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arXiv · 0911.1840

Entropy of semiclassical measures for nonpositively curved surfaces

Gabriel Riviere
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Abstract

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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Gabriel Riviere. 2009-11-10. Entropy of semiclassical measures for nonpositively curved surfaces. https://doi.org/10.1007/s00023-010-0055-2

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