Entropy of semiclassical measures in dimension 2

2008/09/30 by Gabriel Riviere
Physics and Astronomy · Mathematics · #math-ph #math.DS #math.MP #msc:81Q50-37D40-37A35-58J40

paper · pdf · doi:10.1215/00127094-2010-056

published as Duke Math. J. 155, no. 2 (2010), 271-335 · 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)

arxiv created 2009/12/01 · arxiv updated 2019/12/19

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

Citations

• Entropy of Semiclassical Measures for Nonpositively Curved Surfaces

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