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

Nalini Anantharaman·Stéphane Nonnenmacher
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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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BibTeXRIS

Nalini Anantharaman, Stéphane Nonnenmacher. 2007-02-27. Half-delocalization of eigenfunctions for the Laplacian on an Anosov manifold. https://arxiv.org/abs/math-ph/0610019

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