Entropy of semiclassical measures for nonpositively curved surfaces
Dynamical Systems
2011-02-24 v1 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.0911.1840,
title = {Entropy of semiclassical measures for nonpositively curved surfaces},
author = {Gabriel Riviere},
journal= {arXiv preprint arXiv:0911.1840},
year = {2011}
}
Comments
20 pages. This note provides a detailed proof of a result announced in appendix A of a previous work (arXiv:0809.0230, version 2)