Entropy of semiclassical measures in dimension 2
Mathematical Physics
2019-12-19 v3 Dynamical Systems
math.MP
Abstract
We study the asymptotic properties of eigenfunctions of the Laplacian in the case of a compact Riemannian surface of Anosov type. 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
Cite
@article{arxiv.0809.0230,
title = {Entropy of semiclassical measures in dimension 2},
author = {Gabriel Riviere},
journal= {arXiv preprint arXiv:0809.0230},
year = {2019}
}
Comments
42 pages, 3 figures. Compared to the second version, I have removed the proof in the case of surfaces of nonpositive curvature and I have written it in a different article (arXiv:0911.1840)