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1 November 2010 Entropy of semiclassical measures in dimension 2
Gabriel Rivière
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Duke Math. J. 155(2): 271-335 (1 November 2010). DOI: 10.1215/00127094-2010-056

Abstract

We study the high-energy asymptotic properties of eigenfunctions of the Laplacian in the case of a compact Riemannian surface M of Anosov type. To do this, we look at families of distributions associated to them on the cotangent bundle T*M and we derive entropic properties on their accumulation points in the high-energy limit (the so-called semiclassical measures). We show that the Kolmogorov-Sinai entropy of a semiclassical measure μ for the geodesic flow gt is bounded from below by half of the Ruelle upper bound; that is, hKS(μ,g)12S*Mχ+(ρ) dμ(ρ), where χ+(ρ) is the upper Lyapunov exponent at point ρ.

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Gabriel Rivière. "Entropy of semiclassical measures in dimension 2." Duke Math. J. 155 (2) 271 - 335, 1 November 2010. https://doi.org/10.1215/00127094-2010-056

Information

Published: 1 November 2010
First available in Project Euclid: 27 October 2010

zbMATH: 1230.37048
MathSciNet: MR2736167
Digital Object Identifier: 10.1215/00127094-2010-056

Subjects:
Primary: 32F32
Secondary: 53C20, 53C21

Rights: Copyright © 2010 Duke University Press

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Vol.155 • No. 2 • 1 November 2010
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