1⟩
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