  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.
