Entropy of semiclassical measures for nonpositively curved surfaces - Archive ouverte HAL
Article Dans Une Revue Annales Henri Poincaré Année : 2010

Entropy of semiclassical measures for nonpositively curved surfaces

Gabriel Riviere

Résumé

We study the asymptotic properties of eigenfunctions of the Laplacian in the case of a compact Riemannian surface of nonpositive sectional curvature. We show that the Kolmogorov-Sinai entropy of a semiclassical measure for the geodesic flow is bounded from below by half of the Ruelle upper bound. We follow the same main strategy as in the Anosov case (arXiv:0809.0230). We focus on the main differences and refer the reader to (arXiv:0809.0230) for the details of analogous lemmas.
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Dates et versions

hal-00430591 , version 1 (09-11-2009)

Identifiants

Citer

Gabriel Riviere. Entropy of semiclassical measures for nonpositively curved surfaces. Annales Henri Poincaré, 2010, 11, pp.1085-1116. ⟨10.1007/s00023-010-0055-2⟩. ⟨hal-00430591⟩
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