2009/11/10 by Gabriel Rivière, Gabriel Riviere
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math-ph #math.DS #math.MP #msc:81Q50-37D40-37A35-58J40
paper · pdf · doi:10.1007/s00023-010-0055-2
published as Annales Henri Poincaré 11 (2010) 1085-1116 · 20 pages. This note provides a detailed proof of a result announced in appendix A of a previous work (arXiv:0809.0230, version 2)
arxiv created 2009/11/10 · openalex publication_date 2010/09/28 · arxiv updated 2011/02/24 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
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.