Entropy of semiclassical measures for nonpositively curved surfaces
arXiv:0911.1840 · doi:10.1007/s00023-010-0055-2
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.
20 pages. This note provides a detailed proof of a result announced in appendix A of a previous work (arXiv:0809.0230, version 2)